Extrapolated stabilized explicit Runge-Kutta methods
Martín-Vaquero, J.; Kleefeld, B.
2016-12-01
Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve multi-dimensional nonlinear partial differential equations (PDEs). In such methods it is necessary to evaluate the function nt times per step, but the stability region is O (nt2). Hence, the computational cost is O (nt) times lower than for a traditional explicit algorithm. In that way stiff problems can be integrated by the use of simple explicit evaluations in which case implicit methods usually had to be used. Therefore, they are especially well-suited for the method of lines (MOL) discretizations of parabolic nonlinear multi-dimensional PDEs. In this work, first s-stages first-order methods with extended stability along the negative real axis are obtained. They have slightly shorter stability regions than other traditional first-order stabilized explicit Runge-Kutta algorithms (also called Runge-Kutta-Chebyshev codes). Later, they are used to derive nt-stages second- and fourth-order schemes using Richardson extrapolation. The stability regions of these fourth-order codes include the interval [ - 0.01nt2, 0 ] (nt being the number of total functions evaluations), which are shorter than stability regions of ROCK4 methods, for example. However, the new algorithms neither suffer from propagation of errors (as other Runge-Kutta-Chebyshev codes as ROCK4 or DUMKA) nor internal instabilities. Additionally, many other types of higher-order (and also lower-order) methods can be obtained easily in a similar way. These methods also allow adaptation of the length step with no extra cost. Hence, the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way, i.e., with minimal number of additional stages. We compare the new techniques with other well-known algorithms with good results in very stiff diffusion or reaction-diffusion multi-dimensional nonlinear equations.
Internal Error Propagation in Explicit Runge--Kutta Methods
Ketcheson, David I.
2014-09-11
In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can have catastrophic effects for otherwise practical and well-known methods. We perform a general analysis of internal error propagation, emphasizing that it depends significantly on how the method is implemented. We show that for a fixed method, essentially any set of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods and extrapolation methods. These results are used to prove error bounds in the presence of roundoff or other internal errors.
Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order
Hadjimichael, Yiannis
2013-07-23
We apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.
Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order
Hadjimichael, Yiannis; Macdonald, Colin B.; Ketcheson, David I.; Verner, James H.
2013-01-01
We apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.
Internal Error Propagation in Explicit Runge--Kutta Methods
Ketcheson, David I.; Loczi, Lajos; Parsani, Matteo
2014-01-01
of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods
Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method
Parsani, Matteo
2012-01-01
Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.
Parsani, Matteo
2013-04-10
Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.
Parsani, Matteo; Ketcheson, David I.; Deconinck, W.
2013-01-01
Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.
Implicit-explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models
Gardner, David J.; Guerra, Jorge E.; Hamon, François P.; Reynolds, Daniel R.; Ullrich, Paul A.; Woodward, Carol S.
2018-04-01
The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit-explicit (IMEX) additive Runge-Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit - vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored. The accuracy and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.
AbuAlSaud, Moataz
2012-07-01
The purpose of this thesis is to solve unsteady two-dimensional compressible Navier-Stokes equations for a moving mesh using implicit explicit (IMEX) Runge- Kutta scheme. The moving mesh is implemented in the equations using Arbitrary Lagrangian Eulerian (ALE) formulation. The inviscid part of the equation is explicitly solved using second-order Godunov method, whereas the viscous part is calculated implicitly. We simulate subsonic compressible flow over static NACA-0012 airfoil at different angle of attacks. Finally, the moving mesh is examined via oscillating the airfoil between angle of attack = 0 and = 20 harmonically. It is observed that the numerical solution matches the experimental and numerical results in the literature to within 20%.
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove
2010-01-01
The implicit Euler method, normally refered to as the fully implicit (FIM) method, and the implicit pressure explicit saturation (IMPES) method are the traditional choices for temporal discretization in reservoir simulation. The FIM method offers unconditionally stability in the sense of discrete......-Kutta methods, ESDIRK, Newton-Raphson, convergence control, error control, stepsize selection....
Spatially Partitioned Embedded Runge--Kutta Methods
Ketcheson, David I.; MacDonald, Colin B.; Ruuth, Steven J.
2013-01-01
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in nonembedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to nonphysical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted nonoscillatory spatial discretizations. Numerical experiments are provided to support the theory.
Spatially Partitioned Embedded Runge--Kutta Methods
Ketcheson, David I.
2013-10-30
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in nonembedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to nonphysical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted nonoscillatory spatial discretizations. Numerical experiments are provided to support the theory.
Runge-Kutta Methods for Linear Ordinary Differential Equations
Zingg, David W.; Chisholm, Todd T.
1997-01-01
Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.
Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes
Hundsdorfer, Willem; Mozartova, Anna; Savcenco, Valeriu
2013-01-01
of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods.
A Generalized Runge-Kutta Method of order three
DEFF Research Database (Denmark)
Thomsen, Per Grove
2002-01-01
The report presents a numerical method for the solution of stiff systems of ODE's and index one DAE's. The type of method is a 4- stage Generalized Linear Method that is reformulated in a special Semi Implicit Runge Kutta Method of SDIRK type. Error estimation is by imbedding a method of order 4...... based on the same stages as the method and the coefficients are selected for ease of implementation. The method has 4 stages and the stage-order is 2. For purposes of generating dense output and for initializing the iteration in the internal stages a continuous extension is derived. The method is A......-stable and we present the region of absolute stability and the order star of the order 3 method that is used for computing the solution....
Runge-Kutta methods with minimum storage implementations
Ketcheson, David I.
2010-03-01
Solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations, especially if a high order ODE solver is required. We investigate Runge-Kutta methods that require only two storage locations per ODE. Existing methods of this type require additional memory if an error estimate or the ability to restart a step is required. We present a new, more general class of methods that provide error estimates and/or the ability to restart a step while still employing the minimum possible number of memory registers. Examples of such methods are found to have good properties. © 2009 Elsevier Inc. All rights reserved.
Parallel Implicit Runge-Kutta Methods Applied to Coupled Orbit/Attitude Propagation
Hatten, Noble; Russell, Ryan P.
2017-12-01
A variable-step Gauss-Legendre implicit Runge-Kutta (GLIRK) propagator is applied to coupled orbit/attitude propagation. Concepts previously shown to improve efficiency in 3DOF propagation are modified and extended to the 6DOF problem, including the use of variable-fidelity dynamics models. The impact of computing the stage dynamics of a single step in parallel is examined using up to 23 threads and 22 associated GLIRK stages; one thread is reserved for an extra dynamics function evaluation used in the estimation of the local truncation error. Efficiency is found to peak for typical examples when using approximately 8 to 12 stages for both serial and parallel implementations. Accuracy and efficiency compare favorably to explicit Runge-Kutta and linear-multistep solvers for representative scenarios. However, linear-multistep methods are found to be more efficient for some applications, particularly in a serial computing environment, or when parallelism can be applied across multiple trajectories.
International Nuclear Information System (INIS)
Tselios, Kostas; Simos, T.E.
2007-01-01
In this Letter a new explicit fourth-order seven-stage Runge-Kutta method with a combination of minimal dispersion and dissipation error and maximal accuracy and stability limit along the imaginary axes, is developed. This method was produced by a general function that was constructed to satisfy all the above requirements and, from which, all the existing fourth-order six-stage RK methods can be produced. The new method is more efficient than the other optimized methods, for acoustic computations
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
Vaidya, Bhargav; Prasad, Deovrat; Mignone, Andrea; Sharma, Prateek; Rickler, Luca
2017-12-01
An important ingredient in numerical modelling of high temperature magnetized astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures. Magnetohydrodynamics typically involves solving the hyperbolic set of conservation equations along with the induction equation. Incorporating anisotropic thermal conduction requires to also treat parabolic terms arising from the diffusion operator. An explicit treatment of parabolic terms will considerably reduce the simulation time step due to its dependence on the square of the grid resolution (Δx) for stability. Although an implicit scheme relaxes the constraint on stability, it is difficult to distribute efficiently on a parallel architecture. Treating parabolic terms with accelerated super-time-stepping (STS) methods has been discussed in literature, but these methods suffer from poor accuracy (first order in time) and also have difficult-to-choose tuneable stability parameters. In this work, we highlight a second-order (in time) Runge-Kutta-Legendre (RKL) scheme (first described by Meyer, Balsara & Aslam 2012) that is robust, fast and accurate in treating parabolic terms alongside the hyperbolic conversation laws. We demonstrate its superiority over the first-order STS schemes with standard tests and astrophysical applications. We also show that explicit conduction is particularly robust in handling saturated thermal conduction. Parallel scaling of explicit conduction using RKL scheme is demonstrated up to more than 104 processors.
Finite Element Modeling of Thermo Creep Processes Using Runge-Kutta Method
Directory of Open Access Journals (Sweden)
Yu. I. Dimitrienko
2015-01-01
Full Text Available Thermo creep deformations for most heat-resistant alloys, as a rule, nonlinearly depend on stresses and are practically non- reversible. Therefore, to calculate the properties of these materials the theory of plastic flow is most widely used. Finite-element computations of a stress-strain state of structures with account of thermo creep deformations up to now are performed using main commercial software, including ANSYS package. However, in most cases to solve nonlinear creep equations, one should apply explicit or implicit methods based on the Euler method of approximation of time-derivatives. The Euler method is sufficiently efficient in terms of random access memory in computations, however this method is cumbersome in computation time and does not always provide a required accuracy for creep deformation computations.The paper offers a finite-element algorithm to solve a three-dimensional problem of thermo creep based on the Runge-Kutta finite-difference schemes of different orders with respect to time. It shows a numerical test example to solve the problem on the thermo creep of a beam under tensile loading. The computed results demonstrate that using the Runge-Kutta method with increasing accuracy order allows us to obtain a more accurate solution (with increasing accuracy order by 1 a relative error decreases, approximately, by an order too. The developed algorithm proves to be efficient enough and can be recommended for solving the more complicated problems of thermo creep of structures.
Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes
Hundsdorfer, Willem
2013-01-01
Multirate schemes for conservation laws or convection-dominated problems seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods.
Gómez Pueyo, Adrián; Marques, Miguel A L; Rubio, Angel; Castro, Alberto
2018-05-09
We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.
Cockrell, C. R.
1989-01-01
Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.
Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method
Directory of Open Access Journals (Sweden)
T. Jayakumar
2015-01-01
Full Text Available In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.
A Family of Trigonometrically-fitted Partitioned Runge-Kutta Symplectic Methods
International Nuclear Information System (INIS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2007-01-01
We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one dimensional time independent Schroedinger equation is considered by trigonometrically fitted symplectic integrators. The Schroedinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential
International Nuclear Information System (INIS)
Supriyono; Miyoshi, T.
1997-01-01
NECD Method and runge-Kutta method for large system of second order ordinary differential equations in comparing algorithm. The paper introduce a extrapolation method used for solving the large system of second order ordinary differential equation. We call this method the modified extrapolated central difference (MECD) method. for the accuracy and efficiency MECD method. we compare the method with 4-th order runge-Kutta method. The comparison results show that, this method has almost the same accuracy as the 4-th order runge-Kutta method, but the computation time is about half of runge-Kutta. The MECD was declare by the author and Tetsuhiko Miyoshi of the Dept. Applied Science Yamaguchi University Japan
Investigating the use of a rational Runge Kutta method for transport modelling
Dougherty, David E.
An unconditionally stable explicit time integrator has recently been developed for parabolic systems of equations. This rational Runge Kutta (RRK) method, proposed by Wambecq 1 and Hairer 2, has been applied by Liu et al.3 to linear heat conduction problems in a time-partitioned solution context. An important practical question is whether the method has application for the solution of (nearly) hyperbolic equations as well. In this paper the RRK method is applied to a nonlinear heat conduction problem, the advection-diffusion equation, and the hyperbolic Buckley-Leverett problem. The method is, indeed, found to be unconditionally stable for the linear heat conduction problem and performs satisfactorily for the nonlinear heat flow case. A heuristic limitation on the utility of RRK for the advection-diffusion equation arises in the Courant number; for the second-order accurate one-step two-stage RRK method, a limiting Courant number of 2 applies. First order upwinding is not as effective when used with RRK as with Euler one-step methods. The method is found to perform poorly for the Buckley-Leverett problem.
Runge-Kutta methods with minimum storage implementations
Ketcheson, David I.
2010-01-01
Solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations
Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines
Directory of Open Access Journals (Sweden)
M. A. Banaja
2015-01-01
Full Text Available The equal width (EW equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW equation is obtained by using the method of lines (MOL based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the L2 and L∞ error norms. The results are found in good agreement with exact solution.
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
International Nuclear Information System (INIS)
Wang Qiubao; Li Dongsong; Liu, M.Z.
2009-01-01
In this paper, we consider the discretization of parameter-dependent delay differential equation of the form y ' (t)=f(y(t),y(t-1),τ),τ≥0,y element of R d . It is shown that if the delay differential equation undergoes a Hopf bifurcation at τ=τ * , then the discrete scheme undergoes a Hopf bifurcation at τ(h)=τ * +O(h p ) for sufficiently small step size h, where p≥1 is the order of the Runge-Kutta method applied. The direction of numerical Hopf bifurcation and stability of bifurcating invariant curve are the same as that of delay differential equation.
International Nuclear Information System (INIS)
Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.
1991-09-01
A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs
Directory of Open Access Journals (Sweden)
Haiyan Yuan
2013-01-01
Full Text Available This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of (k,l-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a (k,l-algebraically stable two-step Runge-Kutta method with 0
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
International Nuclear Information System (INIS)
Hong Jialin; Li Chun
2006-01-01
In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law
Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations
International Nuclear Information System (INIS)
Aboanber, A E
2006-01-01
A stability and efficiency improved class of generalized Runge-Kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and/or nonlinear coupled differential equations. The determination of the coefficients required by the method is precisely obtained from the so-called equations of condition which in turn are derived by an approach based on Butcher series. Since the equations of condition are fewer in number, free parameters can be chosen for optimizing any desired feature of the process. A further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced. In addition, the A(α) stability properties of the method are investigated. Implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback
Cavaglieri, Daniele; Bewley, Thomas
2015-04-01
Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.
Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review
Kennedy, Christopher A.; Carpenter, Mark H.
2016-01-01
A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.
Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation
Su, Bo; Tuo, Xianguo; Xu, Ling
2017-08-01
Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.
SHOCK, Nonlinear Dynamic Structure Analysis, Spring and Mass Model, Runge-Kutta-Gill Method
International Nuclear Information System (INIS)
Gabrielson, V. K.
1981-01-01
1 - Description of problem or function: SHOCK calculates the dynamic response of a structure modeled as a spring-mass system having one or two degrees of freedom for each mass when subjected to specified environments. The code determines the behavior of each lumped mass (displacement, velocity, and acceleration for each degree of freedom) and the behavior of each spring or coupling (force, shear, moment, and displacement) as a function of time. Two types of models, axial, having one degree of freedom, and lateral, having two degrees of freedom at each mass can be processed. Damping can be included in all models and shock spectrums of responses can be obtained. 2 - Method of solution: Two methods of numerical integration of the second-order dynamic equations are provided: the Runge-Kutta-Gill method with variable step-size is recommended for highly nonlinear problems, and a variation of the Newmark-Beta method is available for use with large linear problems. 3 - Restrictions on the complexity of the problem: Maxima of: 100 masses, 200 springs or couplings. Complex arrangements of nonlinear options must be carefully checked by the user
Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian
2013-09-01
In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
Directory of Open Access Journals (Sweden)
Igumnov Leonid
2015-01-01
Full Text Available The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.
Papadopoulos , D. F.; Anastassi , Z. A.; Simos , T. E.
2010-01-01
Abstract A new Runge-Kutta-Nystrom method, with phase-lag and amplification error of order infinity, for the numerical solution of the Schrodinger equation is developed in this paper. The new method is based on the Runge-Kutta-Nystrom method with fourth algebraic order, developed by Dormand, El-Mikkawy and Prince. Numerical illustrations indicate that the new method is much more efficient than other methods derived for the same purpose. phone: +30-210-9421510 (Simos, T. E.) ...
Order Reduction in High-Order Runge-Kutta Methods for Initial Boundary Value Problems
Rosales, Rodolfo Ruben; Seibold, Benjamin; Shirokoff, David; Zhou, Dong
2017-01-01
This paper studies the order reduction phenomenon for initial-boundary-value problems that occurs with many Runge-Kutta time-stepping schemes. First, a geometric explanation of the mechanics of the phenomenon is provided: the approximation error develops boundary layers, induced by a mismatch between the approximation error in the interior and at the boundaries. Second, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers pers...
Comparison of second and third orders Runge-Kutta methods for ...
African Journals Online (AJOL)
This work is concerned with the analysis of second and third orders Runge- Kutta formulae capable of solving initial value problems in Ordinary Differential Equations of the form: y1 = f(x, y), y(x0) = y0, a £ x £ b. The intention is to find out which of these two orders can improve the performance of results when implemented ...
Directory of Open Access Journals (Sweden)
H. O. Bakodah
2013-01-01
Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.
Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta
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Andresa Pescador
2016-04-01
Full Text Available This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.
Highly efficient strong stability preserving Runge-Kutta methods with Low-Storage Implementations
Ketcheson, David I.
2008-01-01
modified time-step restriction. We consider the problem of finding explicit Runge–Kutta methods with optimal SSP time-step restrictions, first for the case of linear autonomous ordinary differential equations and then for nonlinear or nonautonomous
OSIRIS: a runge kutta solver of systems of ordinary differential equations
International Nuclear Information System (INIS)
Collin, M.; Schett, A.
1983-12-01
The Code OSIRIS (Order and Step Idently Adjusting Runge-Kutta Integrator of Systems) has been developed on the basis of both explicit as well as implicit Runge-Kutta processes of various orders: 4(5), 7(8), 8(9), 10 for explicit processes and 4 and 6 for implicit processes of the Rosenbrock type. This permits an optimization of the integration procedure by choosing the appropriate type of Runge-Kutta methods (explicit or implicit) and by adjusting dynamically the order of the process as well as the step-size. The performance of the Code OSIRIS is demonstrated by some representative examples and is compared with the Code GEAR which is applying multistep methods
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Yanping Yang
2016-01-01
Full Text Available The construction of exponentially fitted two-derivative Runge-Kutta (EFTDRK methods for the numerical solution of first-order differential equations is investigated. The revised EFTDRK methods proposed, with equation-dependent coefficients, take into consideration the errors produced in the internal stages to the update. The local truncation errors and stability of the new methods are analyzed. The numerical results are reported to show the accuracy of the new methods.
Highly efficient strong stability preserving Runge-Kutta methods with Low-Storage Implementations
Ketcheson, David I.
2008-01-01
Strong stability-preserving (SSP) Runge–Kutta methods were developed for time integration of semidiscretizations of partial differential equations. SSP methods preserve stability properties satisfied by forward Euler time integration, under a modified time-step restriction. We consider the problem of finding explicit Runge–Kutta methods with optimal SSP time-step restrictions, first for the case of linear autonomous ordinary differential equations and then for nonlinear or nonautonomous equations. By using alternate formulations of the associated optimization problems and introducing a new, more general class of low-storage implementations of Runge–Kutta methods, new optimal low-storage methods and new low-storage implementations of known optimal methods are found. The results include families of low-storage second and third order methods that achieve the maximum theoretically achievable effective SSP coefficient (independent of stage number), as well as low-storage fourth order methods that are more efficient than current full-storage methods. The theoretical properties of these methods are confirmed by numerical experiment.
D'Alessandro, Valerio; Binci, Lorenzo; Montelpare, Sergio; Ricci, Renato
2018-01-01
Open-source CFD codes provide suitable environments for implementing and testing low-dissipative algorithms typically used to simulate turbulence. In this research work we developed CFD solvers for incompressible flows based on high-order explicit and diagonally implicit Runge-Kutta (RK) schemes for time integration. In particular, an iterated PISO-like procedure based on Rhie-Chow correction was used to handle pressure-velocity coupling within each implicit RK stage. For the explicit approach, a projected scheme was used to avoid the "checker-board" effect. The above-mentioned approaches were also extended to flow problems involving heat transfer. It is worth noting that the numerical technology available in the OpenFOAM library was used for space discretization. In this work, we additionally explore the reliability and effectiveness of the proposed implementations by computing several unsteady flow benchmarks; we also show that the numerical diffusion due to the time integration approach is completely canceled using the solution techniques proposed here.
International Nuclear Information System (INIS)
Aboanber, A.E.; Hamada, Y.M.
2008-01-01
An extensive knowledge of the spatial power distribution is required for the design and analysis of different types of current-generation reactors, and that requires the development of more sophisticated theoretical methods. Therefore, the need to develop new methods for multidimensional transient reactor analysis still exists. The objective of this paper is to develop a computationally efficient numerical method for solving the multigroup, multidimensional, static and transient neutron diffusion kinetics equations. A generalized Runge-Kutta method has been developed for the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic time step control. In addition, the A(α)-stability properties of the method are investigated. The analyses of two- and three-dimensional benchmark problems as well as static and transient problems, demonstrate that very accurate solutions can be obtained with assembly-sized spatial meshes. Preliminary numerical evaluations using two- and three-dimensional finite difference codes showed that the presented generalized Runge-Kutta method is highly accurate and efficient when compared with other optimized iterative numerical and conventional finite difference methods
A New Formulation for Symmetric Implicit Runge-Kutta-Nystrom ...
African Journals Online (AJOL)
In this paper we derive symmetric stable Implicit Runge-Kutta –Nystrom Method for the Integration of General Second Order ODEs by using the collocation approach.The block hybrid method obtained by the evaluation of the continuous interpolant at different nodes of the polynomial is symmetric and suitable for stiff intial ...
Directory of Open Access Journals (Sweden)
Ali Belhocine
2018-01-01
Full Text Available In the thermal entrance region, a thermal boundary layer develops and also reaches the circular tube center. The fully developed region is the zone in which the flow is both hydrodynamically and thermally developed. The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the thickness of the thermal boundary layer is zero and decreases gradually to the fully developed value. In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the analytical solution of the problem with additional boundary conditions, for the temperature field and the boundary layer thickness through the long tube is presented. By defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by Fortran code obtained via using Runge-Kutta fourth order (RK4 method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail.
Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes
Calvo, M.; González-Pinto, S.; Montijano, J. I.
2008-09-01
Modern codes for the numerical solution of Initial Value Problems (IVPs) in ODEs are based in adaptive methods that, for a user supplied tolerance [delta], attempt to advance the integration selecting the size of each step so that some measure of the local error is [similar, equals][delta]. Although this policy does not ensure that the global errors are under the prescribed tolerance, after the early studies of Stetter [Considerations concerning a theory for ODE-solvers, in: R. Burlisch, R.D. Grigorieff, J. Schröder (Eds.), Numerical Treatment of Differential Equations, Proceedings of Oberwolfach, 1976, Lecture Notes in Mathematics, vol. 631, Springer, Berlin, 1978, pp. 188-200; Tolerance proportionality in ODE codes, in: R. März (Ed.), Proceedings of the Second Conference on Numerical Treatment of Ordinary Differential Equations, Humbold University, Berlin, 1980, pp. 109-123] and the extensions of Higham [Global error versus tolerance for explicit Runge-Kutta methods, IMA J. Numer. Anal. 11 (1991) 457-480; The tolerance proportionality of adaptive ODE solvers, J. Comput. Appl. Math. 45 (1993) 227-236; The reliability of standard local error control algorithms for initial value ordinary differential equations, in: Proceedings: The Quality of Numerical Software: Assessment and Enhancement, IFIP Series, Springer, Berlin, 1997], it has been proved that in many existing explicit Runge-Kutta codes the global errors behave asymptotically as some rational power of [delta]. This step-size policy, for a given IVP, determines at each grid point tn a new step-size hn+1=h(tn;[delta]) so that h(t;[delta]) is a continuous function of t. In this paper a study of the tolerance proportionality property under a discontinuous step-size policy that does not allow to change the size of the step if the step-size ratio between two consecutive steps is close to unity is carried out. This theory is applied to obtain global error estimations in a few problems that have been solved with
Explicit strong stability preserving multistep Runge–Kutta methods
Bresten, Christopher; Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel; Ketcheson, David I.; Né meth, Adrian
2015-01-01
High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.
Explicit strong stability preserving multistep Runge–Kutta methods
Bresten, Christopher
2015-10-15
High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.
Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations
Rihan, Fathalla A.; Al-Salti, Nasser S.
2017-09-01
In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.
Rokhzadi, Arman; Mohammadian, Abdolmajid; Charron, Martin
2018-01-01
The objective of this paper is to develop an optimized implicit-explicit (IMEX) Runge-Kutta scheme for atmospheric applications focusing on stability and accuracy. Following the common terminology, the proposed method is called IMEX-SSP2(2,3,2), as it has second-order accuracy and is composed of diagonally implicit two-stage and explicit three-stage parts. This scheme enjoys the Strong Stability Preserving (SSP) property for both parts. This new scheme is applied to nonhydrostatic compressible Boussinesq equations in two different arrangements, including (i) semiimplicit and (ii) Horizontally Explicit-Vertically Implicit (HEVI) forms. The new scheme preserves the SSP property for larger regions of absolute monotonicity compared to the well-studied scheme in the same class. In addition, numerical tests confirm that the IMEX-SSP2(2,3,2) improves the maximum stable time step as well as the level of accuracy and computational cost compared to other schemes in the same class. It is demonstrated that the A-stability property as well as satisfying "second-stage order" and stiffly accurate conditions lead the proposed scheme to better performance than existing schemes for the applications examined herein.
International Nuclear Information System (INIS)
Gunawan, Indra; Sulistyo, Harry; Rochmad
2001-01-01
The numerical analysis of Hooke Jeeves Methods combined with Runge Kutta Methods is used to determine the exact model of reaction rate equation of pyrrole polymerization. Chemical polymerization of pyrrole was conducted with FeCI 3 / pyrrole solution at concentration ratio of 1.62 mole / mole and 2.18 mole / mole with varrying temperature of 28, 40, 50, and 60 o C. FeCl 3 acts as an oxidation agent to form pyrrole cation that will polymerize. The numerical analysis was done to examine the exact model of reaction rate equation which is derived from reaction equation of initiation, propagation, and termination. From its numerical analysis, it is found that the pyrrole polymerization follows third order of pyrrole cation concentration
Two new solutions to the third-order symplectic integration method
International Nuclear Information System (INIS)
Iwatsu, Reima
2009-01-01
Two new solutions are obtained for the symplecticity conditions of explicit third-order partitioned Runge-Kutta time integration method. One of them has larger stability limit and better dispersion property than the Ruth's method.
Institute of Scientific and Technical Information of China (English)
WANG ShunJin; ZHANG Hua
2007-01-01
Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Havasi, Ágnes; Kazemi, Ehsan
2018-04-01
In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.
On Error Estimation in Runge-Kutta Methods
Directory of Open Access Journals (Sweden)
Gbolahan BOLARIN
2011-06-01
Full Text Available The increase in PCs' capabilities and communication bandwidth over the last decade has made distributed computing a more practical idea for solving computational problems. We have developed a decentralized P2P system called ParCop (Parallel Cooperation. ParCop enables each peer in a P2P network to view the rest of the network as a supercomputer, by running ParCop system software on the machine as a daemon service. ParCop allows participants to execute different applications on shared resources owned by other participants. In this paper, we present the new capabilities of ParCop system: efficient resource discovery by using the Blackboard Resource Discovery Mechanism (BRDM, adaptation in dynamic networks, effective data caching, efficient scaling and the provision of a secure environment. We also present three scheduling policies that allow peers in ParCop environment to take scheduling decisions based on the information coming from the peers in the network. The use of these scheduling policies minimizes the processing time of applications in ParCop, improves the ability of dealing with peers which have different capabilities and requirements, and achieves efficient load balancing.
International Nuclear Information System (INIS)
Athanasakis, I E; Papadopoulou, E P; Saridakis, Y G
2014-01-01
Fisher's equation has been widely used to model the biological invasion of single-species communities in homogeneous one dimensional habitats. In this study we develop high order numerical methods to accurately capture the spatiotemporal dynamics of the generalized Fisher equation, a nonlinear reaction-diffusion equation characterized by density dependent non-linear diffusion. Working towards this direction we consider strong stability preserving Runge-Kutta (RK) temporal discretization schemes coupled with the Hermite cubic Collocation (HC) spatial discretization method. We investigate their convergence and stability properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized Fisher equation. The Hadamard product is used to characterize the collocation discretized non linear equation terms as a first step for the treatment of generalized systems of relevant equations. Numerical experimentation is included to demonstrate the performance of the methods
Gottlieb, Sigal
2015-04-10
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Optimizing some 3-stage W-methods for the time integration of PDEs
Gonzalez-Pinto, S.; Hernandez-Abreu, D.; Perez-Rodriguez, S.
2017-07-01
The optimization of some W-methods for the time integration of time-dependent PDEs in several spatial variables is considered. In [2, Theorem 1] several three-parametric families of three-stage W-methods for the integration of IVPs in ODEs were studied. Besides, the optimization of several specific methods for PDEs when the Approximate Matrix Factorization Splitting (AMF) is used to define the approximate Jacobian matrix (W ≈ fy(yn)) was carried out. Also, some convergence and stability properties were presented [2]. The derived methods were optimized on the base that the underlying explicit Runge-Kutta method is the one having the largest Monotonicity interval among the thee-stage order three Runge-Kutta methods [1]. Here, we propose an optimization of the methods by imposing some additional order condition [7] to keep order three for parabolic PDE problems [6] but at the price of reducing substantially the length of the nonlinear Monotonicity interval of the underlying explicit Runge-Kutta method.
DeBonis, James R.
2013-01-01
A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.
Directory of Open Access Journals (Sweden)
Dengfeng Liu
2014-01-01
Full Text Available The core of the Chinese rice wine making is a typical simultaneous saccharification and fermentation (SSF process. In order to control and optimize the SSF process of Chinese rice wine brewing, it is necessary to construct kinetic model and study the influence of temperature on the Chinese rice wine brewing process. An unstructured kinetic model containing 12 kinetics parameters was developed and used to describe the changing of kinetic parameters in Chinese rice wine fermentation at 22, 26, and 30°C. The effects of substrate and product inhibitions were included in the model, and four variable, including biomass, ethanol, sugar and substrate were considered. The R-square values for the model are all above 0.95 revealing that the model prediction values could match experimental data very well. Our model conceivably contributes significantly to the improvement of the industrial process for the production of Chinese rice wine.
Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.
1994-01-01
It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
Application of differential transformation method for solving dengue transmission mathematical model
Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.
2018-03-01
The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.
a Numerical Comparison of Langrange and Kane's Methods of AN Arm Segment
Rambely, Azmin Sham; Halim, Norhafiza Ab.; Ahmad, Rokiah Rozita
A 2-D model of a two-link kinematic chain is developed using two dynamics equations of motion, namely Kane's and Lagrange Methods. The dynamics equations are reduced to first order differential equation and solved using modified Euler and fourth order Runge Kutta to approximate the shoulder and elbow joint angles during a smash performance in badminton. Results showed that Runge-Kutta produced a better and exact approximation than that of modified Euler and both dynamic equations produced better absolute errors.
Rojo García, Diego
2015-01-01
Tras introducir los conceptos y resultados básicos relacionados con las ecuaciones diferenciales algebraicas, en particular los distintos tipos de índice, se ha abordado la integración numérica de las ecuaciones semi-explícitas de índice 2 mediante métodos Runge-Kutta semi-explícitos. Se han estudiado con detalle las condiciones de orden para dichos métodos, obteniendo para ello los desarrollos de Taylor de la solución exacta y de la solución numérica con la ayuda de la teoría de árboles adec...
International Nuclear Information System (INIS)
Goh, S.M.; Noorani, M.S.M.; Hashim, I.
2009-01-01
This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.
Ketcheson, David I.
2014-04-11
In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can have catastrophic effects for otherwise practical and well-known methods. We perform a general analysis of internal error propagation, emphasizing that it depends significantly on how the method is implemented. We show that for a fixed method, essentially any set of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods and extrapolation methods. These results are used to prove error bounds in the presence of roundoff or other internal errors.
Krylov subspace methods for the solution of large systems of ODE's
DEFF Research Database (Denmark)
Thomsen, Per Grove; Bjurstrøm, Nils Henrik
1998-01-01
In Air Pollution Modelling large systems of ODE's arise. Solving such systems may be done efficientliy by Semi Implicit Runge-Kutta methods. The internal stages may be solved using Krylov subspace methods. The efficiency of this approach is investigated and verified.......In Air Pollution Modelling large systems of ODE's arise. Solving such systems may be done efficientliy by Semi Implicit Runge-Kutta methods. The internal stages may be solved using Krylov subspace methods. The efficiency of this approach is investigated and verified....
Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods
Mozartova, A.; Savostianov, I.; Hundsdorfer, W.
2015-01-01
© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods
Mozartova, A.
2015-05-01
© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
KRYSI, Ordinary Differential Equations Solver with Sdirk Krylov Method
International Nuclear Information System (INIS)
Hindmarsh, A.C.; Norsett, S.P.
2001-01-01
1 - Description of program or function: KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and non-stiff systems. When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two pre-conditioners that are natural for its solution by KRYSI. 2 - Method of solution: KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations
Directory of Open Access Journals (Sweden)
Domingues M. O.
2013-12-01
Full Text Available We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via Harten’s cell average multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge–Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution.
Energy Technology Data Exchange (ETDEWEB)
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Waveform relaxation methods for implicit differential equations
P.J. van der Houwen; W.A. van der Veen
1996-01-01
textabstractWe apply a Runge-Kutta-based waveform relaxation method to initial-value problems for implicit differential equations. In the implementation of such methods, a sequence of nonlinear systems has to be solved iteratively in each step of the integration process. The size of these systems
Simurda, Matej; Duggen, Lars; Basse, Nils T; Lassen, Benny
2018-02-01
A numerical model for transit-time ultrasonic flowmeters operating under multiphase flow conditions previously presented by us is extended by mesh refinement and grid point redistribution. The method solves modified first-order stress-velocity equations of elastodynamics with additional terms to account for the effect of the background flow. Spatial derivatives are calculated by a Fourier collocation scheme allowing the use of the fast Fourier transform, while the time integration is realized by the explicit third-order Runge-Kutta finite-difference scheme. The method is compared against analytical solutions and experimental measurements to verify the benefit of using mapped grids. Additionally, a study of clamp-on and in-line ultrasonic flowmeters operating under multiphase flow conditions is carried out.
Cheap arbitrary high order methods for single integrand SDEs
DEFF Research Database (Denmark)
Debrabant, Kristian; Kværnø, Anne
2017-01-01
For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order $p_d$ we obtain methods converging in the mean-square and weak sense with order $\\lfloor p_d/2\\rfloor$. The reason is that the B-series...
DRK methods for time-domain oscillator simulation
Sevat, M.F.; Houben, S.H.M.J.; Maten, ter E.J.W.; Di Bucchianico, A.; Mattheij, R.M.M.; Peletier, M.A.
2006-01-01
This paper presents a new Runge-Kutta type integration method that is well-suited for time-domain simulation of oscillators. A unique property of the new method is that its damping characteristics can be controlled by a continuous parameter.
Computational Method for Ice Crystal Trajectories in a Turbofan Compressor
Grift, E.J.; Norde, Ellen; van der Weide, Edwin Theodorus Antonius; Hoeijmakers, Hendrik Willem Marie
2015-01-01
In this study the characteristics of ice crystals on their trajectory in a single stage of a turbofan engine compressor are determined. The particle trajectories are calculated with a Lagrangian method employing a classical fourth-order Runge-Kutta time integration scheme. The air flow field is
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Ibsen, Lars Bo
2010-01-01
. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability...
DEFF Research Database (Denmark)
Ganji, S.; Barari, Amin; Ibsen, Lars Bo
2012-01-01
. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability...
Application of homotopy-perturbation method to nonlinear population dynamics models
International Nuclear Information System (INIS)
Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.
2007-01-01
In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)
Parallel Störmer-Cowell methods for high-precision orbit computations
P.J. van der Houwen; E. Messina; J.J.B. de Swart (Jacques)
1998-01-01
textabstractMany orbit problems in celestial mechanics are described by (nonstiff) initial-value problems (IVPs) for second-order ordinary differential equations of the form $y' = {bf f (y)$. The most successful integration methods are based on high-order Runge-Kutta-Nyström formulas. However, these
High order spectral volume and spectral difference methods on unstructured grids
Kannan, Ravishekar
The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
International Nuclear Information System (INIS)
Hykes, J. M.; Ferrer, R. M.
2013-01-01
The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is 98 Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)
Solving point reactor kinetic equations by time step-size adaptable numerical methods
International Nuclear Information System (INIS)
Liao Chaqing
2007-01-01
Based on the analysis of effects of time step-size on numerical solutions, this paper showed the necessity of step-size adaptation. Based on the relationship between error and step-size, two-step adaptation methods for solving initial value problems (IVPs) were introduced. They are Two-Step Method and Embedded Runge-Kutta Method. PRKEs were solved by implicit Euler method with step-sizes optimized by using Two-Step Method. It was observed that the control error has important influence on the step-size and the accuracy of solutions. With suitable control errors, the solutions of PRKEs computed by the above mentioned method are accurate reasonably. The accuracy and usage of MATLAB built-in ODE solvers ode23 and ode45, both of which adopt Runge-Kutta-Fehlberg method, were also studied and discussed. (authors)
Workshop on Numerical Methods for Ordinary Differential Equations
Gear, Charles; Russo, Elvira
1989-01-01
Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.
Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations
International Nuclear Information System (INIS)
Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.
2011-01-01
The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)
A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems
Directory of Open Access Journals (Sweden)
A. Karimi Dizicheh
2013-01-01
wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
Accuracy of the Adomian decomposition method applied to the Lorenz system
International Nuclear Information System (INIS)
Hashim, I.; Noorani, M.S.M.; Ahmad, R.; Bakar, S.A.; Ismail, E.S.; Zakaria, A.M.
2006-01-01
In this paper, the Adomian decomposition method (ADM) is applied to the famous Lorenz system. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the fourth-order Runge-Kutta (RK4) numerical solutions are made for various time steps. In particular we look at the accuracy of the ADM as the Lorenz system changes from a non-chaotic system to a chaotic one
International Nuclear Information System (INIS)
Cash, J.R.; Raptis, A.D.; Simos, T.E.
1990-01-01
An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schroedinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are given. (orig.)
Ngwane, F. F.; Jator, S. N.
2017-01-01
In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs). Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one...
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-15
The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the
Asgharzadeh, Hafez; Borazjani, Iman
2016-01-01
The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the
Lafitte, Pauline; Melis, Ward; Samaey, Giovanni
2017-07-01
We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.
Spectral Element Method for the Simulation of Unsteady Compressible Flows
Diosady, Laslo Tibor; Murman, Scott M.
2013-01-01
This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.
Study of flow over object problems by a nodal discontinuous Galerkin-lattice Boltzmann method
Wu, Jie; Shen, Meng; Liu, Chen
2018-04-01
The flow over object problems are studied by a nodal discontinuous Galerkin-lattice Boltzmann method (NDG-LBM) in this work. Different from the standard lattice Boltzmann method, the current method applies the nodal discontinuous Galerkin method into the streaming process in LBM to solve the resultant pure convection equation, in which the spatial discretization is completed on unstructured grids and the low-storage explicit Runge-Kutta scheme is used for time marching. The present method then overcomes the disadvantage of standard LBM for depending on the uniform meshes. Moreover, the collision process in the LBM is completed by using the multiple-relaxation-time scheme. After the validation of the NDG-LBM by simulating the lid-driven cavity flow, the simulations of flows over a fixed circular cylinder, a stationary airfoil and rotating-stationary cylinders are performed. Good agreement of present results with previous results is achieved, which indicates that the current NDG-LBM is accurate and effective for flow over object problems.
Wang, Zhiheng
2014-12-10
A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.
Explicitly represented polygon wall boundary model for the explicit MPS method
Mitsume, Naoto; Yoshimura, Shinobu; Murotani, Kohei; Yamada, Tomonori
2015-05-01
This study presents an accurate and robust boundary model, the explicitly represented polygon (ERP) wall boundary model, to treat arbitrarily shaped wall boundaries in the explicit moving particle simulation (E-MPS) method, which is a mesh-free particle method for strong form partial differential equations. The ERP model expresses wall boundaries as polygons, which are explicitly represented without using the distance function. These are derived so that for viscous fluids, and with less computational cost, they satisfy the Neumann boundary condition for the pressure and the slip/no-slip condition on the wall surface. The proposed model is verified and validated by comparing computed results with the theoretical solution, results obtained by other models, and experimental results. Two simulations with complex boundary movements are conducted to demonstrate the applicability of the E-MPS method to the ERP model.
Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
Directory of Open Access Journals (Sweden)
Hassan Saberi Nik
2014-01-01
Full Text Available We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods
Hundsdorfer, W.
2011-04-29
In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties. © 2011 Springer Science+Business Media, LLC.
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Comparing numerical methods for the solutions of the Chen system
International Nuclear Information System (INIS)
Noorani, M.S.M.; Hashim, I.; Ahmad, R.; Bakar, S.A.; Ismail, E.S.; Zakaria, A.M.
2007-01-01
In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
Directory of Open Access Journals (Sweden)
Liquan Mei
2014-01-01
Full Text Available A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.
Directory of Open Access Journals (Sweden)
seyd ghasem enayati
2017-01-01
Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.
NMPC for Oil Reservoir Production Optimization
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove
2011-01-01
this problem numerically using a single shooting sequential quadratic programming (SQP) based optimization method. Explicit singly diagonally implicit Runge-Kutta (ESDIRK) methods are used for integration of the stiff system of differential equations describing the two-phase flow, and the adjoint method...
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
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A. M. El-Naggar
2015-11-01
Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.
The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system
International Nuclear Information System (INIS)
Chowdhury, M.S.H.; Hashim, I.; Momani, S.
2009-01-01
In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is presented. The HPM is treated as an algorithm in a sequence of intervals (i.e. time step) for finding accurate approximate solutions to the famous Lorenz system. Numerical comparisons between the multistage homotopy-perturbation method (MHPM) and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for the nonlinear systems of ODEs.
Analysis of multi lobe journal bearings with surface roughness using finite difference method
PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.
2018-04-01
Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.
Free terminal time optimal control problem for the treatment of HIV infection
Directory of Open Access Journals (Sweden)
Amine Hamdache
2016-01-01
to provide the explicit formulations of the optimal controls. The corresponding optimality system with the additional transversality condition for the terminal time is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and a gradient method routine.
Explicit integration of extremely stiff reaction networks: partial equilibrium methods
International Nuclear Information System (INIS)
Guidry, M W; Hix, W R; Billings, J J
2013-01-01
In two preceding papers (Guidry et al 2013 Comput. Sci. Disc. 6 015001 and Guidry and Harris 2013 Comput. Sci. Disc. 6 015002), we have shown that when reaction networks are well removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically stabilized integration schemes that rival standard implicit methods in accuracy and speed for extremely stiff systems. However, we also showed that these explicit methods remain accurate but are no longer competitive in speed as the network approaches equilibrium. In this paper, we analyze this failure and show that it is associated with the presence of fast equilibration timescales that neither asymptotic nor quasi-steady-state approximations are able to remove efficiently from the numerical integration. Based on this understanding, we develop a partial equilibrium method to deal effectively with the approach to equilibrium and show that explicit asymptotic methods, combined with the new partial equilibrium methods, give an integration scheme that can plausibly deal with the stiffest networks, even in the approach to equilibrium, with accuracy and speed competitive with that of implicit methods. Thus we demonstrate that such explicit methods may offer alternatives to implicit integration of even extremely stiff systems and that these methods may permit integration of much larger networks than have been possible before in a number of fields. (paper)
Energy Technology Data Exchange (ETDEWEB)
Schmal, M; Russo, Q [Rio de Janeiro Univ. (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia; Almeida, M S; Bozzo, S [Rio de Janeiro Univ. (Brazil). Instituto de Quimica
1975-03-01
A method of solutions is presented for the determination of the velocity profiles in turbulent flow through annular tubes, based on the Von Karman similarity theory developed by Quarmby. The parameters found by Quarmby appearing in the velocity profiles and determined experimentally by different authors were approximated by polynonial functions of variable degree, as function of the Reynolds numbers. The Runge-Kutta-Nystrom method was used in the integration of the differential equations and the systematic of solution is presented in a computer program. The calculated results were compared to the experimental date and presented a deviation of 10/sup -2/%.
Modified Differential Transform Method for Solving the Model of Pollution for a System of Lakes
Directory of Open Access Journals (Sweden)
Brahim Benhammouda
2014-01-01
present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful strategy to extend the domain of convergence of the approximate solutions. The Fehlberg fourth-fifth order Runge-Kutta method with degree four interpolant (RKF45 numerical solution of the lakes system problem is used as a reference to compare with the analytical approximations showing the high accuracy of the results. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend of a perturbation parameter.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding
Efficient integration of stiff kinetics with phase change detection for reactive reservoir processes
DEFF Research Database (Denmark)
Kristensen, Morten Rode; Gerritsen, Margot G.; Thomsen, Per Grove
2007-01-01
We propose the use of implicit one-step Explicit Singly Diagonal Implicit Runge-Kutta (ESDIRK) methods for integration of the stiff kinetics in reactive, compositional and thermal processes that are solved using operator-splitting type approaches. To facilitate the algorithmic development we...
Faster Simulation Methods for the Non-Stationary Random Vibrations of Non-Linear MDOF Systems
DEFF Research Database (Denmark)
Askar, A.; Köylüoglu, H. U.; Nielsen, Søren R. K.
subject to nonstationary Gaussian white noise excitation, as an alternative to conventional direct simulation methods. These alternative simulation procedures rely on an assumption of local Gaussianity during each time step. This assumption is tantamount to various linearizations of the equations....... Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process...
Faster Simulation Methods for the Nonstationary Random Vibrations of Non-linear MDOF Systems
DEFF Research Database (Denmark)
Askar, A.; Köylüo, U.; Nielsen, Søren R.K.
1996-01-01
subject to nonstationary Gaussian white noise excitation, as an alternative to conventional direct simulation methods. These alternative simulation procedures rely on an assumption of local Gaussianity during each time step. This assumption is tantamount to various linearizations of the equations....... Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process...
International Nuclear Information System (INIS)
Schmal, M.; Russo, Q.; Almeida, M.S.; Bozzo, S.
1975-01-01
A method of solutions is presented for the determination of the velocity profiles in turbulent flow through annular tubes, based on the Von Karman similarity theory developed by Quarmby. The parameters found by Quarmby appearing in the velocity profiles and determined experimentally by different authors were approximated by polynonial functions of variable degree, as function of the Reynolds numbers. The Runge-Kutta-Nystrom method was used in the integration of the differential equations and the systematic of solution is presented in a computer program. The calculated results were compared to the experimental date and presented a deviation of 10 -2 % [pt
A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method
Zhan, Lei; Xiong, Juntao; Liu, Feng
2016-05-01
The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.
Muñoz-Esparza, Domingo; Kosović, Branko; Jiménez, Pedro A.; Coen, Janice L.
2018-04-01
The level-set method is typically used to track and propagate the fire perimeter in wildland fire models. Herein, a high-order level-set method using fifth-order WENO scheme for the discretization of spatial derivatives and third-order explicit Runge-Kutta temporal integration is implemented within the Weather Research and Forecasting model wildland fire physics package, WRF-Fire. The algorithm includes solution of an additional partial differential equation for level-set reinitialization. The accuracy of the fire-front shape and rate of spread in uncoupled simulations is systematically analyzed. It is demonstrated that the common implementation used by level-set-based wildfire models yields to rate-of-spread errors in the range 10-35% for typical grid sizes (Δ = 12.5-100 m) and considerably underestimates fire area. Moreover, the amplitude of fire-front gradients in the presence of explicitly resolved turbulence features is systematically underestimated. In contrast, the new WRF-Fire algorithm results in rate-of-spread errors that are lower than 1% and that become nearly grid independent. Also, the underestimation of fire area at the sharp transition between the fire front and the lateral flanks is found to be reduced by a factor of ≈7. A hybrid-order level-set method with locally reduced artificial viscosity is proposed, which substantially alleviates the computational cost associated with high-order discretizations while preserving accuracy. Simulations of the Last Chance wildfire demonstrate additional benefits of high-order accurate level-set algorithms when dealing with complex fuel heterogeneities, enabling propagation across narrow fuel gaps and more accurate fire backing over the lee side of no fuel clusters.
International Nuclear Information System (INIS)
Kupka, F.
1997-11-01
This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)
Liska, Sebastian; Colonius, Tim
2017-02-01
A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.
Convergence studies of deterministic methods for LWR explicit reflector methodology
International Nuclear Information System (INIS)
Canepa, S.; Hursin, M.; Ferroukhi, H.; Pautz, A.
2013-01-01
The standard approach in modem 3-D core simulators, employed either for steady-state or transient simulations, is to use Albedo coefficients or explicit reflectors at the core axial and radial boundaries. In the latter approach, few-group homogenized nuclear data are a priori produced with lattice transport codes using 2-D reflector models. Recently, the explicit reflector methodology of the deterministic CASMO-4/SIMULATE-3 code system was identified to potentially constitute one of the main sources of errors for core analyses of the Swiss operating LWRs, which are all belonging to GII design. Considering that some of the new GIII designs will rely on very different reflector concepts, a review and assessment of the reflector methodology for various LWR designs appeared as relevant. Therefore, the purpose of this paper is to first recall the concepts of the explicit reflector modelling approach as employed by CASMO/SIMULATE. Then, for selected reflector configurations representative of both GII and GUI designs, a benchmarking of the few-group nuclear data produced with the deterministic lattice code CASMO-4 and its successor CASMO-5, is conducted. On this basis, a convergence study with regards to geometrical requirements when using deterministic methods with 2-D homogenous models is conducted and the effect on the downstream 3-D core analysis accuracy is evaluated for a typical GII deflector design in order to assess the results against available plant measurements. (authors)
Dehghan, Mehdi; Mohammadi, Vahid
2017-03-01
As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.
Advanced differential quadrature methods
Zong, Zhi
2009-01-01
Modern Tools to Perform Numerical DifferentiationThe original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales. But now researchers in applied mathematics, computational mechanics, and engineering have developed a range of innovative DQ-based methods to overcome these shortcomings. Advanced Differential Quadrature Methods explores new DQ methods and uses these methods to solve problems beyond the capabilities of the direct DQ method.After a basic introduction to the direct DQ method, the book presents a number of DQ methods, including complex DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain DQ, and localized DQ. It also provides a mathematical compendium that summarizes Gauss elimination, the Runge-Kutta method, complex analysis, and more. The final chapter contains three codes written in the FORTRAN language, enabling readers to q...
Rackauckas, Christopher; Nie, Qing
2017-01-01
Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.
Models and numerical methods for time- and energy-dependent particle transport
Energy Technology Data Exchange (ETDEWEB)
Olbrant, Edgar
2012-04-13
Particles passing through a medium can be described by the Boltzmann transport equation. Therein, all physical interactions of particles with matter are given by cross sections. We compare different analytical models of cross sections for photons, electrons and protons to state-of-the-art databases. The large dimensionality of the transport equation and its integro-differential form make it analytically difficult and computationally costly to solve. In this work, we focus on the following approximative models to the linear Boltzmann equation: (i) the time-dependent simplified P{sub N} (SP{sub N}) equations, (ii) the M{sub 1} model derived from entropy-based closures and (iii) a new perturbed M{sub 1} model derived from a perturbative entropy closure. In particular, an asymptotic analysis for SP{sub N} equations is presented and confirmed by numerical computations in 2D. Moreover, we design an explicit Runge-Kutta discontinuous Galerkin (RKDG) method to the M{sub 1} model of radiative transfer in slab geometry and construct a scheme ensuring the realizability of the moment variables. Among other things, M{sub 1} numerical results are compared with an analytical solution in a Riemann problem and the Marshak wave problem is considered. Additionally, we rigorously derive a new hierarchy of kinetic moment models in the context of grey photon transport in one spatial dimension. For the perturbed M{sub 1} model, we present numerical results known as the two beam instability or the analytical benchmark due to Su and Olson and compare them to the standard M{sub 1} as well as transport solutions.
Directory of Open Access Journals (Sweden)
Dauda GuliburYAKUBU
2012-12-01
Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.
Multiresolution and Explicit Methods for Vector Field Analysis and Visualization
Nielson, Gregory M.
1997-01-01
This is a request for a second renewal (3d year of funding) of a research project on the topic of multiresolution and explicit methods for vector field analysis and visualization. In this report, we describe the progress made on this research project during the second year and give a statement of the planned research for the third year. There are two aspects to this research project. The first is concerned with the development of techniques for computing tangent curves for use in visualizing flow fields. The second aspect of the research project is concerned with the development of multiresolution methods for curvilinear grids and their use as tools for visualization, analysis and archiving of flow data. We report on our work on the development of numerical methods for tangent curve computation first.
Europlexus: a domain decomposition method in explicit dynamics
International Nuclear Information System (INIS)
Faucher, V.; Hariddh, Bung; Combescure, A.
2003-01-01
Explicit time integration methods are used in structural dynamics to simulate fast transient phenomena, such as impacts or explosions. A very fine analysis is required in the vicinity of the loading areas but extending the same method, and especially the same small time-step, to the whole structure frequently yields excessive calculation times. We thus perform a dual Schur domain decomposition, to divide the global problem into several independent ones, to which is added a reduced size interface problem, to ensure connections between sub-domains. Each sub-domain is given its own time-step and its own mesh fineness. Non-matching meshes at the interfaces are handled. An industrial example demonstrates the interest of our approach. (authors)
A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids
Energy Technology Data Exchange (ETDEWEB)
McCorquodale, Peter; Colella, Phillip
2011-01-28
We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.
Generalización a Rn de algunos métodos de interpolación conocidos en ecuaciones diferenciales
Directory of Open Access Journals (Sweden)
Vernor Arguedas Troyo
2009-02-01
Full Text Available We present the Runge-Kutta methods of several one-step levels in Rn , as well as algorithms in pseudo-code for the implicit and explicit methods. We study the problem of error control in Rn and we give numerical examples in tables or parameter schemata. Keywords: n-dimensional runge-Katta methods, explicit and implicit methods, interpolation, pseudo-algorithms, parametric schema.
Subdomain Precise Integration Method for Periodic Structures
Directory of Open Access Journals (Sweden)
F. Wu
2014-01-01
Full Text Available A subdomain precise integration method is developed for the dynamical responses of periodic structures comprising many identical structural cells. The proposed method is based on the precise integration method, the subdomain scheme, and the repeatability of the periodic structures. In the proposed method, each structural cell is seen as a super element that is solved using the precise integration method, considering the repeatability of the structural cells. The computational efforts and the memory size of the proposed method are reduced, while high computational accuracy is achieved. Therefore, the proposed method is particularly suitable to solve the dynamical responses of periodic structures. Two numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method through comparison with the Newmark and Runge-Kutta methods.
Prediction of residual stress using explicit finite element method
Directory of Open Access Journals (Sweden)
W.A. Siswanto
2015-12-01
Full Text Available This paper presents the residual stress behaviour under various values of friction coefficients and scratching displacement amplitudes. The investigation is based on numerical solution using explicit finite element method in quasi-static condition. Two different aeroengine materials, i.e. Super CMV (Cr-Mo-V and Titanium alloys (Ti-6Al-4V, are examined. The usage of FEM analysis in plate under normal contact is validated with Hertzian theoretical solution in terms of contact pressure distributions. The residual stress distributions along with normal and shear stresses on elastic and plastic regimes of the materials are studied for a simple cylinder-on-flat contact configuration model subjected to normal loading, scratching and followed by unloading. The investigated friction coefficients are 0.3, 0.6 and 0.9, while scratching displacement amplitudes are 0.05 mm, 0.10 mm and 0.20 mm respectively. It is found that friction coefficient of 0.6 results in higher residual stress for both materials. Meanwhile, the predicted residual stress is proportional to the scratching displacement amplitude, higher displacement amplitude, resulting in higher residual stress. It is found that less residual stress is predicted on Super CMV material compared to Ti-6Al-4V material because of its high yield stress and ultimate strength. Super CMV material with friction coefficient of 0.3 and scratching displacement amplitude of 0.10 mm is recommended to be used in contact engineering applications due to its minimum possibility of fatigue.
Stiff modes in spinvalve simulations with OOMMF
Energy Technology Data Exchange (ETDEWEB)
Mitropoulos, Spyridon [Department of Computer and Informatics Engineering, TEI of Eastern Macedonia and Thrace, Kavala (Greece); Tsiantos, Vassilis, E-mail: tsianto@teikav.edu.gr [Department of Electrical Engineering, TEI of Eastern Macedonia and Thrace, Kavala, 65404 Greece (Greece); Ovaliadis, Kyriakos [Department of Electrical Engineering, TEI of Eastern Macedonia and Thrace, Kavala, 65404 Greece (Greece); Kechrakos, Dimitris [Department of Education, ASPETE, Heraklion, Athens (Greece); Donahue, Michael [Applied and Computational Mathematics Division, NIST, Gaithersburg, MD (United States)
2016-04-01
Micromagnetic simulations are an important tool for the investigation of magnetic materials. Micromagnetic software uses various techniques to solve differential equations, partial or ordinary, involved in the dynamic simulations. Euler, Runge-Kutta, Adams, and BDF (Backward Differentiation Formulae) are some of the methods used for this purpose. In this paper, spinvalve simulations are investigated. Evidence is presented showing that these systems have stiff modes, and that implicit methods such as BDF are more effective than explicit methods in such cases.
TSOS and TSOS-FK hybrid methods for modelling the propagation of seismic waves
Ma, Jian; Yang, Dinghui; Tong, Ping; Ma, Xiao
2018-05-01
We develop a new time-space optimized symplectic (TSOS) method for numerically solving elastic wave equations in heterogeneous isotropic media. We use the phase-preserving symplectic partitioned Runge-Kutta method to evaluate the time derivatives and optimized explicit finite-difference (FD) schemes to discretize the space derivatives. We introduce the averaged medium scheme into the TSOS method to further increase its capability of dealing with heterogeneous media and match the boundary-modified scheme for implementing free-surface boundary conditions and the auxiliary differential equation complex frequency-shifted perfectly matched layer (ADE CFS-PML) non-reflecting boundaries with the TSOS method. A comparison of the TSOS method with analytical solutions and standard FD schemes indicates that the waveform generated by the TSOS method is more similar to the analytic solution and has a smaller error than other FD methods, which illustrates the efficiency and accuracy of the TSOS method. Subsequently, we focus on the calculation of synthetic seismograms for teleseismic P- or S-waves entering and propagating in the local heterogeneous region of interest. To improve the computational efficiency, we successfully combine the TSOS method with the frequency-wavenumber (FK) method and apply the ADE CFS-PML to absorb the scattered waves caused by the regional heterogeneity. The TSOS-FK hybrid method is benchmarked against semi-analytical solutions provided by the FK method for a 1-D layered model. Several numerical experiments, including a vertical cross-section of the Chinese capital area crustal model, illustrate that the TSOS-FK hybrid method works well for modelling waves propagating in complex heterogeneous media and remains stable for long-time computation. These numerical examples also show that the TSOS-FK method can tackle the converted and scattered waves of the teleseismic plane waves caused by local heterogeneity. Thus, the TSOS and TSOS-FK methods proposed in
Solution methods for large systems of linear equations in BACCHUS
International Nuclear Information System (INIS)
Homann, C.; Dorr, B.
1993-05-01
The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
Multi-scale and multi-physics simulations using the multi-fluid plasma model
2017-04-25
small The simulation uses 512 second-order elements Bz = 1.0, Te = Ti = 0.01, ui = ue = 0 ne = ni = 1.0 + e−10(x−6) 2 Baboolal, Math . and Comp. Sim. 55...DISTRIBUTION Clearance No. 17211 23 / 31 SUMMARY The blended finite element method (BFEM) is presented DG spatial discretization with explicit Runge...Kutta (i+, n) CG spatial discretization with implicit Crank-Nicolson (e−, fileds) DG captures shocks and discontinuities CG is efficient and robust for
RKC time-stepping for advection-diffusion-reaction problems
International Nuclear Information System (INIS)
Verwer, J.G.; Sommeijer, B.P.; Hundsdorfer, W.
2004-01-01
The original explicit Runge-Kutta-Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit-explicit manner to also incorporate highly stiff reaction terms. This implicit-explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit-explicit RKC integration of advection-diffusion-reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly
Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
Directory of Open Access Journals (Sweden)
I. Amirali
2014-01-01
Full Text Available Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
Wu, Shen R
2012-01-01
A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master
Explicit appropriate basis function method for numerical solution of stiff systems
International Nuclear Information System (INIS)
Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling
2015-01-01
Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations
An embedded formula of the Chebyshev collocation method for stiff problems
Piao, Xiangfan; Bu, Sunyoung; Kim, Dojin; Kim, Philsu
2017-12-01
In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge-Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.
Computer modeling of oil spill trajectories with a high accuracy method
International Nuclear Information System (INIS)
Garcia-Martinez, Reinaldo; Flores-Tovar, Henry
1999-01-01
This paper proposes a high accuracy numerical method to model oil spill trajectories using a particle-tracking algorithm. The Euler method, used to calculate oil trajectories, can give adequate solutions in most open ocean applications. However, this method may not predict accurate particle trajectories in certain highly non-uniform velocity fields near coastal zones or in river problems. Simple numerical experiments show that the Euler method may also introduce artificial numerical dispersion that could lead to overestimation of spill areas. This article proposes a fourth-order Runge-Kutta method with fourth-order velocity interpolation to calculate oil trajectories that minimise these problems. The algorithm is implemented in the OilTrack model to predict oil trajectories following the 'Nissos Amorgos' oil spill accident that occurred in the Gulf of Venezuela in 1997. Despite lack of adequate field information, model results compare well with observations in the impacted area. (Author)
Bonito, Andrea; Guermond, Jean-Luc; Popov, Bojan
2013-01-01
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method
A Gas-kinetic Discontinuous Galerkin Method for Viscous Flow Equations
International Nuclear Information System (INIS)
Liu, Hongwei; Xu, Kun
2007-01-01
This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for viscous flow computation. The construction of the RKDG method is based on a gas-kinetic formulation, which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at the cell interface through a simple hybrid gas distribution function. Due to the intrinsic connection between the gaskinetic BGK model and the Navier-Stokes equations, the Navier-Stokes flux is automatically obtained by the present method. Numerical examples for both one dimensional (10) and two dimensional(20) compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current RKDG method
A method for solving the KDV equation and some numerical experiments
International Nuclear Information System (INIS)
Chang Jinjiang.
1993-01-01
In this paper, by means of difference method for discretization of space partial derivatives of KDV equation, an initial value problem in ordinary differential equations of large dimensions is produced. By using this ordinary differential equations the existence and the uniqueness of the solution of the KDV equation and the conservation of scheme are proved. This ordinary differential equation can be solved by using implicit Runge-Kutta methods, so a new method for finding the numerical solution of the KDV equation is presented. Numerical experiments not only describe in detail the procedure of two solitons collision, soliton reflex and soliton produce, but also show that this method is very effective. (author). 7 refs, 3 figs
Directory of Open Access Journals (Sweden)
A. Sami Bataineh
2016-09-01
Full Text Available In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with their operational matrices and collocation method. Under some regularity conditions, upper bounds of the absolute errors are given. We apply the residual correction procedure which may estimate the absolute error to the problem. We may estimate the absolute error by using a procedure depends on the sequence of the approximate solutions. For some certain cases, we apply the method to the problem in the numerical examples. Moreover, we test the impact of changing the flow parameters numerically. The results are consistent with the results of Runge-Kutta fourth order method and homotopy analysis method.
Inverse operator method for solutions of nonlinear dynamical equations and some typical applications
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1993-01-01
The inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coupled generalized Duffing equations are investigated by using the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields
Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
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M. S. H. Chowdhury
2012-01-01
Full Text Available Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4 solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.
Directory of Open Access Journals (Sweden)
F. F. Ngwane
2017-01-01
Full Text Available In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs, including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs. Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one-step hybrid trigonometrically fitted method with an off-grid point. We implement BHTRKNM in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHTRKNM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.
International Nuclear Information System (INIS)
Li Wenjun; China Academy of Engineering Physics, Mianyang; Xu Zhou; Li Ming; Yang Xingfan; Chen Yanan; Liu Jie; Jin Xiao; Lin Yuzheng
2008-01-01
In this paper, a time-domain equivalent circuit method is applied to solve dispersion of coupled-cavity travelling-wave tube (CCTWT). First, the time-domain circuit equations of CCTWT coupled-cavity chain are deduced from the equivalent circuit model. Then, the equations are solved numerically by fourth-order Runge-Kutta method and a program CTTDCP is developed using MATLAB. Last, a L-band CCTWT is calculated using CTTDCP and the cavity pass-band of this tube is computed to be 1.08-1.48 GHz, which is consistent with the experimental results and the simulation results of electromagnetic code and demonstrates the validity of the time-domain equivalent circuit method. In addition, a new design method which uses the equivalent circuit method and electromagnetic simulation together to optimize the cold cavity characteristics of CCTWT is proposed. (authors)
Lee, Eun Seok
2000-10-01
An improved aerodynamics performance of a turbine cascade shape can be achieved by an understanding of the flow-field associated with the stator-rotor interaction. In this research, an axial gas turbine airfoil cascade shape is optimized for improved aerodynamic performance by using an unsteady Navier-Stokes solver and a parallel genetic algorithm. The objective of the research is twofold: (1) to develop a computational fluid dynamics code having faster convergence rate and unsteady flow simulation capabilities, and (2) to optimize a turbine airfoil cascade shape with unsteady passing wakes for improved aerodynamic performance. The computer code solves the Reynolds averaged Navier-Stokes equations. It is based on the explicit, finite difference, Runge-Kutta time marching scheme and the Diagonalized Alternating Direction Implicit (DADI) scheme, with the Baldwin-Lomax algebraic and k-epsilon turbulence modeling. Improvements in the code focused on the cascade shape design capability, convergence acceleration and unsteady formulation. First, the inverse shape design method was implemented in the code to provide the design capability, where a surface transpiration concept was employed as an inverse technique to modify the geometry satisfying the user specified pressure distribution on the airfoil surface. Second, an approximation storage multigrid method was implemented as an acceleration technique. Third, the preconditioning method was adopted to speed up the convergence rate in solving the low Mach number flows. Finally, the implicit dual time stepping method was incorporated in order to simulate the unsteady flow-fields. For the unsteady code validation, the Stokes's 2nd problem and the Poiseuille flow were chosen and compared with the computed results and analytic solutions. To test the code's ability to capture the natural unsteady flow phenomena, vortex shedding past a cylinder and the shock oscillation over a bicircular airfoil were simulated and compared with
A numeric-analytic method for approximating the chaotic Chen system
International Nuclear Information System (INIS)
Mossa Al-sawalha, M.; Noorani, M.S.M.
2009-01-01
The epitome of this paper centers on the application of the differential transformation method (DTM) the renowned Chen system which is described as a three-dimensional system of ODEs with quadratic nonlinearities. Numerical comparisons are made between the DTM and the classical fourth-order Runge-Kutta method (RK4). Our work showcases the precision of the DTM as the Chen system transforms from a non-chaotic system to a chaotic one. Since the Lyapunov exponent for this system is much higher compared to other chaotic systems, we shall highlight the difficulties of the simulations with respect to its accuracy. We wrap up our investigations to reveal that this direct symbolic-numeric scheme is effective and accurate.
A modal method for transient thermal analysis of CANDU fuel channel
International Nuclear Information System (INIS)
Park, J-W.; Muzumdar, A.J.
1996-01-01
The classical modal expansion technique has been applied to predict transient fuel and coolant temperatures under on-power conditions in a CANDU fuel channel. The temperature profile across the fuel pellet is assumed to be parabolic and fuel and coolant temperatures are expanded with Fourier series. The coefficient derivatives are written in state space form and solved by the Runge-Kutta method of fifth order. To validate the present model, the calculated fuel temperatures for several sample cases were compared with HOTSPOT-II, which employs a more rigorous finite-difference model. The agreement was found to be reasonable for the operational transients simulated. The advantage of the modal method is the fast computation speed for application to the real-time system such as the CANDU simulator which is being currently developed at the Institute for Advanced Engineering (IAE). (author)
International Nuclear Information System (INIS)
Atouei, S.A.; Hosseinzadeh, Kh.; Hatami, M.; Ghasemi, Seiyed E.; Sahebi, S.A.R.; Ganji, D.D.
2015-01-01
In this study, heat transfer and temperature distribution equations for semi-spherical convective–radiative porous fins are presented. Temperature-dependent heat generation, convection and radiation effects are considered and after deriving the governing equation, Least Square Method (LSM), Collocation Method (CM) and fourth order Runge-Kutta method (NUM) are applied for predicting the temperature distribution in the described fins. Results reveal that LSM has excellent agreement with numerical method, so can be suitable analytical method for solving the problem. Also, the effect of some physical parameters which are appeared in the mathematical formulation on fin surface temperature is investigated to show the effect of radiation and heat generation in a solid fin temperature. - Highlights: • Thermal analysis of a semi-spherical fin is investigated. • Collocation and Least Square Methods are applied on the problem. • Convection, radiation and heat generation is considered. • Physical results are compared to numerical outcomes.
An explicit method in non-linear soil-structure interaction
International Nuclear Information System (INIS)
Kunar, R.R.
1981-01-01
The explicit method of analysis in the time domain is ideally suited for the solution of transient dynamic non-linear problems. Though the method is not new, its application to seismic soil-structure interaction is relatively new and deserving of public discussion. This paper describes the principles of the explicit approach in soil-structure interaction and it presents a simple algorithm that can be used in the development of explicit computer codes. The paper also discusses some of the practical considerations like non-reflecting boundaries and time steps. The practicality of the method is demonstrated using a computer code, PRESS, which is used to compare the treatment of strain-dependent properties using average strain levels over the whole time history (the equivalent linear method) and using the actual strain levels at every time step to modify the soil properties (non-linear method). (orig.)
Symmetry Methods of Flow and Heat Transfer between Slowly Expanding or Contracting Walls
Directory of Open Access Journals (Sweden)
Gabriel Magalakwe
2013-01-01
Full Text Available An analysis has been carried out for the flow and heat transfer of an incompressible laminar and viscous fluid in a rectangular domain bounded by two moving porous walls which enable the fluid to enter or exit during successive expansions or contractions. The basic equations governing the flow are reduced to the ordinary differential equations using Lie-group analysis. Effects of the permeation Reynolds number , porosity , and the dimensionless wall dilation rate on the self-axial velocity are studied both analytically and numerically. The solutions are represented graphically. The analytical procedure is based on double perturbation in the permeation Reynolds number and the wall expansion ratio , whereas the numerical solution is obtained using Runge-Kutta method with shooting technique. Results are correlated and compared for some values of the physical parameters. Lastly, we look at the temperature distribution.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer
An Efficient Explicit-time Description Method for Timed Model Checking
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Hao Wang
2009-12-01
Full Text Available Timed model checking, the method to formally verify real-time systems, is attracting increasing attention from both the model checking community and the real-time community. Explicit-time description methods verify real-time systems using general model constructs found in standard un-timed model checkers. Lamport proposed an explicit-time description method using a clock-ticking process (Tick to simulate the passage of time together with a group of global variables to model time requirements. Two methods, the Sync-based Explicit-time Description Method using rendezvous synchronization steps and the Semaphore-based Explicit-time Description Method using only one global variable were proposed; they both achieve better modularity than Lamport's method in modeling the real-time systems. In contrast to timed automata based model checkers like UPPAAL, explicit-time description methods can access and store the current time instant for future calculations necessary for many real-time systems, especially those with pre-emptive scheduling. However, the Tick process in the above three methods increments the time by one unit in each tick; the state spaces therefore grow relatively fast as the time parameters increase, a problem when the system's time period is relatively long. In this paper, we propose a more efficient method which enables the Tick process to leap multiple time units in one tick. Preliminary experimental results in a high performance computing environment show that this new method significantly reduces the state space and improves both the time and memory efficiency.
Implicit–explicit (IMEX Runge–Kutta methods for non-hydrostatic atmospheric models
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D. J. Gardner
2018-04-01
Full Text Available The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX additive Runge–Kutta (ARK methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored.The accuracy and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.
Verifying Real-Time Systems using Explicit-time Description Methods
Directory of Open Access Journals (Sweden)
Hao Wang
2009-12-01
Full Text Available Timed model checking has been extensively researched in recent years. Many new formalisms with time extensions and tools based on them have been presented. On the other hand, Explicit-Time Description Methods aim to verify real-time systems with general untimed model checkers. Lamport presented an explicit-time description method using a clock-ticking process (Tick to simulate the passage of time together with a group of global variables for time requirements. This paper proposes a new explicit-time description method with no reliance on global variables. Instead, it uses rendezvous synchronization steps between the Tick process and each system process to simulate time. This new method achieves better modularity and facilitates usage of more complex timing constraints. The two explicit-time description methods are implemented in DIVINE, a well-known distributed-memory model checker. Preliminary experiment results show that our new method, with better modularity, is comparable to Lamport's method with respect to time and memory efficiency.
Energy Technology Data Exchange (ETDEWEB)
Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)
2017-06-15
Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.
Bakholdin, Igor
2018-02-01
Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
International Nuclear Information System (INIS)
Teymourtash, A. R.; Mahpeykar, M. R.
2003-01-01
During the course of expansion in turbines, the steam at first super cools and then nucleated to become a two-phase mixture. This is an area where greater understanding can lead to improved design. This paper describes a numerical method for the solution of two-dimensional two-phase flow of steam in a cascade of turbine blading; the unsteady euler equations governing the overall behaviour of the fluid are combined with equations describing droplet behaviour and treated by Jasmine fourth order runge Kutta time marching scheme which modified to allow for two-phase effects. The theoretical surface pressure distributions, droplet radii and contours of constant wetness fraction are presented and results are discussed in the light of knowledge of actual surface pressure distributions
Czech Academy of Sciences Publication Activity Database
Fuchs, Vladimír; Gunn, J. P.
2004-01-01
Roč. 54, suppl.C (2004), C100-C110 ISSN 0011-4626. [Symposium on Plasma Physics and Technology /21./. Praha, 14.06.2004-17.06.2004] Institutional research plan: CEZ:AV0Z2043910 Keywords : simulation, tokamak edge plasma, lower hybrid antenna Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.292, year: 2004
International Nuclear Information System (INIS)
Oliveira, L.F.S. de; Frutuoso e Melo, P.F.F.; Lima, J.E.P.; Stal, I.L.
1985-01-01
A computacional application of the explicit method for analyzing event trees in the context of probabilistic risk assessments is discussed. A detailed analysis of the explicit method is presented, including the train level analysis (TLA) of safety systems and the impact vector method. It is shown that the penalty for not adopting TLA is that in some cases non-conservative results may be reached. The impact vector method can significantly reduce the number of sequences to be considered, and its use has inspired the definition of a dependency matrix, which enables the proper running of a computer code especially developed for analysing event trees. The code has been extensively used in the Angra 1 PRA currently underway. In its present version it gives as output the dominant sequences for each given initiator, properly classiying them in core-degradation classes as specified by the user. (Author) [pt
Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size
Hadjimichael, Yiannis
2016-09-08
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.
Explicit time marching methods for the time-dependent Euler computations
International Nuclear Information System (INIS)
Tai, C.H.; Chiang, D.C.; Su, Y.P.
1997-01-01
Four explicit type time marching methods, including one proposed by the authors, are examined. The TVD conditions of this method are analyzed with the linear conservation law as the model equation. Performance of these methods when applied to the Euler equations are numerically tested. Seven examples are tested, the main concern is the performance of the methods when discontinuities with different strengths are encountered. When the discontinuity is getting stronger, spurious oscillation shows up for three existing methods, while the method proposed by the authors always gives the results with satisfaction. The effect of the limiter is also investigated. To put these methods in the same basis for the comparison the same spatial discretization is used. Roe's solver is used to evaluate the fluxes at the cell interface; spatially second-order accuracy is achieved by the MUSCL reconstruction. 19 refs., 8 figs
Replica exchange with solute tempering: A method for sampling biological systems in explicit water
Liu, Pu; Kim, Byungchan; Friesner, Richard A.; Berne, B. J.
2005-09-01
An innovative replica exchange (parallel tempering) method called replica exchange with solute tempering (REST) for the efficient sampling of aqueous protein solutions is presented here. The method bypasses the poor scaling with system size of standard replica exchange and thus reduces the number of replicas (parallel processes) that must be used. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST is compared with standard replica exchange for an alanine dipeptide molecule in water. The comparisons confirm that REST greatly reduces the number of CPUs required by regular replica exchange and increases the sampling efficiency. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water. Author contributions: B.J.B. designed research; P.L. and B.K. performed research; P.L. and B.K. analyzed data; and P.L., B.K., R.A.F., and B.J.B. wrote the paper.Abbreviations: REST, replica exchange with solute tempering; REM, replica exchange method; MD, molecular dynamics.*P.L. and B.K. contributed equally to this work.
International Nuclear Information System (INIS)
Kančev, Duško; Čepin, Marko
2012-01-01
Redundancy and diversity are the main principles of the safety systems in the nuclear industry. Implementation of safety components redundancy has been acknowledged as an effective approach for assuring high levels of system reliability. The existence of redundant components, identical in most of the cases, implicates a probability of their simultaneous failure due to a shared cause—a common cause failure. This paper presents a new method for explicit modelling of single component failure event within multiple common cause failure groups simultaneously. The method is based on a modification of the frequently utilised Beta Factor parametric model. The motivation for development of this method lays in the fact that one of the most widespread softwares for fault tree and event tree modelling as part of the probabilistic safety assessment does not comprise the option for simultaneous assignment of single failure event to multiple common cause failure groups. In that sense, the proposed method can be seen as an advantage of the explicit modelling of common cause failures. A standard standby safety system is selected as a case study for application and study of the proposed methodology. The results and insights implicate improved, more transparent and more comprehensive models within probabilistic safety assessment.
International Nuclear Information System (INIS)
Oliveira, L.F.S.; Frutuoso e Melo, P.F.; Lima, J.E.P.; Stal, I.L.
1985-01-01
We discuss in this paper a computational application of the explicit method for analyzing event trees in the context of probabilistic risk assessments. A detailed analysis of the explicit method is presented, including the train level analysis (TLA) of safety systems and the impact vector method. It is shown that the penalty for not adopting TLA is that in some cases non-conservative results may be reached. The impact vector method can significantly reduce the number of sequences to be considered, and its use has inspired the definition of a dependency matrix, which enables the proper running of a computer code especially developed for analysing event trees. This code constructs and quantifies the event trees in the fashion just discussed, by receiving as input the construction and quantification dependencies defined in the dependency matrix. The code has been extensively used in the Angra 1 PRA currently underway. In its present version it gives as output the dominant sequences for each given initiator, properly classifying them in core-degradation classes as specified by the user. This calculation is made in a pointwise fashion. Extensions of this code are being developed in order to perform uncertainty analyses on the dominant sequences and also risk importance measures of the safety systems envolved. (orig.)
International Nuclear Information System (INIS)
Gray, S.K.; Noid, D.W.; Sumpter, B.G.
1994-01-01
We test the suitability of a variety of explicit symplectic integrators for molecular dynamics calculations on Hamiltonian systems. These integrators are extremely simple algorithms with low memory requirements, and appear to be well suited for large scale simulations. We first apply all the methods to a simple test case using the ideas of Berendsen and van Gunsteren. We then use the integrators to generate long time trajectories of a 1000 unit polyethylene chain. Calculations are also performed with two popular but nonsymplectic integrators. The most efficient integrators of the set investigated are deduced. We also discuss certain variations on the basic symplectic integration technique
Song, Yun S; Steinrücken, Matthias
2012-03-01
The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.
Eliasson, Kristina; Palm, Peter; Nyman, Teresia; Forsman, Mikael
2017-07-01
A common way to conduct practical risk assessments is to observe a job and report the observed long term risks for musculoskeletal disorders. The aim of this study was to evaluate the inter- and intra-observer reliability of ergonomists' risk assessments without the support of an explicit risk assessment method. Twenty-one experienced ergonomists assessed the risk level (low, moderate, high risk) of eight upper body regions, as well as the global risk of 10 video recorded work tasks. Intra-observer reliability was assessed by having nine of the ergonomists repeat the procedure at least three weeks after the first assessment. The ergonomists made their risk assessment based on his/her experience and knowledge. The statistical parameters of reliability included agreement in %, kappa, linearly weighted kappa, intraclass correlation and Kendall's coefficient of concordance. The average inter-observer agreement of the global risk was 53% and the corresponding weighted kappa (K w ) was 0.32, indicating fair reliability. The intra-observer agreement was 61% and 0.41 (K w ). This study indicates that risk assessments of the upper body, without the use of an explicit observational method, have non-acceptable reliability. It is therefore recommended to use systematic risk assessment methods to a higher degree. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.
Static Behaviour of Natural Gas and its Flow in Pipes
Ohirhian, Peter
2010-01-01
1. 2. A general differential equation that governs static behavior of any fluid and its flow in horizontal, uphill and downhill pipes has been developed. classical fourth order Runge-Kutta numerical method is programmed in Fortran 77, to test the equation and results are accurate. The program shows that a length ncrement as large as 10,000 ft can be used in the Runge-Kutta method of solution to differential equation during uphill gas flow and up to 5700ft for downhill gas flow The Runge-Kutta...
Explicit hydration of ammonium ion by correlated methods employing molecular tailoring approach
Singh, Gurmeet; Verma, Rahul; Wagle, Swapnil; Gadre, Shridhar R.
2017-11-01
Explicit hydration studies of ions require accurate estimation of interaction energies. This work explores the explicit hydration of the ammonium ion (NH4+) employing Møller-Plesset second order (MP2) perturbation theory, an accurate yet relatively less expensive correlated method. Several initial geometries of NH4+(H2O)n (n = 4 to 13) clusters are subjected to MP2 level geometry optimisation with correlation consistent aug-cc-pVDZ (aVDZ) basis set. For large clusters (viz. n > 8), molecular tailoring approach (MTA) is used for single point energy evaluation at MP2/aVTZ level for the estimation of MP2 level binding energies (BEs) at complete basis set (CBS) limit. The minimal nature of the clusters upto n ≤ 8 is confirmed by performing vibrational frequency calculations at MP2/aVDZ level of theory, whereas for larger clusters (9 ≤ n ≤ 13) such calculations are effected via grafted MTA (GMTA) method. The zero point energy (ZPE) corrections are done for all the isomers lying within 1 kcal/mol of the lowest energy one. The resulting frequencies in N-H region (2900-3500 cm-1) and in O-H stretching region (3300-3900 cm-1) are in found to be in excellent agreement with the available experimental findings for 4 ≤ n ≤ 13. Furthermore, GMTA is also applied for calculating the BEs of these clusters at coupled cluster singles and doubles with perturbative triples (CCSD(T)) level of theory with aVDZ basis set. This work thus represents an art of the possible on contemporary multi-core computers for studying explicit molecular hydration at correlated level theories.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.
2009-01-01
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations
Directory of Open Access Journals (Sweden)
Yadong Shang
2012-01-01
Full Text Available This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.
Time-explicit methods for joint economical and geological risk mitigation in production optimization
DEFF Research Database (Denmark)
Christiansen, Lasse Hjuler; Capolei, Andrea; Jørgensen, John Bagterp
2016-01-01
Real-life applications of production optimization face challenges of risks related to unpredictable fluctuations in oil prices and sparse geological data. Consequently, operating companies are reluctant to adopt model-based production optimization into their operations. Conventional production...... of mitigating economical and geological risks. As opposed to conventional strategies that focus on a single long-term objective, TE methods seek to reduce risks and promote returns over the entire reservoir life by optimization of a given ensemble-based geological risk measure over time. By explicit involvement...... of time, economical risks are implicitly addressed by balancing short-term and long-term objectives throughout the reservoir life. Open-loop simulations of a two-phase synthetic reservoir demonstrate that TE methods may significantly improve short-term risk measures such as expected return, standard...
Thermal Analysis of Ball screw Systems by Explicit Finite Difference Method
Energy Technology Data Exchange (ETDEWEB)
Min, Bog Ki [Hanyang Univ., Seoul (Korea, Republic of); Park, Chun Hong; Chung, Sung Chong [KIMM, Daejeon (Korea, Republic of)
2016-01-15
Friction generated from balls and grooves incurs temperature rise in the ball screw system. Thermal deformation due to the heat degrades positioning accuracy of the feed drive system. To compensate for the thermal error, accurate prediction of the temperature distribution is required first. In this paper, to predict the temperature distribution according to the rotational speed, solid and hollow cylinders are applied for analysis of the ball screw shaft and nut, respectively. Boundary conditions such as the convective heat transfer coefficient, friction torque, and thermal contact conductance (TCC) between balls and grooves are formulated according to operating and fabrication conditions of the ball screw. Explicit FDM (finite difference method) is studied for development of a temperature prediction simulator. Its effectiveness is verified through numerical analysis.
Deng, Nanjie; Zhang, Bin W; Levy, Ronald M
2015-06-09
The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.
EVALUATION OF THE POUNDING FORCES DURING EARTHQUAKE USING EXPLICIT DYNAMIC TIME INTEGRATION METHOD
Directory of Open Access Journals (Sweden)
Nica George Bogdan
2017-09-01
Full Text Available Pounding effects during earthquake is a subject of high significance for structural engineers performing in the urban areas. In this paper, two ways to account for structural pounding are used in a MATLAB code, namely classical stereomechanics approach and nonlinear viscoelastic impact element. The numerical study is performed on SDOF structures acted by ELCentro recording. While most of the studies available in the literature are related to Newmark implicit time integration method, in this study the equations of motion are numerical integrated using central finite difference method, an explicit method, having the main advantage that in the displacement at the ith+1 step is calculated based on the loads from the ith step. Thus, the collision is checked and the pounding forces are taken into account into the equation of motion in an easier manner than in an implicit integration method. First, a comparison is done using available data in the literature. Both linear and nonlinear behavior of the structures during earthquake is further investigated. Several layout scenarios are also investigated, in which one or more weak buildings are adjacent to a stiffer building. One of the main findings in this paper is related to the behavior of a weak structure located between two stiff structures.
Isegawa, Miho; Gao, Jiali; Truhlar, Donald G
2011-08-28
Molecular fragmentation algorithms provide a powerful approach to extending electronic structure methods to very large systems. Here we present a method for including charge transfer between molecular fragments in the explicit polarization (X-Pol) fragment method for calculating potential energy surfaces. In the conventional X-Pol method, the total charge of each fragment is preserved, and charge transfer between fragments is not allowed. The description of charge transfer is made possible by treating each fragment as an open system with respect to the number of electrons. To achieve this, we applied Mermin's finite temperature method to the X-Pol wave function. In the application of this method to X-Pol, the fragments are open systems that partially equilibrate their number of electrons through a quasithermodynamics electron reservoir. The number of electrons in a given fragment can take a fractional value, and the electrons of each fragment obey the Fermi-Dirac distribution. The equilibrium state for the electrons is determined by electronegativity equalization with conservation of the total number of electrons. The amount of charge transfer is controlled by re-interpreting the temperature parameter in the Fermi-Dirac distribution function as a coupling strength parameter. We determined this coupling parameter so as to reproduce the charge transfer energy obtained by block localized energy decomposition analysis. We apply the new method to ten systems, and we show that it can yield reasonable approximations to potential energy profiles, to charge transfer stabilization energies, and to the direction and amount of charge transferred. © 2011 American Institute of Physics
Adjustment technique without explicit formation of normal equations /conjugate gradient method/
Saxena, N. K.
1974-01-01
For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
The system of non-linear differential equations was solved numerically using Runge-kutta. Nystroms method. ... artery occlusion. Keywords: Mathematical modeling, Intraretinal oxygen pressure, Retinal capillaries, Oxygen ..... Mass transfer,.
nonlinear kinetics and mechanism of nile blue reaction
African Journals Online (AJOL)
Prof. S.B. Jonnalagadda
under varied oxidative and reducing media is pivotal in their applications as dyes ..... implicate Runge-Kutta method, which solves differential equations .... The authors acknowledge the financial support received from the University of Durban-.
A TWO-MOMENT RADIATION HYDRODYNAMICS MODULE IN ATHENA USING A TIME-EXPLICIT GODUNOV METHOD
Energy Technology Data Exchange (ETDEWEB)
Skinner, M. Aaron; Ostriker, Eve C., E-mail: askinner@astro.umd.edu, E-mail: eco@astro.princeton.edu [Department of Astronomy, University of Maryland, College Park, MD 20742-2421 (United States)
2013-06-01
We describe a module for the Athena code that solves the gray equations of radiation hydrodynamics (RHD), based on the first two moments of the radiative transfer equation. We use a combination of explicit Godunov methods to advance the gas and radiation variables including the non-stiff source terms, and a local implicit method to integrate the stiff source terms. We adopt the M{sub 1} closure relation and include all leading source terms to O({beta}{tau}). We employ the reduced speed of light approximation (RSLA) with subcycling of the radiation variables in order to reduce computational costs. Our code is dimensionally unsplit in one, two, and three space dimensions and is parallelized using MPI. The streaming and diffusion limits are well described by the M{sub 1} closure model, and our implementation shows excellent behavior for a problem with a concentrated radiation source containing both regimes simultaneously. Our operator-split method is ideally suited for problems with a slowly varying radiation field and dynamical gas flows, in which the effect of the RSLA is minimal. We present an analysis of the dispersion relation of RHD linear waves highlighting the conditions of applicability for the RSLA. To demonstrate the accuracy of our method, we utilize a suite of radiation and RHD tests covering a broad range of regimes, including RHD waves, shocks, and equilibria, which show second-order convergence in most cases. As an application, we investigate radiation-driven ejection of a dusty, optically thick shell in the ISM. Finally, we compare the timing of our method with other well-known iterative schemes for the RHD equations. Our code implementation, Hyperion, is suitable for a wide variety of astrophysical applications and will be made freely available on the Web.
Linear-scaling explicitly correlated treatment of solids: Periodic local MP2-F12 method
Energy Technology Data Exchange (ETDEWEB)
Usvyat, Denis, E-mail: denis.usvyat@chemie.uni-regensburg.de [Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg (Germany)
2013-11-21
Theory and implementation of the periodic local MP2-F12 method in the 3*A fixed-amplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atom-centered Gaussian-type orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pair-specific domains on the basis of spatial proximity of respective orbitals. The 4-index two-electron integrals appearing in the formalism are approximated via the direct-space density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fit-domains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the site-group symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2-F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolution-of-the-identity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2-F12 correlation energy with respect to both the size of the PAO-domains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2-F12 calculations, but problematic in the periodic context, are not necessary for LMP2-F12 treatment of crystals.
Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods
International Nuclear Information System (INIS)
Awrejcewicz, J.; Krysko, V.A.; Papkova, I.V.; Krysko, A.V.
2012-01-01
In this work chaotic dynamics of continuous mechanical systems such as flexible plates and shallow shells is studied. Namely, a wide class of the mentioned objects is analyzed including flexible plates and cylinder-like panels of infinite length, rectangular spherical and cylindrical shells, closed cylindrical shells, axially symmetric plates, as well as spherical and conical shells. The considered problems are solved by the Bubnov–Galerkin and higher approximation Ritz methods. Convergence and validation of those methods are studied. The Cauchy problems are solved mainly by the fourth Runge-Kutta method, although all variants of the Runge-Kutta methods are considered. New scenarios of transition from regular to chaotic orbits are detected, analyzed and discussed. First part of the paper is devoted to the validation of results obtained. This is why the same infinite length problem is reduced to that of a finite dimension through the FDM (Finite Difference Method) with the approximation order of O(c 2 ), BGM (Bubnov–Galerkin Method) or RM (Ritz Method) with higher approximations. We pay attention not only to convergence of the mentioned methods regarding the number of partitions of the interval [0, 1] in the FDM or regarding the number of terms in the series applied either in the BGM or RM methods, but we also compare the results obtained via the mentioned different approaches. Furthermore, a so called practical convergence of different Runge-Kutta type methods are tested starting from the second and ending with the eighth order. Second part of the work is devoted to a study of routes to chaos in the so far mentioned mechanical objects. For this purpose the so-called “dynamical charts” are constructed versus control parameters {q 0 , ω p }, where q 0 denotes the loading amplitude, and ω p is the loading frequency. The charts are constructed through analyses of frequency power spectra and the largest Lyapunov exponent (LE). Analysis of the mentioned charts
Creating a spatially-explicit index: a method for assessing the global wildfire-water risk
Robinne, François-Nicolas; Parisien, Marc-André; Flannigan, Mike; Miller, Carol; Bladon, Kevin D.
2017-04-01
The wildfire-water risk (WWR) has been defined as the potential for wildfires to adversely affect water resources that are important for downstream ecosystems and human water needs for adequate water quantity and quality, therefore compromising the security of their water supply. While tools and methods are numerous for watershed-scale risk analysis, the development of a toolbox for the large-scale evaluation of the wildfire risk to water security has only started recently. In order to provide managers and policy-makers with an adequate tool, we implemented a method for the spatial analysis of the global WWR based on the Driving forces-Pressures-States-Impacts-Responses (DPSIR) framework. This framework relies on the cause-and-effect relationships existing between the five categories of the DPSIR chain. As this approach heavily relies on data, we gathered an extensive set of spatial indicators relevant to fire-induced hydrological hazards and water consumption patterns by human and natural communities. When appropriate, we applied a hydrological routing function to our indicators in order to simulate downstream accumulation of potentially harmful material. Each indicator was then assigned a DPSIR category. We collapsed the information in each category using a principal component analysis in order to extract the most relevant pixel-based information provided by each spatial indicator. Finally, we compiled our five categories using an additive indexation process to produce a spatially-explicit index of the WWR. A thorough sensitivity analysis has been performed in order to understand the relationship between the final risk values and the spatial pattern of each category used during the indexation. For comparison purposes, we aggregated index scores by global hydrological regions, or hydrobelts, to get a sense of regional DPSIR specificities. This rather simple method does not necessitate the use of complex physical models and provides a scalable and efficient tool
International Nuclear Information System (INIS)
Menouillard, T.
2007-09-01
Computerized simulation is nowadays an integrating part of design and validation processes of mechanical structures. Simulation tools are more and more performing allowing a very acute description of the phenomena. Moreover, these tools are not limited to linear mechanics but are developed to describe more difficult behaviours as for instance structures damage which interests the safety domain. A dynamic or static load can thus lead to a damage, a crack and then a rupture of the structure. The fast dynamics allows to simulate 'fast' phenomena such as explosions, shocks and impacts on structure. The application domain is various. It concerns for instance the study of the lifetime and the accidents scenario of the nuclear reactor vessel. It is then very interesting, for fast dynamics codes, to be able to anticipate in a robust and stable way such phenomena: the assessment of damage in the structure and the simulation of crack propagation form an essential stake. The extended finite element method has the advantage to break away from mesh generation and from fields projection during the crack propagation. Effectively, crack is described kinematically by an appropriate strategy of enrichment of supplementary freedom degrees. Difficulties connecting the spatial discretization of this method with the temporal discretization of an explicit calculation scheme has then been revealed; these difficulties are the diagonal writing of the mass matrix and the associated stability time step. Here are presented two methods of mass matrix diagonalization based on the kinetic energy conservation, and studies of critical time steps for various enriched finite elements. The interest revealed here is that the time step is not more penalizing than those of the standard finite elements problem. Comparisons with numerical simulations on another code allow to validate the theoretical works. A crack propagation test in mixed mode has been exploited in order to verify the simulation
Keslerová, Radka; Trdlička, David
2015-09-01
This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.
Modeling the Bergeron-Findeisen Process Using PDF Methods With an Explicit Representation of Mixing
Jeffery, C.; Reisner, J.
2005-12-01
Currently, the accurate prediction of cloud droplet and ice crystal number concentration in cloud resolving, numerical weather prediction and climate models is a formidable challenge. The Bergeron-Findeisen process in which ice crystals grow by vapor deposition at the expense of super-cooled droplets is expected to be inhomogeneous in nature--some droplets will evaporate completely in centimeter-scale filaments of sub-saturated air during turbulent mixing while others remain unchanged [Baker et al., QJRMS, 1980]--and is unresolved at even cloud-resolving scales. Despite the large body of observational evidence in support of the inhomogeneous mixing process affecting cloud droplet number [most recently, Brenguier et al., JAS, 2000], it is poorly understood and has yet to be parameterized and incorporated into a numerical model. In this talk, we investigate the Bergeron-Findeisen process using a new approach based on simulations of the probability density function (PDF) of relative humidity during turbulent mixing. PDF methods offer a key advantage over Eulerian (spatial) models of cloud mixing and evaporation: the low probability (cm-scale) filaments of entrained air are explicitly resolved (in probability space) during the mixing event even though their spatial shape, size and location remain unknown. Our PDF approach reveals the following features of the inhomogeneous mixing process during the isobaric turbulent mixing of two parcels containing super-cooled water and ice, respectively: (1) The scavenging of super-cooled droplets is inhomogeneous in nature; some droplets evaporate completely at early times while others remain unchanged. (2) The degree of total droplet evaporation during the initial mixing period depends linearly on the mixing fractions of the two parcels and logarithmically on Damköhler number (Da)---the ratio of turbulent to evaporative time-scales. (3) Our simulations predict that the PDF of Lagrangian (time-integrated) subsaturation (S) goes as
Pavošević, Fabijan; Neese, Frank; Valeev, Edward F.
2014-08-01
We present a production implementation of reduced-scaling explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) method based on pair-natural orbitals (PNOs). A key feature is the reformulation of the explicitly correlated terms using geminal-spanning orbitals that greatly reduce the truncation errors of the F12 contribution. For the standard S66 benchmark of weak intermolecular interactions, the cc-pVDZ-F12 PNO CCSD F12 interaction energies reproduce the complete basis set CCSD limit with mean absolute error cost compared to the conventional CCSD F12.
Czech Academy of Sciences Publication Activity Database
Demel, Ondřej; Kedžuch, S.; Noga, J.; Pittner, Jiří
2013-01-01
Roč. 111, 16-17 (2013), s. 2477-2488 ISSN 0026-8976 R&D Projects: GA ČR GPP208/10/P041; GA ČR GAP208/11/2222 Institutional support: RVO:61388955 Keywords : explicitly correlated * coupled cluster * multireference Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.642, year: 2013
International Nuclear Information System (INIS)
Kamitani, A.; Takayama, T.; Itoh, T.; Ikuno, S.
2011-01-01
A fast method is proposed for calculating the shielding current density in an HTS. The J-E constitutive relation is modified so as not to change the solution. A numerical code is developed on the basis of the proposed method. The permanent magnet method is successfully simulated by means of the code. A fast method has been proposed for calculating the shielding current density in a high-temperature superconducting thin film. An initial-boundary-value problem of the shielding current density cannot be always solved by means of the Runge-Kutta method even when an adaptive step-size control algorithm is incorporated to the method. In order to suppress an overflow in the algorithm, the J-E constitutive relation is modified so that its solution may satisfy the original constitutive relation. A numerical code for analyzing the shielding current density has been developed on the basis of this method and, as an application of the code, the permanent magnet method for measuring the critical current density has been investigated numerically.
Stone, Christopher P.; Alferman, Andrew T.; Niemeyer, Kyle E.
2018-05-01
Accurate and efficient methods for solving stiff ordinary differential equations (ODEs) are a critical component of turbulent combustion simulations with finite-rate chemistry. The ODEs governing the chemical kinetics at each mesh point are decoupled by operator-splitting allowing each to be solved concurrently. An efficient ODE solver must then take into account the available thread and instruction-level parallelism of the underlying hardware, especially on many-core coprocessors, as well as the numerical efficiency. A stiff Rosenbrock and a nonstiff Runge-Kutta ODE solver are both implemented using the single instruction, multiple thread (SIMT) and single instruction, multiple data (SIMD) paradigms within OpenCL. Both methods solve multiple ODEs concurrently within the same instruction stream. The performance of these parallel implementations was measured on three chemical kinetic models of increasing size across several multicore and many-core platforms. Two separate benchmarks were conducted to clearly determine any performance advantage offered by either method. The first benchmark measured the run-time of evaluating the right-hand-side source terms in parallel and the second benchmark integrated a series of constant-pressure, homogeneous reactors using the Rosenbrock and Runge-Kutta solvers. The right-hand-side evaluations with SIMD parallelism on the host multicore Xeon CPU and many-core Xeon Phi co-processor performed approximately three times faster than the baseline multithreaded C++ code. The SIMT parallel model on the host and Phi was 13%-35% slower than the baseline while the SIMT model on the NVIDIA Kepler GPU provided approximately the same performance as the SIMD model on the Phi. The runtimes for both ODE solvers decreased significantly with the SIMD implementations on the host CPU (2.5-2.7 ×) and Xeon Phi coprocessor (4.7-4.9 ×) compared to the baseline parallel code. The SIMT implementations on the GPU ran 1.5-1.6 times faster than the baseline
Comparative analysis of solution methods of the punctual kinetic equations
International Nuclear Information System (INIS)
Hernandez S, A.
2003-01-01
The following one written it presents a comparative analysis among different analytical solutions for the punctual kinetics equation, which present two variables of interest: a) the temporary behavior of the neutronic population, and b) The temporary behavior of the different groups of precursors of delayed neutrons. The first solution is based on a method that solves the transfer function of the differential equation for the neutronic population, in which intends to obtain the different poles that give the stability of this transfer function. In this section it is demonstrated that the temporary variation of the reactivity of the system can be managed as it is required, since the integration time for this method doesn't affect the result. However, the second solution is based on an iterative method like that of Runge-Kutta or the Euler method where the algorithm was only used to solve first order differential equations giving this way solution to each differential equation that conforms the equations of punctual kinetics. In this section it is demonstrated that only it can obtain a correct temporary behavior of the neutronic population when it is integrated on an interval of very short time, forcing to the temporary variation of the reactivity to change very quick way without one has some control about the time. In both methods the same change is used so much in the reactivity of the system like in the integration times, giving validity to the results graph the one the temporary behavior of the neutronic population vs. time. (Author)
The differential method for grating efficiencies implemented in mathematica
Energy Technology Data Exchange (ETDEWEB)
Valdes, V.; McKinney, W. [Lawrence Berkeley Lab., CA (United States); Palmer, C. [Milton Co., Rochester, NY (United States). Roy Analytical Products Div.
1993-08-01
In order to facilitate the accurate calculation of diffraction grating efficiencies in the soft x-ray region, we have implemented the differential method of Neviere and Vincent in Mathematica [1]. This simplifies the programming to maximize the transparency of the theory for the user. We alleviate some of the overhead burden of the Mathematica program by coding the time-consuming numerical integration in C subprograms. We recall the differential method directly from Maxwell`s equations. The pseudo-periodicity of the grating profile and the electromagnetic fields allows us to use their Fourier series expansions to formulate an infinite set of coupled differential equations. A finite subset of the equations are then numerically integrated using the Numerov method for the transverse electric (TE) case and a fourth-order Runge-Kutta algorithm for the transverse magnetic (TM) case. We have tested our program by comparisons with the scalar theory and with published theoretical results for the blazed, sinusoidal and square wave profiles. The Reciprocity Theorem has also been used as a means to verify the method. We have found it to be verified for several cases to within the computational accuracy of the method.
Directory of Open Access Journals (Sweden)
Rek Václav
2016-11-01
Full Text Available In this paper, the form of modifications of the existing sequential code written in C or C++ programming language for the calculation of various kind of structures using the explicit form of the Finite Element Method (Dynamic Relaxation Method, Explicit Dynamics in the NEXX system is introduced. The NEXX system is the core of engineering software NEXIS, Scia Engineer, RFEM and RENEX. It has the possibilities of multithreaded running, which can now be supported at the level of native C++ programming language using standard libraries. Thanks to the high degree of abstraction that a contemporary C++ programming language provides, a respective library created in this way can be very generalized for other purposes of usage of parallelism in computational mechanics.
Directory of Open Access Journals (Sweden)
Huiqing Fang
2016-01-01
Full Text Available Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.
International Nuclear Information System (INIS)
Ngoc Tam, Nguyen; Nakamura, Yasunori; Terao, Toshihiro; Kuramae, Hiroyuki; Nakamachi, Eiji; Sakamoto, Hidetoshi; Morimoto, Hideo
2007-01-01
Recently, the asymmetric rolling (ASR) has been applied to the material processing of aluminum alloy sheet to control micro-crystal structure and texture in order to improve the mechanical properties. Previously, several studies aimed at high formability sheet generation have been carried out experimentally, but finite element simulations to predict the deformation induced texture evolution of the asymmetrically rolled sheet metals have not been investigated rigorously. In this study, crystallographic homogenized finite element (FE) codes are developed and applied to analyze the asymmetrical rolling processes. The textures of sheet metals were measured by electron back scattering diffraction (EBSD), and compared with FE simulations. The results from the dynamic explicit type Crystallographic homogenization FEM code shows that this type of simulation is a comprehensive tool to predict the plastic induced texture evolution
Directory of Open Access Journals (Sweden)
Rachel R. Sleeter
2015-06-01
Full Text Available Spatially-explicit state-and-transition simulation models of land use and land cover (LULC increase our ability to assess regional landscape characteristics and associated carbon dynamics across multiple scenarios. By characterizing appropriate spatial attributes such as forest age and land-use distribution, a state-and-transition model can more effectively simulate the pattern and spread of LULC changes. This manuscript describes the methods and input parameters of the Land Use and Carbon Scenario Simulator (LUCAS, a customized state-and-transition simulation model utilized to assess the relative impacts of LULC on carbon stocks for the conterminous U.S. The methods and input parameters are spatially explicit and describe initial conditions (strata, state classes and forest age, spatial multipliers, and carbon stock density. Initial conditions were derived from harmonization of multi-temporal data characterizing changes in land use as well as land cover. Harmonization combines numerous national-level datasets through a cell-based data fusion process to generate maps of primary LULC categories. Forest age was parameterized using data from the North American Carbon Program and spatially-explicit maps showing the locations of past disturbances (i.e. wildfire and harvest. Spatial multipliers were developed to spatially constrain the location of future LULC transitions. Based on distance-decay theory, maps were generated to guide the placement of changes related to forest harvest, agricultural intensification/extensification, and urbanization. We analyze the spatially-explicit input parameters with a sensitivity analysis, by showing how LUCAS responds to variations in the model input. This manuscript uses Mediterranean California as a regional subset to highlight local to regional aspects of land change, which demonstrates the utility of LUCAS at many scales and applications.
Sleeter, Rachel; Acevedo, William; Soulard, Christopher E.; Sleeter, Benjamin M.
2015-01-01
Spatially-explicit state-and-transition simulation models of land use and land cover (LULC) increase our ability to assess regional landscape characteristics and associated carbon dynamics across multiple scenarios. By characterizing appropriate spatial attributes such as forest age and land-use distribution, a state-and-transition model can more effectively simulate the pattern and spread of LULC changes. This manuscript describes the methods and input parameters of the Land Use and Carbon Scenario Simulator (LUCAS), a customized state-and-transition simulation model utilized to assess the relative impacts of LULC on carbon stocks for the conterminous U.S. The methods and input parameters are spatially explicit and describe initial conditions (strata, state classes and forest age), spatial multipliers, and carbon stock density. Initial conditions were derived from harmonization of multi-temporal data characterizing changes in land use as well as land cover. Harmonization combines numerous national-level datasets through a cell-based data fusion process to generate maps of primary LULC categories. Forest age was parameterized using data from the North American Carbon Program and spatially-explicit maps showing the locations of past disturbances (i.e. wildfire and harvest). Spatial multipliers were developed to spatially constrain the location of future LULC transitions. Based on distance-decay theory, maps were generated to guide the placement of changes related to forest harvest, agricultural intensification/extensification, and urbanization. We analyze the spatially-explicit input parameters with a sensitivity analysis, by showing how LUCAS responds to variations in the model input. This manuscript uses Mediterranean California as a regional subset to highlight local to regional aspects of land change, which demonstrates the utility of LUCAS at many scales and applications.
Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars
2018-02-01
The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration
Flux weighted method for solution of stiff neutron dynamic equations and its application
International Nuclear Information System (INIS)
Li Huiyun; Jiao Huixian
1987-12-01
To analyze reactivity event for nuclear power plants, it is necessary to solve the neutron dynamic equations, which is a group of typical stiff constant differential equations. Very small time steps could only be adopted when the group of equations is solved by common methods. However, a large time steps might be selected if the Flux Weighted Medthod introduced in this paper is used. Generally, weighted factor θ i1 is set as a constant. Naturally, this treatment method can decrease the accuracy of calculation for the increase of the steadiness of solving the equations. An accurate theoretical formula of 4 x 4 matrix of θ i1 is rigorously derived so that the accuracy of calculation is ensured, as well as the steadiness of solved equations is increased. This method have the advantage over classical Runge-kutta Method and other methods. The time steps could be increased by a factor of 1 ∼ 3 orders of magnitude so as to save a lot of computating time. The programe solving neutron dynamic equation, which is prepared by using Flux Weighted Method, could be sued for real time analog of training simulator, as well as for analysis and computation of reactivity event (including rod jumping out event)
International Nuclear Information System (INIS)
Yamamoto, Akio; Tatsumi, Masahiro; Sugimura, Naoki
2007-01-01
The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide burnup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO 2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s ( 106 Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time. (author)
The effects of emotion regulation on explicit memory depend on strategy and testing method.
Knight, Marisa; Ponzio, Allison
2013-12-01
Although previous work has shown that emotion regulation strategies can influence memory, the mechanisms through which different strategies produce different memory outcomes are not well understood. We examined how two cognitive reappraisal strategies with similar elaboration demands but diverging effects on visual attention and emotional arousal influenced explicit memory for emotional stimuli and for the strategies used to evaluate the stimuli. At encoding, participants used reappraisal to increase and decrease the personal relevance of neutral and emotional pictures. In two experiments, recall accuracy was highest for emotional pictures featured on increase trials, intermediate for emotional pictures featured on look (respond naturally) trials, and lowest for emotional pictures featured on decrease trials. This recall pattern emerged after a short delay (15 min) and persisted over a longer delay (48 hr). Memory accuracy for the strategies used to evaluate the pictures showed a different pattern: Strategy memory was better for emotional pictures featured on decrease and increase trials than for pictures featured on look trials. Our findings show that the effects of emotion regulation on memory depend both on the particular strategy engaged and the particular aspect of memory being tested.
Development of efficient time-evolution method based on three-term recurrence relation
International Nuclear Information System (INIS)
Akama, Tomoko; Kobayashi, Osamu; Nanbu, Shinkoh
2015-01-01
The advantage of the real-time (RT) propagation method is a direct solution of the time-dependent Schrödinger equation which describes frequency properties as well as all dynamics of a molecular system composed of electrons and nuclei in quantum physics and chemistry. Its applications have been limited by computational feasibility, as the evaluation of the time-evolution operator is computationally demanding. In this article, a new efficient time-evolution method based on the three-term recurrence relation (3TRR) was proposed to reduce the time-consuming numerical procedure. The basic formula of this approach was derived by introducing a transformation of the operator using the arcsine function. Since this operator transformation causes transformation of time, we derived the relation between original and transformed time. The formula was adapted to assess the performance of the RT time-dependent Hartree-Fock (RT-TDHF) method and the time-dependent density functional theory. Compared to the commonly used fourth-order Runge-Kutta method, our new approach decreased computational time of the RT-TDHF calculation by about factor of four, showing the 3TRR formula to be an efficient time-evolution method for reducing computational cost
Directory of Open Access Journals (Sweden)
Leo Gallus Bont
2018-03-01
Full Text Available Despite relatively high road density in the forests of Switzerland, a large percentage of that road network does not fulfill best practice requirements. Before upgrading or rebuilding the road network, harvesting planners must first determine which areas have insufficient access. Traditional assessment methods tend to only report specific values such as road density. However, those values do not identify the exact parcels or areas that are inaccessible. Here, we present a model that assesses the economic suitability of each timbered parcel for wood-harvesting operations, including tree-felling and processing, and off- and on-road transport (hauling, based on the existing road network. The entire wood supply chain from forest (standing trees to a virtual pile at the border of the planning unit was captured. This method was particularly designed for steep terrain and was tested in the Canton of Grisons in Switzerland. Compared with classical approaches, such as the road density concept, which only deliver average values, this new method enables planners to assess the development of a road network in a spatially explicit manner and to easily identify the reason and the location of shortcomings in the road network. Moreover, while other related spatially explicit approaches focus only on harvesting operations, the assessment method proposed here also includes limitations (road standards of the road network.
Energy Technology Data Exchange (ETDEWEB)
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size
Hadjimichael, Yiannis; Ketcheson, David I.; Loczi, Lajos; Né meth, Adriá n
2016-01-01
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order
Non-linear heat transfer computer code by finite element method
International Nuclear Information System (INIS)
Nagato, Kotaro; Takikawa, Noboru
1977-01-01
The computer code THETA-2D for the calculation of temperature distribution by the two-dimensional finite element method was made for the analysis of heat transfer in a high temperature structure. Numerical experiment was performed for the numerical integration of the differential equation of heat conduction. The Runge-Kutta method of the numerical experiment produced an unstable solution. A stable solution was obtained by the β method with the β value of 0.35. In high temperature structures, the radiative heat transfer can not be neglected. To introduce a term of the radiative heat transfer, a functional neglecting the radiative heat transfer was derived at first. Then, the radiative term was added after the discretion by variation method. Five model calculations were carried out by the computer code. Calculation of steady heat conduction was performed. When estimated initial temperature is 1,000 degree C, reasonable heat blance was obtained. In case of steady-unsteady temperature calculation, the time integral by THETA-2D turned out to be under-estimation for enthalpy change. With a one-dimensional model, the temperature distribution in a structure, in which heat conductivity is dependent on temperature, was calculated. Calculation with a model which has a void inside was performed. Finally, model calculation for a complex system was carried out. (Kato, T.)
Energy Technology Data Exchange (ETDEWEB)
Mezzacappa, Anthony [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Endeve, Eirik [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Hauck, Cory D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Xing, Yulong [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2015-02-01
We extend the positivity-preserving method of Zhang & Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stabilitypreserving, Runge-Kutta (SSP-RK) time integration. Special care in taken to ensure that the method preserves strict bounds for the phase space distribution function f; i.e., f ϵ [0, 1]. The combination of suitable CFL conditions and the use of the high-order limiter proposed in [49] is su cient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergencefree property of the phase space ow. Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates). Results from numerical experiments - including one example in spherical symmetry adopting the Schwarzschild metric - demonstrate that the method achieves high-order accuracy and that the distribution function satisfies the maximum principle.
Computation of Aerodynamic Noise Radiated from Ducted Tail Rotor Using Boundary Element Method
Directory of Open Access Journals (Sweden)
Yunpeng Ma
2017-01-01
Full Text Available A detailed aerodynamic performance of a ducted tail rotor in hover has been numerically studied using CFD technique. The general governing equations of turbulent flow around ducted tail rotor are given and directly solved by using finite volume discretization and Runge-Kutta time integration. The calculations of the lift characteristics of the ducted tail rotor can be obtained. In order to predict the aerodynamic noise, a hybrid method combining computational aeroacoustic with boundary element method (BEM has been proposed. The computational steps include the following: firstly, the unsteady flow around rotor is calculated using the CFD method to get the noise source information; secondly, the radiate sound pressure is calculated using the acoustic analogy Curle equation in the frequency domain; lastly, the scattering effect of the duct wall on the propagation of the sound wave is presented using an acoustic thin-body BEM. The aerodynamic results and the calculated sound pressure levels are compared with the known technique for validation. The sound pressure directivity and scattering effect are shown to demonstrate the validity and applicability of the method.
Ying, Wenjun; Henriquez, Craig S
2007-04-01
A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.
Yulia, M.; Suhandy, D.
2018-03-01
NIR spectra obtained from spectral data acquisition system contains both chemical information of samples as well as physical information of the samples, such as particle size and bulk density. Several methods have been established for developing calibration models that can compensate for sample physical information variations. One common approach is to include physical information variation in the calibration model both explicitly and implicitly. The objective of this study was to evaluate the feasibility of using explicit method to compensate the influence of different particle size of coffee powder in NIR calibration model performance. A number of 220 coffee powder samples with two different types of coffee (civet and non-civet) and two different particle sizes (212 and 500 µm) were prepared. Spectral data was acquired using NIR spectrometer equipped with an integrating sphere for diffuse reflectance measurement. A discrimination method based on PLS-DA was conducted and the influence of different particle size on the performance of PLS-DA was investigated. In explicit method, we add directly the particle size as predicted variable results in an X block containing only the NIR spectra and a Y block containing the particle size and type of coffee. The explicit inclusion of the particle size into the calibration model is expected to improve the accuracy of type of coffee determination. The result shows that using explicit method the quality of the developed calibration model for type of coffee determination is a little bit superior with coefficient of determination (R2) = 0.99 and root mean square error of cross-validation (RMSECV) = 0.041. The performance of the PLS2 calibration model for type of coffee determination with particle size compensation was quite good and able to predict the type of coffee in two different particle sizes with relatively high R2 pred values. The prediction also resulted in low bias and RMSEP values.
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2012-01-01
Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator. This multilevel analysis is used to optimize the coefficients in the semi-implicit
Métodos Numéricos tipo Runge-Kutta-Nyström para la integración eficiente de problemas oscilatorios
García Garrosa, Amelia
2001-01-01
En la segunda mitad del siglo pasado se han realizado numerosos trabajos sobre métodos numéricos para la integración de ecuaciones diferenciales ordinarias. En la actualidad, numerosos paquetes de software contienen rutinas de propósito general para la resolución de sistemas de ecuaciones diferenciales de primer orden. Dado que una ecuación diferencial de cualquier orden puede ser escrita como un sistema de ecuaciones de primer orden, dichas rutinas pueden utilizarse para resolver ecuaciones ...
DEFF Research Database (Denmark)
Löwgren, Jonas; Eriksen, Mette Agger; Linde, Per
2006-01-01
We report an ongoing study of palpable computing to support surgical rehabilitation, in the general field of interaction design for ubiquitous computing. Through explorative design, fieldwork and participatory design techniques, we explore the design principle of explicit interaction as an interp...
Khanday, M A; Hussain, Fida
2015-02-01
During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25 °C, 20 °C, 15 °C, 5 °C, -5 °C and -10 °C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure. Copyright © 2014 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.
2014-01-01
Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s 2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful
Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method
International Nuclear Information System (INIS)
Souza de Paula, Aline; Savi, Marcelo Amorim
2009-01-01
Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge-Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.
Estimation of coefficient of rolling friction by the evolvent pendulum method
Alaci, S.; Ciornei, F. C.; Ciogole, A.; Ciornei, M. C.
2017-05-01
The paper presents a method for finding the coefficient of rolling friction using an evolvent pendulum. The pendulum consists in a fixed cylindrical body and a mobile body presenting a plane surface in contact with a cylindrical surface. The mobile body is placed over the fixed one in an equilibrium state; after applying a small impulse, the mobile body oscillates. The motion of the body is video recorded and afterwards the movie is analyzed by frames and the decrease with time of angular amplitude of the pendulum is found. The equation of motion is established for oscillations of the mobile body. The equation of motion, differential nonlinear, is integrated by Runge-Kutta method. Imposing the same damping both to model’s solution and to theoretical model, the value of coefficient of rolling friction is obtained. The last part of the paper presents results for actual pairs of materials. The main advantage of the method is the fact that the dimensions of contact regions are small, of order a few millimeters, and thus is substantially reduced the possibility of variation of mechanical characteristic for the two surfaces.
A first course in ordinary differential equations analytical and numerical methods
Hermann, Martin
2014-01-01
This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed t...
Optimization of an auto-thermal ammonia synthesis reactor using cyclic coordinate method
A-N Nguyen, T.; Nguyen, T.-A.; Vu, T.-D.; Nguyen, K.-T.; K-T Dao, T.; P-H Huynh, K.
2017-06-01
The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration. In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found. However, they just focus on the optimization of the reactor length while keeping the others parameters constant. In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone, the initial nitrogen proportion. The optimal problem requires the maximization of an objective function which is multivariable function and subject to a number of equality constraints involving the solution of coupled differential equations and also inequality constraint. The cyclic coordinate search was applied to solve the multivariable-optimization problem. In each coordinate, the golden section method was applied to find the maximum value. The inequality constraints were treated using penalty method. The coupled differential equations system was solved using Runge-Kutta 4th order method. The results obtained from this study are also compared to the results from the literature.
A Three Step Explicit Method for Direct Solution of Third Order ...
African Journals Online (AJOL)
This study produces a three step discrete Linear Multistep Method for Direct solution of third order initial value problems of ordinary differential equations of the form y'''= f(x,y,y',y''). Taylor series expansion technique was adopted in the development of the method. The differential system from the basis polynomial function to ...
Directory of Open Access Journals (Sweden)
Jeong-Hoon Song
2013-01-01
Full Text Available A simplified implementation of the conventional extended finite element method (XFEM for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.
Explicit evaluation of discontinuities in 2-D unsteady flows solved by the method of characteristics
Osnaghi, C.
When shock waves appear in the numerical solution of flows, a choice is necessary between shock capturing techniques, possible when equations are written in conservative form, and shock fitting techniques. If the second one is preferred, e.g. in order to obtain better definition and more physical description of the shock evolution in time, the method of characteristics is advantageous in the vicinity of the shock and it seems natural to use this method everywhere. This choice requires to improve the efficiency of the numerical scheme in order to produce competitive codes, preserving accuracy and flexibility, which are intrinsic features of the method: this is the goal of the present work.
Application of State Quantization-Based Methods in HEP Particle Transport Simulation
Santi, Lucio; Ponieman, Nicolás; Jun, Soon Yung; Genser, Krzysztof; Elvira, Daniel; Castro, Rodrigo
2017-10-01
Simulation of particle-matter interactions in complex geometries is one of the main tasks in high energy physics (HEP) research. An essential aspect of it is an accurate and efficient particle transportation in a non-uniform magnetic field, which includes the handling of volume crossings within a predefined 3D geometry. Quantized State Systems (QSS) is a family of numerical methods that provides attractive features for particle transportation processes, such as dense output (sequences of polynomial segments changing only according to accuracy-driven discrete events) and lightweight detection and handling of volume crossings (based on simple root-finding of polynomial functions). In this work we present a proof-of-concept performance comparison between a QSS-based standalone numerical solver and an application based on the Geant4 simulation toolkit, with its default Runge-Kutta based adaptive step method. In a case study with a charged particle circulating in a vacuum (with interactions with matter turned off), in a uniform magnetic field, and crossing up to 200 volume boundaries twice per turn, simulation results showed speedups of up to 6 times in favor of QSS while it being 10 times slower in the case with zero volume boundaries.
Voltage effect in PTCR ceramics: Calculation by the method of tilted energy band
International Nuclear Information System (INIS)
Fang Chao; Zhou Dongxiang; Gong Shuping
2010-01-01
A numerical model for the calculation of the electrical characteristics of donor-doped BaTiO 3 semiconducting ceramics is suggested. This paper established a differential equation about electron level on the base of Poisson equation, and solved the equation with Runge-Kutta method. Under extra electric field, electrical characteristics have been calculated by the method of tilted energy band. We have quantitatively computed the positive temperature coefficient of resistivity (PTCR) behavior of donor-doped BaTiO 3 semiconducting ceramics and its voltage effect, and further obtained non-linear current-voltage characteristics with different grain sizes at different temperature. The results pointed out that the resistance jumping is reduced with increasing electric field applied; current and voltage relation follows Ohm's law below Curie temperature, and exhibits strong non-linear above Curie temperature; the non-linear coefficient shows a maximum value at temperature the resistivity reaches maximum and with grain size closed to depletion region width. The results are compared with experimental data.
Overview on methods for formulating explicit damping matrices for non-classically damped structures
International Nuclear Information System (INIS)
Xu, J.
1998-04-01
In computing the dynamic response of a connected system with multiple components having dissimilar damping characteristics, which is often referred to as nonclassically damped system such as nuclear power plant piping systems supported by stiff structures, one needs to define the system-level damping based upon the damping information of components. This is frequently done in practice using approximate methods expressed as composite modal damping with weighting functions. However, when the difference in damping among components is substantial, the composite modal damping may become inappropriate in the characterization of the damping behavior of such systems. In recent years, several new methods have emerged with the expectation that they could produce more exact system-level damping for a group of nonclassically damped structures which are comprised of components that possess classical modal damping. In this paper, an overview is presented to examine these methods in the light of their theoretical basis, the technical merits, and practical applications. To this end, a synthesis method is described, which was shown to reduce to the other methods in the literature
Asgharzadeh, Hafez; Borazjani, Iman
2014-11-01
Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.
On the Linear Stability of the Fifth-Order WENO Discretization
Motamed, Mohammad
2010-10-03
We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.
A Parallel Compact Multi-Dimensional Numerical Algorithm with Aeroacoustics Applications
Povitsky, Alex; Morris, Philip J.
1999-01-01
In this study we propose a novel method to parallelize high-order compact numerical algorithms for the solution of three-dimensional PDEs (Partial Differential Equations) in a space-time domain. For this numerical integration most of the computer time is spent in computation of spatial derivatives at each stage of the Runge-Kutta temporal update. The most efficient direct method to compute spatial derivatives on a serial computer is a version of Gaussian elimination for narrow linear banded systems known as the Thomas algorithm. In a straightforward pipelined implementation of the Thomas algorithm processors are idle due to the forward and backward recurrences of the Thomas algorithm. To utilize processors during this time, we propose to use them for either non-local data independent computations, solving lines in the next spatial direction, or local data-dependent computations by the Runge-Kutta method. To achieve this goal, control of processor communication and computations by a static schedule is adopted. Thus, our parallel code is driven by a communication and computation schedule instead of the usual "creative, programming" approach. The obtained parallelization speed-up of the novel algorithm is about twice as much as that for the standard pipelined algorithm and close to that for the explicit DRP algorithm.
Methods for compressible fluid simulation on GPUs using high-order finite differences
Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer
2017-08-01
We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.
Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation
Zhao, Zhonglong; Han, Bo
2018-04-01
In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.
Using case method to explicitly teach formative assessment in preservice teacher science education
Bentz, Amy Elizabeth
The process of formative assessment improves student understanding; however, the topic of formative assessment in preservice education has been severely neglected. Since a major goal of teacher education is to create reflective teaching professionals, preservice teachers should be provided an opportunity to critically reflect on the use of formative assessment in the classroom. Case method is an instructional methodology that allows learners to engage in and reflect on real-world situations. Case based pedagogy can play an important role in enhancing preservice teachers' ability to reflect on teaching and learning by encouraging alternative ways of thinking about assessment. Although the literature on formative assessment and case methodology are extensive, using case method to explore the formative assessment process is, at best, sparse. The purpose of this study is to answer the following research questions: To what extent does the implementation of formative assessment cases in methods instruction influence preservice elementary science teachers' knowledge of formative assessment? What descriptive characteristics change between the preservice teachers' pre-case and post-case written reflection that would demonstrate learning had occurred? To investigate these questions, preservice teachers in an elementary methods course were asked to reflect on and discuss five cases. Pre/post-case data was analyzed. Results indicate that the preservice teachers modified their ideas to reflect the themes that were represented within the cases and modified their reflections to include specific ideas or examples taken directly from the case discussions. Comparing pre- and post-case reflections, the data supports a noted change in how the preservice teachers interpreted the case content. The preservice teachers began to evaluate the case content, question the lack of formative assessment concepts and strategies within the case, and apply formative assessment concepts and
Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul
2018-03-01
In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.
Poyatos, Rafael; Sus, Oliver; Badiella, Llorenç; Mencuccini, Maurizio; Martínez-Vilalta, Jordi
2018-05-01
The ubiquity of missing data in plant trait databases may hinder trait-based analyses of ecological patterns and processes. Spatially explicit datasets with information on intraspecific trait variability are rare but offer great promise in improving our understanding of functional biogeography. At the same time, they offer specific challenges in terms of data imputation. Here we compare statistical imputation approaches, using varying levels of environmental information, for five plant traits (leaf biomass to sapwood area ratio, leaf nitrogen content, maximum tree height, leaf mass per area and wood density) in a spatially explicit plant trait dataset of temperate and Mediterranean tree species (Ecological and Forest Inventory of Catalonia, IEFC, dataset for Catalonia, north-east Iberian Peninsula, 31 900 km2). We simulated gaps at different missingness levels (10-80 %) in a complete trait matrix, and we used overall trait means, species means, k nearest neighbours (kNN), ordinary and regression kriging, and multivariate imputation using chained equations (MICE) to impute missing trait values. We assessed these methods in terms of their accuracy and of their ability to preserve trait distributions, multi-trait correlation structure and bivariate trait relationships. The relatively good performance of mean and species mean imputations in terms of accuracy masked a poor representation of trait distributions and multivariate trait structure. Species identity improved MICE imputations for all traits, whereas forest structure and topography improved imputations for some traits. No method performed best consistently for the five studied traits, but, considering all traits and performance metrics, MICE informed by relevant ecological variables gave the best results. However, at higher missingness (> 30 %), species mean imputations and regression kriging tended to outperform MICE for some traits. MICE informed by relevant ecological variables allowed us to fill the gaps in
Directory of Open Access Journals (Sweden)
R. Poyatos
2018-05-01
Full Text Available The ubiquity of missing data in plant trait databases may hinder trait-based analyses of ecological patterns and processes. Spatially explicit datasets with information on intraspecific trait variability are rare but offer great promise in improving our understanding of functional biogeography. At the same time, they offer specific challenges in terms of data imputation. Here we compare statistical imputation approaches, using varying levels of environmental information, for five plant traits (leaf biomass to sapwood area ratio, leaf nitrogen content, maximum tree height, leaf mass per area and wood density in a spatially explicit plant trait dataset of temperate and Mediterranean tree species (Ecological and Forest Inventory of Catalonia, IEFC, dataset for Catalonia, north-east Iberian Peninsula, 31 900 km2. We simulated gaps at different missingness levels (10–80 % in a complete trait matrix, and we used overall trait means, species means, k nearest neighbours (kNN, ordinary and regression kriging, and multivariate imputation using chained equations (MICE to impute missing trait values. We assessed these methods in terms of their accuracy and of their ability to preserve trait distributions, multi-trait correlation structure and bivariate trait relationships. The relatively good performance of mean and species mean imputations in terms of accuracy masked a poor representation of trait distributions and multivariate trait structure. Species identity improved MICE imputations for all traits, whereas forest structure and topography improved imputations for some traits. No method performed best consistently for the five studied traits, but, considering all traits and performance metrics, MICE informed by relevant ecological variables gave the best results. However, at higher missingness (> 30 %, species mean imputations and regression kriging tended to outperform MICE for some traits. MICE informed by relevant ecological variables
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1992-12-01
Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science
Ketcheson, David I.; Loczi, Lajos; Parsani, Matteo
2014-01-01
of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods
A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2013-01-01
Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.
Method for Determining the Time Parameter
Directory of Open Access Journals (Sweden)
K. P. Baslyk
2014-01-01
values of multipliers and parameter of penalty. The solving problem of the optimization without constraints is one step of the optimization problem with constraints.The proposed method was realized as a computational Pascal-language program. There is the multiple call of Runge-Kutta method procedure for integration of motion equations. To reduce operation-use time, normalization of motion equations is used, and the 4-th order RungeKutta method time step accuracy control is also applied.The program test results were compared with the solution, which was obtained using the existing software for the one stage missile design.The general results obtained in this paper are following: numerical determination method of the attack angle time parameter and maximum allowed value of the attack angle amplitude as functions of the projected and ballistic parameters; software implementation of this method. Deviation of angle trajectory value at the end of active trajectory leg as a function of the error of the time parameter was obtained as well. This paper can be used in the courses of learning such as “Introduction to rocketry” and “Launch vehicle design”.
Energy Technology Data Exchange (ETDEWEB)
Menouillard, T
2007-09-15
Computerized simulation is nowadays an integrating part of design and validation processes of mechanical structures. Simulation tools are more and more performing allowing a very acute description of the phenomena. Moreover, these tools are not limited to linear mechanics but are developed to describe more difficult behaviours as for instance structures damage which interests the safety domain. A dynamic or static load can thus lead to a damage, a crack and then a rupture of the structure. The fast dynamics allows to simulate 'fast' phenomena such as explosions, shocks and impacts on structure. The application domain is various. It concerns for instance the study of the lifetime and the accidents scenario of the nuclear reactor vessel. It is then very interesting, for fast dynamics codes, to be able to anticipate in a robust and stable way such phenomena: the assessment of damage in the structure and the simulation of crack propagation form an essential stake. The extended finite element method has the advantage to break away from mesh generation and from fields projection during the crack propagation. Effectively, crack is described kinematically by an appropriate strategy of enrichment of supplementary freedom degrees. Difficulties connecting the spatial discretization of this method with the temporal discretization of an explicit calculation scheme has then been revealed; these difficulties are the diagonal writing of the mass matrix and the associated stability time step. Here are presented two methods of mass matrix diagonalization based on the kinetic energy conservation, and studies of critical time steps for various enriched finite elements. The interest revealed here is that the time step is not more penalizing than those of the standard finite elements problem. Comparisons with numerical simulations on another code allow to validate the theoretical works. A crack propagation test in mixed mode has been exploited in order to verify the simulation
Energy Technology Data Exchange (ETDEWEB)
Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Prolo Filho, Joao Francisco [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica, Estatistica e Fisica; Dias da Cunha, Rudnei; Basso Barichello, Liliane [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica
2014-04-15
In this work a study of two-dimensional fixed-source neutron transport problems, in Cartesian geometry, is reported. The approach reduces the complexity of the multidimensional problem using a combination of nodal schemes and the Analytical Discrete Ordinates Method (ADO). The unknown leakage terms on the boundaries that appear from the use of the derivation of the nodal scheme are incorporated to the problem source term, such as to couple the one-dimensional integrated solutions, made explicit in terms of the x and y spatial variables. The formulation leads to a considerable reduction of the order of the associated eigenvalue problems when combined with the usual symmetric quadratures, thereby providing solutions that have a higher degree of computational efficiency. Reflective-type boundary conditions are introduced to represent the domain on a simpler form than that previously considered in connection with the ADO method. Numerical results obtained with the technique are provided and compared to those present in the literature. (orig.)
Macías-Díaz, J. E.
2018-06-01
In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.
Energy Technology Data Exchange (ETDEWEB)
Aid, R.
1998-01-07
This work comes from an industrial problem of validating numerical solutions of ordinary differential equations modeling power systems. This problem is solved using asymptotic estimators of the global error. Four techniques are studied: Richardson estimator (RS), Zadunaisky's techniques (ZD), integration of the variational equation (EV), and Solving for the correction (SC). We give some precisions on the relative order of SC w.r.t. the order of the numerical method. A new variant of ZD is proposed that uses the Modified Equation. In the case of variable step-size, it is shown that under suitable restriction, on the hypothesis of the step-size selection, ZD and SC are still valid. Moreover, some Runge-Kutta methods are shown to need less hypothesis on the step-sizes to exhibit a valid order of convergence for ZD and SC. Numerical tests conclude this analysis. Industrial cases are given. Finally, an algorithm to avoid the a priori specification of the integration path for complex time differential equations is proposed. (author)
International Nuclear Information System (INIS)
Xing Yulong; Shu Chiwang
2006-01-01
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions
Simulation methods with extended stability for stiff biochemical Kinetics
Directory of Open Access Journals (Sweden)
Rué Pau
2010-08-01
Full Text Available Abstract Background With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (biochemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA. The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes. Conclusions The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (biochemical systems.
Yang, Z.; Li, Z.; Dollevoet, R.P.B.J.; Tournay, H; Grassie, S
2015-01-01
The precise mechanism which activates squeal, especially flange squeal has not been fully explained. The complex non-Hertzian contact and the broad-band high frequency feature bring great challenges to the modelling work of flange squeal. In this paper, an explicit integration finite element method
2–stage stochastic Runge–Kutta for stochastic delay differential equations
Energy Technology Data Exchange (ETDEWEB)
Rosli, Norhayati; Jusoh Awang, Rahimah [Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300, Gambang, Pahang (Malaysia); Bahar, Arifah; Yeak, S. H. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-05-15
This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.
Chao, W. C.
1982-01-01
With appropriate modifications, a recently proposed explicit-multiple-time-step scheme (EMTSS) is incorporated into the UCLA model. In this scheme, the linearized terms in the governing equations that generate the gravity waves are split into different vertical modes. Each mode is integrated with an optimal time step, and at periodic intervals these modes are recombined. The other terms are integrated with a time step dictated by the CFL condition for low-frequency waves. This large time step requires a special modification of the advective terms in the polar region to maintain stability. Test runs for 72 h show that EMTSS is a stable, efficient and accurate scheme.
Gould, Matthew J.; Cain, James W.; Roemer, Gary W.; Gould, William R.
2016-01-01
During the 2004–2005 to 2015–2016 hunting seasons, the New Mexico Department of Game and Fish (NMDGF) estimated black bear abundance (Ursus americanus) across the state by coupling density estimates with the distribution of primary habitat generated by Costello et al. (2001). These estimates have been used to set harvest limits. For example, a density of 17 bears/100 km2 for the Sangre de Cristo and Sacramento Mountains and 13.2 bears/100 km2 for the Sandia Mountains were used to set harvest levels. The advancement and widespread acceptance of non-invasive sampling and mark-recapture methods, prompted the NMDGF to collaborate with the New Mexico Cooperative Fish and Wildlife Research Unit and New Mexico State University to update their density estimates for black bear populations in select mountain ranges across the state.We established 5 study areas in 3 mountain ranges: the northern (NSC; sampled in 2012) and southern Sangre de Cristo Mountains (SSC; sampled in 2013), the Sandia Mountains (Sandias; sampled in 2014), and the northern (NSacs) and southern Sacramento Mountains (SSacs; both sampled in 2014). We collected hair samples from black bears using two concurrent non-invasive sampling methods, hair traps and bear rubs. We used a gender marker and a suite of microsatellite loci to determine the individual identification of hair samples that were suitable for genetic analysis. We used these data to generate mark-recapture encounter histories for each bear and estimated density in a spatially explicit capture-recapture framework (SECR). We constructed a suite of SECR candidate models using sex, elevation, land cover type, and time to model heterogeneity in detection probability and the spatial scale over which detection probability declines. We used Akaike’s Information Criterion corrected for small sample size (AICc) to rank and select the most supported model from which we estimated density.We set 554 hair traps, 117 bear rubs and collected 4,083 hair
Nonlinear Model Predictive Control for Oil Reservoirs Management
DEFF Research Database (Denmark)
Capolei, Andrea
expensive gradient computation by using high-order ESDIRK (Explicit Singly Diagonally Implicit Runge-Kutta) temporal integration methods and continuous adjoints. The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the continuous...... gradient-based optimization and the required gradients are computed by the adjoint method. We propose the use of efficient high order implicit time integration methods for the solution of the forward and the adjoint equations of the dynamical model. The Ensemble Kalman filter is used for data assimilation...... equivalent strategy is not justified for the particular case studied in this paper. The third contribution of this thesis is a mean-variance method for risk mitigation in production optimization of oil reservoirs. We introduce a return-risk bicriterion objective function for the profit-risk tradeoff...
Nodal DG-FEM solution of high-order Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan S.; Bingham, Harry B.
2006-01-01
We present a discontinuous Galerkin finite element method (DG-FEM) solution to a set of high-order Boussinesq-type equations for modelling highly nonlinear and dispersive water waves in one and two horizontal dimensions. The continuous equations are discretized using nodal polynomial basis...... functions of arbitrary order in space on each element of an unstructured computational domain. A fourth order explicit Runge-Kutta scheme is used to advance the solution in time. Methods for introducing artificial damping to control mild nonlinear instabilities are also discussed. The accuracy...... and convergence of the model with both h (grid size) and p (order) refinement are verified for the linearized equations, and calculations are provided for two nonlinear test cases in one horizontal dimension: harmonic generation over a submerged bar; and reflection of a steep solitary wave from a vertical wall...
Production Optimization for Two-Phase Flow in an Oil Reservoir
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove
2012-01-01
framework to increase the production and economic value of an oil reservoir. Wether the objective is to maximize recovery or some financial measure like Net Present Value, the increased production is achieved by manipulation of the well rates and bottom-hole pressures of the injection and production wells....... The optimal water injection rates and production well bottom-hole pressures are computed by solution of a large-scale constrained optimal control problem. The objective is to maximize production by manipulating the well rates and bottom hole pressures of injection and production wells. Optimal control...... settings of injection and production wells are computed by solution of a large scale constrained optimal control problem. We describe a gradient based method to compute the optimal control strategy of the water flooding process. An explicit singly diagonally implicit Runge-Kutta (ESDIRK) method...
Coupling Chemical Kinetics and Flashes in Reactive, Thermal and Compositional Reservoir Simulation
DEFF Research Database (Denmark)
Kristensen, Morten Rode; Gerritsen, Margot G.; Thomsen, Per Grove
2007-01-01
of convergence and error test failures by more than 50% compared to direct integration without the new algorithm. To facilitate the algorithmic development we construct a virtual kinetic cell model. We use implicit one-step ESDIRK (Explicit Singly Diagonal Implicit Runge-Kutta) methods for integration......Phase changes are known to cause convergence problems for integration of stiff kinetics in thermal and compositional reservoir simulations. We propose an algorithm for detection and location of phase changes based on discrete event system theory. The algorithm provides a robust way for handling...... the switching of variables and equations required when the number of phases changes. We extend the method to handle full phase equilibrium described by an equation of state. Experiments show that the new algorithm improves the robustness of the integration process near phase boundaries by lowering the number...
Finite volume model for two-dimensional shallow environmental flow
Simoes, F.J.M.
2011-01-01
This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.
Wu, Hulin; Xue, Hongqi; Kumar, Arun
2012-06-01
Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.
International Nuclear Information System (INIS)
Sabry, R.; Zahran, M.A.; Fan Engui
2004-01-01
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found
Mono- and Di-Alkylation Processes of DNA Bases by Nitrogen Mustard Mechlorethamine.
Larrañaga, Olatz; de Cózar, Abel; Cossío, Fernando P
2017-12-06
The reactivity of nitrogen mustard mechlorethamine (mec) with purine bases towards formation of mono- (G-mec and A-mec) and dialkylated (AA-mec, GG-mec and AG-mec) adducts has been studied using density functional theory (DFT). To gain a complete overview of DNA-alkylation processes, direct chloride substitution and formation through activated aziridinium species were considered as possible reaction paths for adduct formation. Our results confirm that DNA alkylation by mec occurs via aziridine intermediates instead of direct substitution. Consideration of explicit water molecules in conjunction with polarizable continuum model (PCM) was shown as an adequate computational method for a proper representation of the system. Moreover, Runge-Kutta numerical kinetic simulations including the possible bisadducts have been performed. These simulations predicted a product ratio of 83:17 of GG-mec and AG-mec diadducts, respectively. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Coupling Chemical Kinetics and Flashes in Reactive, Thermal and Compositional Reservoir Simulation
DEFF Research Database (Denmark)
Kristensen, Morten Rode; Gerritsen, Margot G.; Thomsen, Per Grove
2007-01-01
of convergence and error test failures by more than 50% compared to direct integration without the new algorithm. To facilitate the algorithmic development we construct a virtual kinetic cell model. We use implicit one-step ESDIRK (Explicit Singly Diagonal Implicit Runge-Kutta) methods for integration...... of the kinetics. The kinetic cell model serves both as a tool for the development and testing of tailored solvers as well as a testbed for studying the interactions between chemical kinetics and phase behavior. A comparison between a Kvalue correlation based approach and a more rigorous equation of state based......Phase changes are known to cause convergence problems for integration of stiff kinetics in thermal and compositional reservoir simulations. We propose an algorithm for detection and location of phase changes based on discrete event system theory. The algorithm provides a robust way for handling...
Energy Technology Data Exchange (ETDEWEB)
Kwon, Kyung [Tuskegee Univ., Tuskegee, AL (United States); Fan, Liang-Shih [The Ohio State Univ., Columbus, OH (United States); Zhou, Qiang [The Ohio State Univ., Columbus, OH (United States); Yang, Hui [The Ohio State Univ., Columbus, OH (United States)
2014-09-30
A new and efficient direct numerical method with second-order convergence accuracy was developed for fully resolved simulations of incompressible viscous flows laden with rigid particles. The method combines the state-of-the-art immersed boundary method (IBM), the multi-direct forcing method, and the lattice Boltzmann method (LBM). First, the multi-direct forcing method is adopted in the improved IBM to better approximate the no-slip/no-penetration (ns/np) condition on the surface of particles. Second, a slight retraction of the Lagrangian grid from the surface towards the interior of particles with a fraction of the Eulerian grid spacing helps increase the convergence accuracy of the method. An over-relaxation technique in the procedure of multi-direct forcing method and the classical fourth order Runge-Kutta scheme in the coupled fluid-particle interaction were applied. The use of the classical fourth order Runge-Kutta scheme helps the overall IB-LBM achieve the second order accuracy and provides more accurate predictions of the translational and rotational motion of particles. The preexistent code with the first-order convergence rate is updated so that the updated new code can resolve the translational and rotational motion of particles with the second-order convergence rate. The updated code has been validated with several benchmark applications. The efficiency of IBM and thus the efficiency of IB-LBM were improved by reducing the number of the Lagragian markers on particles by using a new formula for the number of Lagrangian markers on particle surfaces. The immersed boundary-lattice Boltzmann method (IBLBM) has been shown to predict correctly the angular velocity of a particle. Prior to examining drag force exerted on a cluster of particles, the updated IB-LBM code along with the new formula for the number of Lagrangian markers has been further validated by solving several theoretical problems. Moreover, the unsteadiness of the drag force is examined when a
Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.
2017-12-01
We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.
A finite difference method for off-fault plasticity throughout the earthquake cycle
Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash
2017-12-01
We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).
Discrete singular convolution for the generalized variable-coefficient ...
African Journals Online (AJOL)
Numerical solutions of the generalized variable-coefficient Korteweg-de Vries equation are obtained using a discrete singular convolution and a fourth order singly diagonally implicit Runge-Kutta method for space and time discretisation, respectively. The theoretical convergence of the proposed method is rigorously ...
Numerical simulation of interface movement in gas-liquid two-phase flows with Level Set method
International Nuclear Information System (INIS)
Li Huixiong; Chinese Academy of Sciences, Beijing; Deng Sheng; Chen Tingkuan; Zhao Jianfu; Wang Fei
2005-01-01
Numerical simulation of gas-liquid two-phase flow and heat transfer has been an attractive work for a quite long time, but still remains as a knotty difficulty due to the inherent complexities of the gas-liquid two-phase flow resulted from the existence of moving interfaces with topology changes. This paper reports the effort and the latest advances that have been made by the authors, with special emphasis on the methods for computing solutions to the advection equation of the Level set function, which is utilized to capture the moving interfaces in gas-liquid two-phase flows. Three different schemes, i.e. the simple finite difference scheme, the Superbee-TVD scheme and the 5-order WENO scheme in combination with the Runge-Kutta method are respectively applied to solve the advection equation of the Level Set. A numerical procedure based on the well-verified SIMPLER method is employed to numerically calculate the momentum equations of the two-phase flow. The above-mentioned three schemes are employed to simulate the movement of four typical interfaces under 5 typical flowing conditions. Analysis of the numerical results shows that the 5-order WENO scheme and the Superbee-TVD scheme are much better than the simple finite difference scheme, and the 5-order WENO scheme is the best to compute solutions to the advection equation of the Level Set. The 5-order WENO scheme will be employed as the main scheme to get solutions to the advection equations of the Level Set when gas-liquid two-phase flows are numerically studied in the future. (authors)
Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel
2015-01-01
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search
Dang, Trang Thi Doan; Nguyen, Huong Thu
2013-01-01
Two approaches to grammar instruction are often discussed in the ESL literature: direct explicit grammar instruction (DEGI) (deduction) and indirect explicit grammar instruction (IEGI) (induction). This study aims to explore the effects of indirect explicit grammar instruction on EFL learners' mastery of English tenses. Ninety-four…
Simos, T. E.
2017-11-01
A family of four stages high algebraic order embedded explicit six-step methods, for the numerical solution of second order initial or boundary-value problems with periodical and/or oscillating solutions, are studied in this paper. The free parameters of the new proposed methods are calculated solving the linear system of equations which is produced by requesting the vanishing of the phase-lag of the methods and the vanishing of the phase-lag's derivatives of the schemes. For the new obtained methods we investigate: • Its local truncation error (LTE) of the methods.• The asymptotic form of the LTE obtained using as model problem the radial Schrödinger equation.• The comparison of the asymptotic forms of LTEs for several methods of the same family. This comparison leads to conclusions on the efficiency of each method of the family.• The stability and the interval of periodicity of the obtained methods of the new family of embedded finite difference pairs.• The applications of the new obtained family of embedded finite difference pairs to the numerical solution of several second order problems like the radial Schrödinger equation, astronomical problems etc. The above applications lead to conclusion on the efficiency of the methods of the new family of embedded finite difference pairs.
Ketcheson, David I.
2014-06-13
We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four through twelve, including both serial and parallel implementations. We cast extrapolation and deferred correction methods as fixed-order Runge–Kutta methods, providing a natural framework for the comparison. The stability and accuracy properties of the methods are analyzed by theoretical measures, and these are compared with the results of numerical tests. In serial, the eighth-order pair of Prince and Dormand (DOP8) is most efficient. But other high-order methods can be more efficient than DOP8 when implemented in parallel. This is demonstrated by comparing a parallelized version of the wellknown ODEX code with the (serial) DOP853 code. For an N-body problem with N = 400, the experimental extrapolation code is as fast as the tuned Runge–Kutta pair at loose tolerances, and is up to two times as fast at tight tolerances.
Energy Technology Data Exchange (ETDEWEB)
Hernandez S, A. [UNAM-LAIRN, Jiutepec, Morelos (Mexico)] e-mail: augusto_vib@yahoo.com.mx
2003-07-01
The following one written it presents a comparative analysis among different analytical solutions for the punctual kinetics equation, which present two variables of interest: a) the temporary behavior of the neutronic population, and b) The temporary behavior of the different groups of precursors of delayed neutrons. The first solution is based on a method that solves the transfer function of the differential equation for the neutronic population, in which intends to obtain the different poles that give the stability of this transfer function. In this section it is demonstrated that the temporary variation of the reactivity of the system can be managed as it is required, since the integration time for this method doesn't affect the result. However, the second solution is based on an iterative method like that of Runge-Kutta or the Euler method where the algorithm was only used to solve first order differential equations giving this way solution to each differential equation that conforms the equations of punctual kinetics. In this section it is demonstrated that only it can obtain a correct temporary behavior of the neutronic population when it is integrated on an interval of very short time, forcing to the temporary variation of the reactivity to change very quick way without one has some control about the time. In both methods the same change is used so much in the reactivity of the system like in the integration times, giving validity to the results graph the one the temporary behavior of the neutronic population vs. time. (Author)
On the Linear Stability of the Fifth-Order WENO Discretization
Motamed, Mohammad; Macdonald, Colin B.; Ruuth, Steven J.
2010-01-01
, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC
Numerical integration subprogrammes in Fortran II-D
Energy Technology Data Exchange (ETDEWEB)
Fry, C. R.
1966-12-15
This note briefly describes some integration subprogrammes written in FORTRAN II-D for the IBM 1620-II at CARDE. These presented are two Newton-Cotes, Chebyshev polynomial summation, Filon's, Nordsieck's and optimum Runge-Kutta and predictor-corrector methods. A few miscellaneous numerical integration procedures are also mentioned covering statistical functions, oscillating integrands and functions occurring in electrical engineering.
Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil
Kryštůfek, P.; Kozel, K.
2014-03-01
The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.
Study of the Nonlinear Dropping Shock Response of Expanded Foam Packaging System
Directory of Open Access Journals (Sweden)
Huan-xin Jiang
2013-01-01
Full Text Available The variational iteration method-2 (VIM-2 is applied to obtain approximate analytical solutions of EPS foam cushioning packaging system. The first-order frequency solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this VIM with convenient calculation.
A Differential Equation for Downhill Compressible Flow in Pipes and ...
African Journals Online (AJOL)
The differential equation was first numerically solved by use of the classical fourth order Runge-Kutta method in the form of a FORTRAN program. A test of the accuracy of the solution was ... The formula was tested with a problem from the book “Fluid Mechanics and Hydraulics”. The test showed the formula to be accurate.
Analysis of the glow curve of SrB 4O 7:Dy compounds employing the GOT model
Ortega, F.; Molina, P.; Santiago, M.; Spano, F.; Lester, M.; Caselli, E.
2006-02-01
The glow curve of SrB 4O 7:Dy phosphors has been analysed with the general one trap model (GOT). To solve the differential equation describing the GOT model a novel algorithm has been employed, which reduces significantly the deconvolution time with respect to the time required by usual integration algorithms, such as the Runge-Kutta method.
Analysis of the glow curve of SrB4O7:Dy compounds employing the GOT model
International Nuclear Information System (INIS)
Ortega, F.; Molina, P.; Santiago, M.; Spano, F.; Lester, M.; Caselli, E.
2006-01-01
The glow curve of SrB 4 O 7 :Dy phosphors has been analysed with the general one trap model (GOT). To solve the differential equation describing the GOT model a novel algorithm has been employed, which reduces significantly the deconvolution time with respect to the time required by usual integration algorithms, such as the Runge-Kutta method
Caffo, Michele; Czyz, Henryk; Gunia, Michal; Remiddi, Ettore
2008-01-01
We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.
Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil
Directory of Open Access Journals (Sweden)
Kryštůfek P.
2014-03-01
Full Text Available The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.
Numerical Solution of Compressible Steady Flows around the NACA 0012 Airfoil
Directory of Open Access Journals (Sweden)
Kozel K
2013-04-01
Full Text Available The article presents results of a numerical solution of subsonic and transonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the NACA 0012 airfoil. Authors used Runge-Kutta method to numerically solve the flows around the NACA 0012 airfoil.
Directory of Open Access Journals (Sweden)
Rahma Sadat
2018-03-01
Full Text Available In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary differential equations (ODEs. Some of these ODEs had no quadrature. We here derive several new solutions for these non-solvable ODEs.
Xiao, Li; Luo, Ray
2017-12-07
We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.
International Nuclear Information System (INIS)
Unseren, M.A.
1997-01-01
The paper reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restrict the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for the closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system
Energy Technology Data Exchange (ETDEWEB)
Unseren, M.A.
1997-04-20
The paper reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restrict the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for the closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.
Feller, David; Peterson, Kirk A
2013-08-28
The effectiveness of the recently developed, explicitly correlated coupled cluster method CCSD(T)-F12b is examined in terms of its ability to reproduce atomization energies derived from complete basis set extrapolations of standard CCSD(T). Most of the standard method findings were obtained with aug-cc-pV7Z or aug-cc-pV8Z basis sets. For a few homonuclear diatomic molecules it was possible to push the basis set to the aug-cc-pV9Z level. F12b calculations were performed with the cc-pVnZ-F12 (n = D, T, Q) basis set sequence and were also extrapolated to the basis set limit using a Schwenke-style, parameterized formula. A systematic bias was observed in the F12b method with the (VTZ-F12/VQZ-F12) basis set combination. This bias resulted in the underestimation of reference values associated with small molecules (valence correlation energies 0.5 E(h)) and an even larger overestimation of atomization energies for bigger systems. Consequently, caution should be exercised in the use of F12b for high accuracy studies. Root mean square and mean absolute deviation error metrics for this basis set combination were comparable to complete basis set values obtained with standard CCSD(T) and the aug-cc-pVDZ through aug-cc-pVQZ basis set sequence. However, the mean signed deviation was an order of magnitude larger. Problems partially due to basis set superposition error were identified with second row compounds which resulted in a weak performance for the smaller VDZ-F12/VTZ-F12 combination of basis sets.
Explicit formulas for Clebsch-Gordan coefficients
International Nuclear Information System (INIS)
Rudnicki-Bujnowski, G.
1975-01-01
The problem is to obtain explicit algebraic formulas of Clebsch-Gordan coefficients for high values of angular momentum. The method of solution is an algebraic method based on the Racah formula using the FORMAC programming language. (Auth.)
Acceleration methods for multi-physics compressible flow
Peles, Oren; Turkel, Eli
2018-04-01
In this work we investigate the Runge-Kutta (RK)/Implicit smoother scheme as a convergence accelerator for complex multi-physics flow problems including turbulent, reactive and also two-phase flows. The flows considered are subsonic, transonic and supersonic flows in complex geometries, and also can be either steady or unsteady flows. All of these problems are considered to be a very stiff. We then introduce an acceleration method for the compressible Navier-Stokes equations. We start with the multigrid method for pure subsonic flow, including reactive flows. We then add the Rossow-Swanson-Turkel RK/Implicit smoother that enables performing all these complex flow simulations with a reasonable CFL number. We next discuss the RK/Implicit smoother for time dependent problem and also for low Mach numbers. The preconditioner includes an intrinsic low Mach number treatment inside the smoother operator. We also develop a modified Roe scheme with a corresponding flux Jacobian matrix. We then give the extension of the method for real gas and reactive flow. Reactive flows are governed by a system of inhomogeneous Navier-Stokes equations with very stiff source terms. The extension of the RK/Implicit smoother requires an approximation of the source term Jacobian. The properties of the Jacobian are very important for the stability of the method. We discuss what the chemical physics theory of chemical kinetics tells about the mathematical properties of the Jacobian matrix. We focus on the implication of the Le-Chatelier's principle on the sign of the diagonal entries of the Jacobian. We present the implementation of the method for turbulent flow. We use a two RANS turbulent model - one equation model - Spalart-Allmaras and a two-equation model - k-ω SST model. The last extension is for two-phase flows with a gas as a main phase and Eulerian representation of a dispersed particles phase (EDP). We present some examples for such flow computations inside a ballistic evaluation
Multigrid time-accurate integration of Navier-Stokes equations
Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.
1993-01-01
Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.
Building an explicit de Sitter
International Nuclear Information System (INIS)
Louis, Jan; Hamburg Univ.; Rummel, Markus; Valandro, Roberto; Westphal, Alexander
2012-11-01
We construct an explicit example of a de Sitter vacuum in type IIB string theory that realizes the proposal of Kaehler uplifting. As the large volume limit in this method depends on the rank of the largest condensing gauge group we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric Calabi-Yau threefolds. We find large numbers of models with the largest gauge group factor easily exceeding a rank of one hundred. We construct a global model with Kaehler uplifting on a two-parameter model on CP 4 11169 , by an explicit analysis from both the type IIB and F-theory point of view. The explicitness of the construction lies in the realization of a D7 brane configuration, gauge flux and RR and NS flux choices, such that all known consistency conditions are met and the geometric moduli are stabilized in a metastable de Sitter vacuum with spontaneous GUT scale supersymmetry breaking driven by an F-term of the Kaehler moduli.
Building an explicit de Sitter
Energy Technology Data Exchange (ETDEWEB)
Louis, Jan [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Rummel, Markus; Valandro, Roberto [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie
2012-11-15
We construct an explicit example of a de Sitter vacuum in type IIB string theory that realizes the proposal of Kaehler uplifting. As the large volume limit in this method depends on the rank of the largest condensing gauge group we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric Calabi-Yau threefolds. We find large numbers of models with the largest gauge group factor easily exceeding a rank of one hundred. We construct a global model with Kaehler uplifting on a two-parameter model on CP{sup 4}{sub 11169}, by an explicit analysis from both the type IIB and F-theory point of view. The explicitness of the construction lies in the realization of a D7 brane configuration, gauge flux and RR and NS flux choices, such that all known consistency conditions are met and the geometric moduli are stabilized in a metastable de Sitter vacuum with spontaneous GUT scale supersymmetry breaking driven by an F-term of the Kaehler moduli.
DEFF Research Database (Denmark)
Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter
1995-01-01
The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...... has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual...... stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method....
An appraisal of computational techniques for transient heat conduction equation
International Nuclear Information System (INIS)
Kant, T.
1983-01-01
A semi-discretization procedure in which the ''space'' dimension is discretized by the finite element method is emphasized for transient problems. This standard methodology transforms the space-time partial differential equation (PDE) system into a set of ordinary differential equations (ODE) in time. Existing methods for transient heat conduction calculations are then reviewed. Existence of two general classes of time integration schemes- implicit and explicit is noted. Numerical stability characteristics of these two methods are elucidated. Implicit methods are noted to be numerically stable, permitting large time steps, but the cost per step is high. On the otherhand, explicit schemes are noted to be inexpensive per step, but small step size is required. Low computational cost of the explicit schemes make it very attractive for nonlinear problems. However, numerical stability considerations requiring use of very small time steps come in the way of its general adoption. Effectiveness of the fourth-order Runge-Kutta-Gill explicit integrator is then numerically evaluated. Finally we discuss some very recent works on development of computational algorithms which not only achieve unconditional stability, high accuracy and convergence but involve computations on matrix equations of elements only. This development is considered to be very significant in the light of our experience gained for simple heat conduction calculations. We conclude that such algorithms have the potential for further developments leading to development of economical methods for general transient analysis of complex physical systems. (orig.)
Explicit dissipative structures
International Nuclear Information System (INIS)
Roessler, O.E.
1987-01-01
Dissipative structures consisting of a few macrovariables arise out of a sea of reversible microvariables. Unexpected residual effects of the massive underlying reversibility, on the macrolevel, cannot therefore be excluded. In the age of molecular-dynamics simulations, explicit dissipative structures like excitable systems (explicit observers) can be generated in a computer from first reversible principles. A class of classical, 1-D Hamiltonian systems of chaotic type is considered which has the asset that the trajectorial behavior in phase space can be understood geometrically. If, as nuatural, the number of particle types is much smaller than that of particles, the Gibbs symmetry must be taken into account. The permutation invariance drastically changes the behavior in phase space (quasi-periodization). The explicity observer becomes effectively reversible on a short time scale. In consequence, his ability to measure microscopic motions is suspended in a characteristic fashion. Unlike quantum mechanics whose holistic nature cannot be transcended, the present holistic (internal-interface) effects - mimicking the former to some extent - can be understood fully in principle
DEFF Research Database (Denmark)
Blasco, Maribel
2015-01-01
The article proposes an approach, broadly inspired by culturally inclusive pedagogy, to facilitate international student academic adaptation based on rendering tacit aspects of local learning cultures explicit to international full degree students, rather than adapting them. Preliminary findings...... are presented from a focus group-based exploratory study of international student experiences at different stages of their studies at a Danish business school, one of Denmark’s most international universities. The data show how a major source of confusion for these students has to do with the tacit logics...... and expectations that shape how the formal steps of the learning cycle are understood and enacted locally, notably how learning and assessment moments are defined and related to one another. Theoretically, the article draws on tacit knowledge and sense-making theories to analyse student narratives...
Asymptotic solution for heat convection-radiation equation
Energy Technology Data Exchange (ETDEWEB)
Mabood, Fazle; Ismail, Ahmad Izani Md [School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Khan, Waqar A. [Department of Engineering Sciences, National University of Sciences and Technology, PN Engineering College, Karachi, 75350 (Pakistan)
2014-07-10
In this paper, we employ a new approximate analytical method called the optimal homotopy asymptotic method (OHAM) to solve steady state heat transfer problem in slabs. The heat transfer problem is modeled using nonlinear two-point boundary value problem. Using OHAM, we obtained the approximate analytical solution for dimensionless temperature with different values of a parameter ε. Further, the OHAM results for dimensionless temperature have been presented graphically and in tabular form. Comparison has been provided with existing results from the use of homotopy perturbation method, perturbation method and numerical method. For numerical results, we used Runge-Kutta Fehlberg fourth-fifth order method. It was found that OHAM produces better approximate analytical solutions than those which are obtained by homotopy perturbation and perturbation methods, in the sense of closer agreement with results obtained from the use of Runge-Kutta Fehlberg fourth-fifth order method.
Nonlinear punctual dynamic applied to simulation of PWR type reactors
International Nuclear Information System (INIS)
Cysne, F.S.
1978-01-01
In order to study some kinds of nuclear reactor accidents, a simulation is made using the punctual kinetics model to the reactor core. The following integration methods are used: Hansen's method in which a linearization is made and C S M P using a variable interval fourth-order Runge Kutta method. The results were good and were compared with those obtained by the code Dinamica I which uses a finite difference integration method of backward kind. (author)
Non-linear punctual kinetics applied to PWR reactors simulation
International Nuclear Information System (INIS)
Cysne, F.S.
1978-11-01
In order to study some kinds of nuclear reactor accidents, a simulation is made using the punctual kinetics model for the reactor core. The following integration methods are used: Hansen's method in which a linearization is made and CSMP using a variable interval fourth-order Runge Kutta method. The results were good and were compared with those obtained by the code Dinamica I which uses a finite difference integration method of backward kind. (Author) [pt
A new particle-like method for high-speed flows with chemical non-equilibrium
Directory of Open Access Journals (Sweden)
Fábio Rodrigues Guzzo
2010-04-01
Full Text Available The present work is concerned with the numerical simulation of hypersonic blunt body flows with chemical non-equilibrium. New theoretical and numerical formulations for coupling the chemical reaction to the fluid dynamics are presented and validated. The fluid dynamics is defined for a stationary unstructured mesh and the chemical reaction process is defined for “finite quantities” moving through the stationary mesh. The fluid dynamics is modeled by the Euler equations and the chemical reaction rates by the Arrhenius law. Ideal gases are considered. The thermodynamical data are based on JANNAF tables and Burcat’s database. The algorithm proposed by Liou, known as AUSM+, is implemented in a cell-centered based finite volume method and in an unstructured mesh context. Multidimensional limited MUSCL interpolation method is used to perform property reconstructions and to achieve second-order accuracy in space. The minmod limiter is used. The second order accuracy, five stage, Runge-Kutta time-stepping scheme is employed to perform the time march for the fluid dynamics. The numerical code VODE, which is part of the CHEMKIN-II package, is adopted to perform the time integration for the chemical reaction equations. The freestream reacting fluid is composed of H2 and air at the stoichiometric ratio. The emphasis of the present paper is on the description of the new methodology for handling the coupling of chemical and fluid mechanic processes, and its validation by comparison with the standard time-splitting procedure. The configurations considered are the hypersonic flow over a wedge, in which the oblique detonation wave is induced by an oblique shock wave, and the hypersonic flow over a blunt body. Differences between the solutions obtained with each formulation are presented and discussed, including the effects of grid refinement in each case. The primary objective of such comparisons is the validation of the proposed methodology. Moreover, for
Energy Technology Data Exchange (ETDEWEB)
Wang, Hailong; Rasch, Philip J.; Easter, Richard C.; Singh, Balwinder; Zhang, Rudong; Ma, Po-Lun; Qian, Yun; Ghan, Steven J.; Beagley, Nathaniel
2014-11-27
We introduce an explicit emission tagging technique in the Community Atmosphere Model to quantify source-region-resolved characteristics of black carbon (BC), focusing on the Arctic. Explicit tagging of BC source regions without perturbing the emissions makes it straightforward to establish source-receptor relationships and transport pathways, providing a physically consistent and computationally efficient approach to produce a detailed characterization of the destiny of regional BC emissions and the potential for mitigation actions. Our analysis shows that the contributions of major source regions to the global BC burden are not proportional to the respective emissions due to strong region-dependent removal rates and lifetimes, while the contributions to BC direct radiative forcing show a near-linear dependence on their respective contributions to the burden. Distant sources contribute to BC in remote regions mostly in the mid- and upper troposphere, having much less impact on lower-level concentrations (and deposition) than on burden. Arctic BC concentrations, deposition and source contributions all have strong seasonal variations. Eastern Asia contributes the most to the wintertime Arctic burden. Northern Europe emissions are more important to both surface concentration and deposition in winter than in summer. The largest contribution to Arctic BC in the summer is from Northern Asia. Although local emissions contribute less than 10% to the annual mean BC burden and deposition within the Arctic, the per-emission efficiency is much higher than for major non-Arctic sources. The interannual variability (1996-2005) due to meteorology is small in annual mean BC burden and radiative forcing but is significant in yearly seasonal means over the Arctic. When a slow aging treatment of BC is introduced, the increase of BC lifetime and burden is source-dependent. Global BC forcing-per-burden efficiency also increases primarily due to changes in BC vertical distributions. The
He, Ying; Puckett, Elbridge Gerry; Billen, Magali I.
2017-02-01
Mineral composition has a strong effect on the properties of rocks and is an essentially non-diffusive property in the context of large-scale mantle convection. Due to the non-diffusive nature and the origin of compositionally distinct regions in the Earth the boundaries between distinct regions can be nearly discontinuous. While there are different methods for tracking rock composition in numerical simulations of mantle convection, one must consider trade-offs between computational cost, accuracy or ease of implementation when choosing an appropriate method. Existing methods can be computationally expensive, cause over-/undershoots, smear sharp boundaries, or are not easily adapted to tracking multiple compositional fields. Here we present a Discontinuous Galerkin method with a bound preserving limiter (abbreviated as DG-BP) using a second order Runge-Kutta, strong stability-preserving time discretization method for the advection of non-diffusive fields. First, we show that the method is bound-preserving for a point-wise divergence free flow (e.g., a prescribed circular flow in a box). However, using standard adaptive mesh refinement (AMR) there is an over-shoot error (2%) because the cell average is not preserved during mesh coarsening. The effectiveness of the algorithm for convection-dominated flows is demonstrated using the falling box problem. We find that the DG-BP method maintains sharper compositional boundaries (3-5 elements) as compared to an artificial entropy-viscosity method (6-15 elements), although the over-/undershoot errors are similar. When used with AMR the DG-BP method results in fewer degrees of freedom due to smaller regions of mesh refinement in the neighborhood of the discontinuity. However, using Taylor-Hood elements and a uniform mesh there is an over-/undershoot error on the order of 0.0001%, but this error increases to 0.01-0.10% when using AMR. Therefore, for research problems in which a continuous field method is desired the DG
Muralidharan, Balaji; Menon, Suresh
2018-03-01
A high-order adaptive Cartesian cut-cell method, developed in the past by the authors [1] for simulation of compressible viscous flow over static embedded boundaries, is now extended for reacting flow simulations over moving interfaces. The main difficulty related to simulation of moving boundary problems using immersed boundary techniques is the loss of conservation of mass, momentum and energy during the transition of numerical grid cells from solid to fluid and vice versa. Gas phase reactions near solid boundaries can produce huge source terms to the governing equations, which if not properly treated for moving boundaries, can result in inaccuracies in numerical predictions. The small cell clustering algorithm proposed in our previous work is now extended to handle moving boundaries enforcing strict conservation. In addition, the cell clustering algorithm also preserves the smoothness of solution near moving surfaces. A second order Runge-Kutta scheme where the boundaries are allowed to change during the sub-time steps is employed. This scheme improves the time accuracy of the calculations when the body motion is driven by hydrodynamic forces. Simple one dimensional reacting and non-reacting studies of moving piston are first performed in order to demonstrate the accuracy of the proposed method. Results are then reported for flow past moving cylinders at subsonic and supersonic velocities in a viscous compressible flow and are compared with theoretical and previously available experimental data. The ability of the scheme to handle deforming boundaries and interaction of hydrodynamic forces with rigid body motion is demonstrated using different test cases. Finally, the method is applied to investigate the detonation initiation and stabilization mechanisms on a cylinder and a sphere, when they are launched into a detonable mixture. The effect of the filling pressure on the detonation stabilization mechanisms over a hyper-velocity sphere launched into a hydrogen
Symplectic discretization for spectral element solution of Maxwell's equations
International Nuclear Information System (INIS)
Zhao Yanmin; Dai Guidong; Tang Yifa; Liu Qinghuo
2009-01-01
Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.
Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun
2018-03-01
Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The advantage of this kind of space-time separation approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which can be very time and memory consuming due to the reconstruction at each stage for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function. For traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the second-order or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd- to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th- and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a
Numerical analysis for Darcy-Forchheimer flow in presence of homogeneous-heterogeneous reactions
Directory of Open Access Journals (Sweden)
Muhammad Ijaz Khan
Full Text Available A mathematical study is presented to investigate the influences of homogeneous and heterogeneous reactions in local similar flow caused by stretching sheet with a non-linear velocity and variable thickness. Porous medium effects are characterized by using Darcy-Forchheimer porous-media. A simple isothermal model of homogeneous-heterogeneous reactions is used. The multiphysical boundary value problem is dictated by ten thermophysical parameters: ratio of mass diffusion coefficients, Prandtl number, local inertia coefficient parameter, inverse Darcy number, shape parameter, surface thickness parameter, Hartman number, Homogeneous heat reaction, strength of homogeneous-heterogeneous reactions and Schmidt number. Resulting systems are computed by Runge-Kutta-Fehlberg method. Different shapes of velocity are noticed for n > 1 and n < 1. Keywords: Homogeneous-heterogeneous reactions, Non Darcy porous medium, Variable sheet thickness, Homogeneous heat reaction with stoichiometric coefficient, Runge-Kutta-Fehlberg method
Radtke, H.; Burchard, H.
2015-01-01
In this paper, an unconditionally positive and multi-element conserving time stepping scheme for systems of non-linearly coupled ODE's is presented. These systems of ODE's are used to describe biogeochemical transformation processes in marine ecosystem models. The numerical scheme is a positive-definite modification of the Runge-Kutta method, it can have arbitrarily high order of accuracy and does not require time step adaption. If the scheme is combined with a modified Patankar-Runge-Kutta method from Burchard et al. (2003), it also gets the ability to solve a certain class of stiff numerical problems, but the accuracy is restricted to second-order then. The performance of the new scheme on two test case problems is shown.
Rational functions with maximal radius of absolute monotonicity
Loczi, Lajos
2014-05-19
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parameter families of rational functions. Moreover, we prove earlier conjectured optimal radii in some families with 2 or 3 parameters via uniqueness arguments for systems of polynomial inequalities. Our results also prove the optimality of some strong stability preserving implicit and singly diagonally implicit Runge-Kutta methods. Whereas previous results in this area were primarily numerical, we give all constants as exact algebraic numbers.
Variational and symplectic integrators for satellite relative orbit propagation including drag
Palacios, Leonel; Gurfil, Pini
2018-04-01
Orbit propagation algorithms for satellite relative motion relying on Runge-Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge-Kutta-based integrators, even in the presence of atmospheric drag.
On reinitializing level set functions
Min, Chohong
2010-04-01
In this paper, we consider reinitializing level functions through equation ϕt+sgn(ϕ0)(‖∇ϕ‖-1)=0[16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation. We compare the three temporal discretizations: the second order Runge-Kutta method, the forward Euler method, and a Gauss-Seidel iteration of the forward Euler method. The fact that the time in the equation is fictitious makes a hypothesis that all the temporal discretizations result in the same result in their stationary states. The fact that the absolute stability region of the forward Euler method is not wide enough to include all the eigenvalues of the linearized semi-discrete system of the second order ENO spatial discretization makes another hypothesis that the forward Euler temporal discretization should invoke numerical instability. Our results in this paper contradict both the hypotheses. The Runge-Kutta and Gauss-Seidel methods obtain the second order accuracy, and the forward Euler method converges with order between one and two. Examining all their properties, we conclude that the Gauss-Seidel method is the best among the three. Compared to the Runge-Kutta, it is twice faster and requires memory two times less with the same accuracy.
Implicit, explicit and speculative knowledge
van Ditmarsch, H.; French, T.; Velázquez-Quesada, F.R.; Wáng, Y.N.
We compare different epistemic notions in the presence of awareness of propositional variables: the logic of implicit knowledge (in which explicit knowledge is definable), the logic of explicit knowledge, and the logic of speculative knowledge. Speculative knowledge is a novel epistemic notion that
Implicit time accurate simulation of unsteady flow
van Buuren, René; Kuerten, Hans; Geurts, Bernard J.
2001-03-01
Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright
The human body metabolism process mathematical simulation based on Lotka-Volterra model
Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur
2017-08-01
The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.
Polarized seismic and solitary waves run-up at the sea bed
Energy Technology Data Exchange (ETDEWEB)
Dennis, L. C.C.; Zainal, A. A.; Faisal, S. Y. [Universiti Teknologi PETRONAS, 31750 Tronoh, Perak (Malaysia); Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia)
2012-09-26
The polarization effects in hydrodynamics are studied. Hydrodynamic equation for the nonlinear wave is used along with the polarized solitary waves and seismic waves act as initial waves. The model is then solved by Fourier spectral and Runge-Kutta 4 methods, and the surface plot is drawn. The output demonstrates the inundation behaviors. Consequently, the polarized seismic waves along with the polarized solitary waves tend to generate dissimilar inundation which is more disastrous.
Interactions of microwave with plasmas
International Nuclear Information System (INIS)
Zhang Haifeng; Shao Fuqiu; Wang Long
2003-01-01
When plasma size scale is comparable with the wavelength of electromagnetic waves, W.K.B. solution isn't applicable. In this paper a new numerical solution technique to investigate interactions of microwave with plasmas is presented by using Runge-Kutta method. The results of numerical solution coincide with that of analytical solution while the model is linear electron density profile in calculated accuracy
Directory of Open Access Journals (Sweden)
J. M. Jawdat
2012-01-01
Full Text Available The effect of nanofluids on chaotic convection in a fluid layer heated from below was studied in this paper for low Prandtl number based on the theory of dynamical systems. A low-dimensional, Lorenz-like model was obtained using Galerkin-truncated approximations. The fourth-order Runge-Kutta method was employed to solve the nonlinear system. The results show that inhibition of chaotic convection can be observed when using nanofluids.
Simulation of the accumulation kinetics for radiation point defects in a metals with impurity
International Nuclear Information System (INIS)
Iskakov, B.M.; Nurova, A.B.
2001-01-01
In the work a kinetics of vacancies (V) and interstitial atoms (IA) accumulation for cases when the V and IA are recombining with each other, absorbing by drain and capturing by impurity atoms has been simulated. The differential equations system numerical solution was carried out by the Runge-Kutta method. The dynamical equilibrium time achievement for the point radiation defects accumulation process in the metal with impurity is considered
Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil
Kryštůfek, P.; Kozel, K.
2015-05-01
The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Euler equations in 2D compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil. The results are compared with the solution using the software Ansys Fluent 15.0.7.
Availability Evaluation of the serial processes in a Paper Production Industry-A Numerical Approach
Directory of Open Access Journals (Sweden)
Archana Sharma
2010-12-01
Full Text Available The purpose of this research is to compute availability of the process of a paper production industry consisting of four subsystems. Mathematical formulation of the problem is carried out using probability considerations and the governing differential equations are solved using Runge-Kutta method of order four. Availability of the serial process in the paper production industry have been computed for various choice of failure and repair rates of subsystems of this plant.
Numerical solution of kinetics equation for point defects accumulation in metals under irradiation
International Nuclear Information System (INIS)
Aldzhambekova, G.T.; Iskakov, B.M.
1999-01-01
In the report the mathematical model, describing processes of generation and accumulation of defects in solids under irradiation is considered. The equations of this model take into account the velocity of Frenkel pairs generation, the mutual recombination of vacancies and the interstitials, as well as velocity of defects absorption by discharge channeling of vacancies and interstitials. By Runge-Kutta method the numerical solution of the model was carried out
Designing of a Quadrupole Paul Ion Trap
Kiyani, Abouzar; Abdollahzadeh, M.; Sadat Kiai, S. M.; Zirak, A. R.
2011-08-01
The ion motion equation in a Paul ion trap known as Mathieu differential equation has been solved for the first time by using Runge-Kutta methods with 4th, 6th, and 8th orders. The first stability regions in az - qz plane and the corresponding qmax values were determined and compared. Also, the first stability regions of , , , ions in the Vdc - Vac plane were drown, and the threshold voltages for the ion separation was investigated.
Einstein gravity with torsion induced by the scalar field
Özçelik, H. T.; Kaya, R.; Hortaçsu, M.
2018-06-01
We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge-Kutta method. From the numerical solution, we make an ansatz for the rotation parameter in the proposed metric, which gives an analytical solution for the scalar field for asymptotic regions.
Explicitly computing geodetic coordinates from Cartesian coordinates
Zeng, Huaien
2013-04-01
This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.
"Tacit Knowledge" versus "Explicit Knowledge"
DEFF Research Database (Denmark)
Sanchez, Ron
creators and carriers. By contrast, the explicit knowledge approach emphasizes processes for articulating knowledge held by individuals, the design of organizational approaches for creating new knowledge, and the development of systems (including information systems) to disseminate articulated knowledge...
Explicit Versus Implicit Income Insurance
Thomas J. Kniesner; James P. Ziliak
2001-01-01
October 2001 (Revised from July 2001). Abstract: By supplementing income explicitly through payments or implicitly through taxes collected, income-based taxes and transfers make disposable income less variable. Because disposable income determines consumption, policies that smooth disposable income also create welfare improving consumption insurance. With data from the Panel Study of Income Dynamics we find that annual consumption variation is reduced by almost 20 percent due to explicit and ...
Implicit vs. Explicit Trust in Social Matrix Factorization
Fazeli, Soude; Loni, Babak; Bellogin, Alejandro; Drachsler, Hendrik; Sloep, Peter
2014-01-01
Incorporating social trust in Matrix Factorization (MF) methods demonstrably improves accuracy of rating prediction. Such approaches mainly use the trust scores explicitly expressed by users. However, it is often challenging to have users provide explicit trust scores of each other. There exist
Discretization analysis of bifurcation based nonlinear amplifiers
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Directory of Open Access Journals (Sweden)
Eun Seok Lee
2003-01-01
Full Text Available An axial turbine rotor cascade-shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using an unsteady flow, Reynolds-averaged Navier-Stokes equations solver that was based on explicit, finite difference; Runge-Kutta multistage time marching; and the diagonalized alternating direction implicit scheme. The code utilized Baldwin-Lomax algebraic and k-ε turbulence modeling. The full approximation storage multigrid method and preconditioning were implemented as iterative convergence-acceleration techniques. An implicit dual-time stepping method was incorporated in order to simulate the unsteady flow fields. The objective function was defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed during the optimization. The design variables were several geometric parameters characterizing airfoil leading edge, camber, stagger angle, and inter-row spacing. The genetic algorithm was used as an optimizer, and the penalty method was introduced for combining the constraints with the objective function. Each individual's objective function was computed simultaneously by using a 32-processor distributedmemory computer. The optimization results indicated that only minor improvements are possible in unsteady rotor/stator aerodynamics by varying these geometric parameters.
International Nuclear Information System (INIS)
Singh, Tej; Kumar, Jainendra; Mazumdar, Tanay; Raina, V.K.
2013-01-01
Highlights: • A point reactor kinetics code coupled with thermal hydraulics of plate type fuel is developed. • This code is applicable for two phase flow of coolant. • Safety analysis of IAEA benchmark reactor core is carried out. • Results agree well with the results available in literature. - Abstract: A point reactor kinetics code SAC-RIT, acronym of Safety Analysis Code for Reactivity Initiated Transient, coupled with thermal hydraulics of two phase coolant flow for plate type fuel, is developed to calculate reactivity initiated transient analysis of nuclear research and test reactors. Point kinetics equations are solved by fourth order Runge Kutta method. Reactivity feedback effect is included into the code. Solution of kinetics equations gives neutronic power and it is then fed into a thermal hydraulic code where mass, momentum and thermal energy conservation equations are solved by explicit finite difference method to find out fuel, clad and coolant temperatures during transients. In this code, all possible flow regimes including laminar flow, transient flow and turbulent flow have been covered. Various heat transfer coefficients suitable for single liquid, sub-cooled boiling, saturation boiling, film boiling and single vapor phases are incorporated in the thermal hydraulic code
Development and acceleration of unstructured mesh-based cfd solver
Emelyanov, V.; Karpenko, A.; Volkov, K.
2017-06-01
The study was undertaken as part of a larger effort to establish a common computational fluid dynamics (CFD) code for simulation of internal and external flows and involves some basic validation studies. The governing equations are solved with ¦nite volume code on unstructured meshes. The computational procedure involves reconstruction of the solution in each control volume and extrapolation of the unknowns to find the flow variables on the faces of control volume, solution of Riemann problem for each face of the control volume, and evolution of the time step. The nonlinear CFD solver works in an explicit time-marching fashion, based on a three-step Runge-Kutta stepping procedure. Convergence to a steady state is accelerated by the use of geometric technique and by the application of Jacobi preconditioning for high-speed flows, with a separate low Mach number preconditioning method for use with low-speed flows. The CFD code is implemented on graphics processing units (GPUs). Speedup of solution on GPUs with respect to solution on central processing units (CPU) is compared with the use of different meshes and different methods of distribution of input data into blocks. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.
Mang, Andreas; Biros, George
2017-01-01
We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.
International Nuclear Information System (INIS)
Unseren, M.A.
1997-09-01
The report reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restricts the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for the closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system
Energy Technology Data Exchange (ETDEWEB)
Unseren, M.A.
1997-09-01
The report reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restricts the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for the closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.
Understanding and making practice explicit
Directory of Open Access Journals (Sweden)
Gráinne Conole
2006-12-01
Full Text Available This issue contains four, on the face of it, quite different papers, but on looking a little closer there are a number of interesting themes running through them that illustrate some of the key methodological and theoretical issues that e-learning researchers are currently struggling with; central to these is the issue of how do we understand and make practice explicit?
Age effects on explicit and implicit memory
Directory of Open Access Journals (Sweden)
Emma eWard
2013-09-01
Full Text Available It is well documented that explicit memory (e.g., recognition declines with age. In contrast, many argue that implicit memory (e.g., priming is preserved in healthy aging. For example, priming on tasks such as perceptual identification is often not statistically different in groups of young and older adults. Such observations are commonly taken as evidence for distinct explicit and implicit learning/memory systems. In this article we discuss several lines of evidence that challenge this view. We describe how patterns of differential age-related decline may arise from differences in the ways in which the two forms of memory are commonly measured, and review recent research suggesting that under improved measurement methods, implicit memory is not age-invariant. Formal computational models are of considerable utility in revealing the nature of underlying systems. We report the results of applying single and multiple-systems models to data on age effects in implicit and explicit memory. Model comparison clearly favours the single-system view. Implications for the memory systems debate are discussed.
Age effects on explicit and implicit memory.
Ward, Emma V; Berry, Christopher J; Shanks, David R
2013-01-01
It is well-documented that explicit memory (e.g., recognition) declines with age. In contrast, many argue that implicit memory (e.g., priming) is preserved in healthy aging. For example, priming on tasks such as perceptual identification is often not statistically different in groups of young and older adults. Such observations are commonly taken as evidence for distinct explicit and implicit learning/memory systems. In this article we discuss several lines of evidence that challenge this view. We describe how patterns of differential age-related decline may arise from differences in the ways in which the two forms of memory are commonly measured, and review recent research suggesting that under improved measurement methods, implicit memory is not age-invariant. Formal computational models are of considerable utility in revealing the nature of underlying systems. We report the results of applying single and multiple-systems models to data on age effects in implicit and explicit memory. Model comparison clearly favors the single-system view. Implications for the memory systems debate are discussed.
Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids
Otero, Evelyn; Eliasson, Peter
2015-03-01
An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.
Energy Technology Data Exchange (ETDEWEB)
Falcao, Carlos E.G.; Vielmo, Horacio A. [Federal University of Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Mechanical Engineering Dept.], E-mails: vielmoh@mecanica.ufrgs.br; Hanriot, Sergio M. [Pontifical Catholic University of Minas Gerais (PUC-Minas), Belo Horizonte, MG (Brazil). Mechanical Engineering Dept.], E-mail: hanriot@pucminas.br
2010-07-01
The work investigates the pressure waves behavior in the intake system of an internal combustion engine. For the purpose of examining this problem, it was chosen an experimental study in order to validate the results of the present simulation. At the literature there are several experimental studies, and some numerical simulations, but the most of the numerical studies treat the problem only in one dimension in practical problems, or two dimensions in specific problems. Using a CFD code it is possible to analyze more complex systems, including tridimensional effects. The pulsating phenomenon is originated from the periodic movement of the intake valve, and produces waves that propagate within the system. The intake system studied was composed by a straight pipe connected to a 1000 cc engine with a single operating cylinder. The experiments were carried out in a flow bench. In the present work, the governing equations was discretized by Finite Volumes Method with an explicit formulation, and the time integration was made using the multi-stage Runge-Kutta time stepping scheme. The solution is independent of mesh or time step. The numerical analysis presents a good agreement with the experimental results. (author)
Development of a Three-Dimensional Unstructured Euler Solver for High-Speed Flows
Directory of Open Access Journals (Sweden)
Tudorel Petronel AFILIPOAE
2015-12-01
Full Text Available This paper addresses the solution of the compressible Euler equations on hexahedral meshes for supersonic and hypersonic flows. Spatial discretization is accomplished by a cell-centered finite-volume formulation which employs two different upwind schemes for the computation of convective fluxes. Second-order solutions are attained through a linear state reconstruction technique that yields highly resolved flows in smooth regions while providing a sharp and clean resolution of shocks. The solution gradients required for the higher-order spatial discretization are estimated by a least-square method while Venkatakrishnan limiter is employed to preserve monotonicity and avoid oscillations in the presence of shocks. Furthermore, solutions are advanced in time by an explicit third-order Runge-Kutta scheme and convergence to steady state is accelerated using implicit residual smoothing. Flow around a circular arc in a channel and flow past a circular cylinder are studied and results are presented for various Mach numbers together with comparisons to theoretical and experimental data where possible.
Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.
2018-06-01
A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.
Explicit TE/TM scheme for particle beam simulations
International Nuclear Information System (INIS)
Dohlus, M.; Zagorodnov, I.
2008-10-01
In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version. It does not have dispersion in the longitudinal direction and the dispersion properties in the transversal plane are improved. The explicit character of the new scheme allows a uniformly stable conformal method without iterations and the scheme can be parallelized easily. It assures energy and charge conservation. A version of this explicit scheme for rotationally symmetric structures is free from the progressive time step reducing for higher order azimuthal modes as it takes place for Yee's explicit method used in the most popular electrodynamics codes. (orig.)
The effect of explicit financial incentives on physician behavior.
Armour, B S; Pitts, M M; Maclean, R; Cangialose, C; Kishel, M; Imai, H; Etchason, J
2001-05-28
Managed care organizations use explicit financial incentives to influence physicians' use of resources. This has contributed to concerns regarding conflicts of interest for physicians and adverse effects on the quality of patient care. In light of recent publicized legislative and legal battles about this issue, we reviewed the literature and analyzed studies that examine the effect of these explicit financial incentives on the behavior of physicians. The method used to undertake the literature review followed the approach set forth in the Cochrane Collaboration handbook. Our literature review revealed a paucity of data on the effect of explicit financial incentives. Based on this limited evidence, explicit incentives that place individual physicians at financial risk appear to be effective in reducing physician resource use. However, the empirical evidence regarding the effectiveness of bonus payments on physician resource use is mixed. Similarly, our review revealed mixed effects of the influence of explicit financial incentives on the quality of patient care. The effect of explicit financial incentives on physician behavior is complicated by a lack of understanding of the incentive structure by the managed care organization and the physician. The lack of a universally acceptable definition of quality renders it important that future researchers identify the term explicitly.
A simple model of the batch electrochemical reduction of nitrate/nitrite waste
International Nuclear Information System (INIS)
Wingard, D.A.; Weidner, J.W.; Van Zee, J.W.
1994-01-01
A model of a divided parallel plate electrochemical cell operated in a batch mode for the destruction of NO 3 - /NO 2 - in alkaline waste streams is presented. The model uses boundary layer approximations at each electrode and at the separator to minimize computation time. Five competing electrochemical reactions are included at the cathode. The model uses either an explicit Runge-Kutta routine with empirically determined current efficiencies or an implicit stepping routine for each electrode if the current efficiencies are to be predicted. Tim dependent changes of the concentration, temperature, and cell voltage are predicted for constant current operation. Model predictions are compared with experimental data
Tacit to explicit knowledge conversion.
Cairó Battistutti, Osvaldo; Bork, Dominik
2017-11-01
The ability to create, use and transfer knowledge may allow the creation or improvement of new products or services. But knowledge is often tacit: It lives in the minds of individuals, and therefore, it is difficult to transfer it to another person by means of the written word or verbal expression. This paper addresses this important problem by introducing a methodology, consisting of a four-step process that facilitates tacit to explicit knowledge conversion. The methodology utilizes conceptual modeling, thus enabling understanding and reasoning through visual knowledge representation. This implies the possibility of understanding concepts and ideas, visualized through conceptual models, without using linguistic or algebraic means. The proposed methodology is conducted in a metamodel-based tool environment whose aim is efficient application and ease of use.
Fast isogeometric solvers for explicit dynamics
Gao, Longfei
2014-06-01
In finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that has linear computational complexity, i.e., O(N), where N is the total number of degrees of freedom in the system. We refer to these matrices as separable matrices. For non-separable mass matrices, we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative. We demonstrate that these preconditioners, which are easy to construct and cheap to apply (O(N)), can deliver significant convergence acceleration. The performances of these preconditioners are independent of the polynomial order (p independence) and mesh resolution (h independence) for maximum continuity B-splines, as verified by various numerical tests. © 2014 Elsevier B.V.
Topology Optimization using an Explicit Interface Representation
DEFF Research Database (Denmark)
Christiansen, Asger Nyman; Nobel-Jørgensen, Morten; Bærentzen, J. Andreas
to handle topology changes. It does so by discretizing the entire design domain into an irregular adaptive triangle mesh and thereby explicitly representing both the structure and the embedding space. In other words, the entire design domain is divided into triangles, where the interface is represented....... To increase performance, degrees of freedom associated with void triangles are eliminated from the FE equation. Using the triangle mesh for computations is possible since the DSC method ensures a mesh with no degenerate elements. If the mesh contained degenerate or close to degenerate elements the FEM...... seconds on an ordinary laptop utilizing a single thread. In addition, a coarse solution to the same problem has been obtained in approximately 10 seconds....
Generating transverse response explicitly from harmonic oscillators
Yao, Yuan; Tang, Ying; Ao, Ping
2017-10-01
We obtain stochastic dynamics from a system-plus-bath mechanism as an extension of the Caldeira-Leggett (CL) model in the classical regime. An effective magnetic field and response functions with both longitudinal and transverse parts are exactly generated from the bath of harmonic oscillators. The effective magnetic field and transverse response are antisymmetric matrices: the former is explicitly time-independent corresponding to the geometric magnetism, while the latter can have memory. The present model can be reduced to previous representative examples of stochastic dynamics describing nonequilibrium processes. Our results demonstrate that a system coupled with a bath of harmonic oscillators is a general approach to studying stochastic dynamics, and provides a method to experimentally implement an effective magnetic field from coupling to the environment.
Subramanian, Ramanathan Vishnampet Ganapathi
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme
Steady-State-Preserving Simulation of Genetic Regulatory Systems
Directory of Open Access Journals (Sweden)
Ruqiang Zhang
2017-01-01
Full Text Available A novel family of exponential Runge-Kutta (expRK methods are designed incorporating the stable steady-state structure of genetic regulatory systems. A natural and convenient approach to constructing new expRK methods on the base of traditional RK methods is provided. In the numerical integration of the one-gene, two-gene, and p53-mdm2 regulatory systems, the new expRK methods are shown to be more accurate than their prototype RK methods. Moreover, for nonstiff genetic regulatory systems, the expRK methods are more efficient than some traditional exponential RK integrators in the scientific literature.
Particle tracking in a small electron storage ring
International Nuclear Information System (INIS)
Tsumaki, K.
1987-01-01
A particle tracking method for a ring system in which a sextupole magnetic field is distributed along the beam axis has been developed. This method uses Jacobi's elliptic functions inside the bending magnet and the canonical integration method in the fringes. The calculation time for the new method is the same or faster than that of the canonical integration method, and it is ten times faster than the Runge-Kutta-Gill and thin lens approximation. A special characteristic of our method is that the calculation time is always constant, even if the magnet length is increased
Implicit and Explicit Instruction of Spelling Rules
Kemper, M. J.; Verhoeven, L.; Bosman, A. M. T.
2012-01-01
The study aimed to compare the differential effectiveness of explicit and implicit instruction of two Dutch spelling rules. Students with and without spelling disabilities were instructed a spelling rule either implicitly or explicitly in two experiments. Effects were tested in a pretest-intervention-posttest control group design. Experiment 1…
Taatgen, N.A.; Schmid, U; Krems, J; Wysotzky, F
1999-01-01
A popular distinction in the learning literature is the distinction between implicit and explicit learning. Although many studies elaborate on the nature of implicit learning, little attention is left for explicit learning. The unintentional aspect of implicit learning corresponds well to the
EdgeMaps: visualizing explicit and implicit relations
Dörk, Marian; Carpendale, Sheelagh; Williamson, Carey
2011-01-01
In this work, we introduce EdgeMaps as a new method for integrating the visualization of explicit and implicit data relations. Explicit relations are specific connections between entities already present in a given dataset, while implicit relations are derived from multidimensional data based on shared properties and similarity measures. Many datasets include both types of relations, which are often difficult to represent together in information visualizations. Node-link diagrams typically focus on explicit data connections, while not incorporating implicit similarities between entities. Multi-dimensional scaling considers similarities between items, however, explicit links between nodes are not displayed. In contrast, EdgeMaps visualize both implicit and explicit relations by combining and complementing spatialization and graph drawing techniques. As a case study for this approach we chose a dataset of philosophers, their interests, influences, and birthdates. By introducing the limitation of activating only one node at a time, interesting visual patterns emerge that resemble the aesthetics of fireworks and waves. We argue that the interactive exploration of these patterns may allow the viewer to grasp the structure of a graph better than complex node-link visualizations.
Memory Efficient Data Structures for Explicit Verification of Timed Systems
DEFF Research Database (Denmark)
Taankvist, Jakob Haahr; Srba, Jiri; Larsen, Kim Guldstrand
2014-01-01
Timed analysis of real-time systems can be performed using continuous (symbolic) or discrete (explicit) techniques. The explicit state-space exploration can be considerably faster for models with moderately small constants, however, at the expense of high memory consumption. In the setting of timed......-arc Petri nets, we explore new data structures for lowering the used memory: PTries for efficient storing of configurations and time darts for semi-symbolic description of the state-space. Both methods are implemented as a part of the tool TAPAAL and the experiments document at least one order of magnitude...... of memory savings while preserving comparable verification times....
Control of error and convergence in ODE solvers
International Nuclear Information System (INIS)
Gustafsson, K.
1992-03-01
Feedback is a general principle that can be used in many different contexts. In this thesis it is applied to numerical integration of ordinary differential equations. An advanced integration method includes parameters and variables that should be adjusted during the execution. In addition, the integration method should be able to automatically handle situations such as: initialization, restart after failures, etc. In this thesis we regard the algorithms for parameter adjustment and supervision as a controller. The controlled measures different variable that tell the current status of the integration, and based on this information it decides how to continue. The design of the controller is vital in order to accurately and efficiently solve a large class of ordinary differential equations. The application of feedback control may appear farfetched, but numerical integration methods are in fact dynamical systems. This is often overlooked in traditional numerical analysis. We derive dynamic models that describe the behavior of the integration method as well as the standard control algorithms in use today. Using these models it is possible to analyze properties of current algorithms, and also explain some generally observed misbehaviors. Further, we use the acquired insight to derive new and improved control algorithms, both for explicit and implicit Runge-Kutta methods. In the explicit case, the new controller gives good overall performance. In particular it overcomes the problem with oscillating stepsize sequence that is often experienced when the stepsize is restricted by numerical stability. The controller for implicit methods is designed so that it tracks changes in the differential equation better than current algorithms. In addition, it includes a new strategy for the equation solver, which allows the stepsize to vary more freely. This leads to smoother error control without excessive operations on the iteration matrix. (87 refs.) (au)
Directory of Open Access Journals (Sweden)
Firat Evirgen
2016-04-01
Full Text Available In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational İteration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
Splitting Strategy for Simulating Genetic Regulatory Networks
Directory of Open Access Journals (Sweden)
Xiong You
2014-01-01
Full Text Available The splitting approach is developed for the numerical simulation of genetic regulatory networks with a stable steady-state structure. The numerical results of the simulation of a one-gene network, a two-gene network, and a p53-mdm2 network show that the new splitting methods constructed in this paper are remarkably more effective and more suitable for long-term computation with large steps than the traditional general-purpose Runge-Kutta methods. The new methods have no restriction on the choice of stepsize due to their infinitely large stability regions.
DEFF Research Database (Denmark)
Deng, Jie; Yang, Ming; Ma, Rongjiang
2016-01-01
dynamic model based on the first-order difference method is compared to that of the numerical solution of the collector ordinary differential equation (ODE) model using the fourth-order Runge-Kutta method. The improved thermal inertia model (TIM) on the basis of closed-form solution presented by Deng et....... (2012) for the model turns out to be the collector static response time constant τC by analytical derivation. The nonlinear least squares method is applied to determine the characteristic parameters of a flat-plate solar air collector previously tested by the authors. Then the obtained parameters...
International Nuclear Information System (INIS)
Angrand, F.
1990-10-01
In this HDR (Accreditation to Supervise Researches) report, the author gives an overview of his activities in the field of numerical methods, notably in the field of fluid mechanics and aeronautics. He more particularly addresses the resolution of Euler equations of gas dynamics in transonic and supersonic regimes (equations, centered and off-centered flow calculation, case of one-dimensional and non linear systems), the extension of this work to Navier-Stokes equations (equations, grid adaptation), the study of resolution methods and cost optimisation (Runge-Kutta method, implicit schemes, multi-grid approach). He also addresses the case of hypersonic flows behind a base
Managers' implicit and explicit risk-attitudes in managerial decision making
Bittner, Jenny; Landwehr, Julia; Hertel, Guido; Binnewies, Carmen; Krumm, Stefan; Holling, Heinz; Kleinmar, Martin
2013-01-01
Purpose We examined the contribution of implicit and explicit risk-attitudes to the prediction of risky management decisions. Indirect methods allow for the measurement of implicit attitudes, while self-report is typically used to measure explicit, reflective attitudes. Indirect methods make it
New explicit and exact solutions of the Benney–Kawahara–Lin equation
International Nuclear Information System (INIS)
Yuan-Xi, Xie
2009-01-01
In this paper, we present a combination method of constructing the explicit and exact solutions of nonlinear partial differential equations. And as an illustrative example, we apply the method to the Benney–Kawahara–Lin equation and derive its many explicit and exact solutions which are all new solutions. (general)
AIREK-PUL, Periodic Kinetics Problems of Pulsed Reactors
International Nuclear Information System (INIS)
Inzaghi, A.; Misenta, R.
1984-01-01
1 - Nature of physical problem solved: Solves periodic problems about the kinetics of pulsed reactors or problems where the reactivity has rapid variations. The program uses two constant steps for the integration of the system of differential equations, the first step during the first half-period and the second step during the second half-period. Available for either single or double precision. 2 - Method of solution: The differential equations are integrated using the fourth-order Runge-Kutta method as modified by E.R. Cohen (Geneva Conference, 1958). 3 - Restrictions on the complexity of the problem: The maximum number of differential equations that can be solved simultaneously is 50
Neural network error correction for solving coupled ordinary differential equations
Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.
1992-01-01
A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.
Energy Technology Data Exchange (ETDEWEB)
Isa, Sharena Mohamad; Ali, Anati [Department of Mathematical Sciences, Faculty of Science Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia sharena-ina@yahoo.com, anati@utm.my (Malaysia)
2015-10-22
In this paper, the hydromagnetic flow of dusty fluid over a vertical stretching sheet with thermal radiation is investigated. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformation. These nonlinear ordinary differential equations are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method (RKF45 Method). The behavior of velocity and temperature profiles of hydromagnetic fluid flow of dusty fluid is analyzed and discussed for different parameters of interest such as unsteady parameter, fluid-particle interaction parameter, the magnetic parameter, radiation parameter and Prandtl number on the flow.
Unsteady axisymmetric flow and heat transfer over time-dependent radially stretching sheet
Directory of Open Access Journals (Sweden)
Azeem Shahzad
2017-03-01
Full Text Available This article address the boundary layer flow and heat transfer of unsteady and incompressible viscous fluid over an unsteady stretching permeable surface. First of all modeled nonlinear partial differential equations are transformed to a system of ordinary differential equations by using similarity transformations. Analytic solution of the reduced problem is constructed by using homotopy analysis method (HAM. To validate the constructed series solution a numerical counterpart is developed using shooting algorithm based on Runge-Kutta method. Both schemes are in an excellent agreement. The effects of the pertinent parameters on the velocity and energy profile are shown graphically and examined in detail.
Manual for COMSYN: A orbit integration code for the study of beam dynamics in compact synchrotrons
International Nuclear Information System (INIS)
Huang, Y.
1991-10-01
COMSYN is a numerical integration code which is written for the study and design of the compact synchrotrons. An improved 4th-order Runge-Kutta method is used in COMSYN to integrate the exact equations of motion in a rectangular coordinate system. The magnetic field components of the dipole B x , B y and B z can be obtained from either measurement or directly computed data (MAGNUS, TOSCA). A spline interpolation method is then used to get the field value at the particle position. For standard quadrupole and sextupole, the analytical expression is employed to compute its field distribution
Second Law Analysis for a Variable Viscosity Reactive Couette Flow under Arrhenius Kinetics
Directory of Open Access Journals (Sweden)
N. S. Kobo
2010-01-01
Full Text Available This study investigates the inherent irreversibility associated with the Couette flow of a reacting variable viscosity combustible material under Arrhenius kinetics. The nonlinear equations of momentum and energy governing the flow system are solved both analytically using a perturbation method and numerically using the standard Newton Raphson shooting method along with a fourth-order Runge Kutta integration algorithm to obtain the velocity and temperature distributions which essentially expedite to obtain expressions for volumetric entropy generation numbers, irreversibility distribution ratio, and the Bejan number in the flow field.
Energy Technology Data Exchange (ETDEWEB)
Lebelo, Ramoshweu Solomon, E-mail: sollyl@vut.ac.za [Department of Mathematics, Vaal University of Technology, Private Bag X021, Vanderbijlpark, 1911 (South Africa)
2014-10-24
In this paper the CO{sub 2} emission and thermal stability in a long cylindrical pipe of combustible reactive material with variable thermal conductivity are investigated. It is assumed that the cylindrical pipe loses heat by both convection and radiation at the surface. The nonlinear differential equations governing the problem are tackled numerically using Runge-Kutta-Fehlberg method coupled with shooting technique method. The effects of various thermophysical parameters on the temperature and carbon dioxide fields, together with critical conditions for thermal ignition are illustrated and discussed quantitatively.
Group analysis for natural convection from a vertical plate
Rashed, A. S.; Kassem, M. M.
2008-12-01
The steady laminar natural convection of a fluid having chemical reaction of order n past a semi-infinite vertical plate is considered. The solution of the problem by means of one-parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations. Two different similarity transformations are found. In each case the set of differential equations are solved numerically using Runge-Kutta and the shooting method. For each transformation different Schmidt numbers and chemical reaction orders are tested.
SHOCK-JR: a computer program to analyze impact response of shipping container
International Nuclear Information System (INIS)
Ikushima, Takeshi; Nakazato, Chikara; Shimoda, Osamu; Uchino, Mamoru.
1983-02-01
The report is provided for using a computer program, SHOCK-JR, which is used to analyze the impact response of shipping containers. Descriptions are the mathematical model, method of analysis, structures of the program and the input and output variables. The program solves the equations of motion for a one-dimensional, lumped mass and nonlinear spring model. The solution procedure uses Runge-Kutta-Gill and Newmark-β methods. SHOCK-JR is a revised version of SHOCK, which was developed by ORNL. In SHOCK-JR, SI dimension is used and graphical output is available. (author)
Ulku, Huseyin Arda; Bagci, Hakan; Michielssen, Eric
2012-01-01
An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.
Ulku, Huseyin Arda
2012-09-01
An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.
Explicit constructions of automorphic L-functions
Gelbart, Stephen; Rallis, Stephen
1987-01-01
The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory.
Depth migration in transversely isotropic media with explicit operators
Energy Technology Data Exchange (ETDEWEB)
Uzcategui, Omar [Colorado School of Mines, Golden, CO (United States)
1994-12-01
The author presents and analyzes three approaches to calculating explicit two-dimensional (2D) depth-extrapolation filters for all propagation modes (P, SV, and SH) in transversely isotropic media with vertical and tilted axis of symmetry. These extrapolation filters are used to do 2D poststack depth migration, and also, just as for isotropic media, these 2D filters are used in the McClellan transformation to do poststack 3D depth migration. Furthermore, the same explicit filters can also be used to do depth-extrapolation of prestack data. The explicit filters are derived by generalizations of three different approaches: the modified Taylor series, least-squares, and minimax methods initially developed for isotropic media. The examples here show that the least-squares and minimax methods produce filters with accurate extrapolation (measured in the ability to position steep reflectors) for a wider range of propagation angles than that obtained using the modified Taylor series method. However, for low propagation angles, the modified Taylor series method has smaller amplitude and phase errors than those produced by the least-squares and minimax methods. These results suggest that to get accurate amplitude estimation, modified Taylor series filters would be somewhat preferred in areas with low dips. In areas with larger dips, the least-squares and minimax methods would give a distinctly better delineation of the subsurface structures.
A computational analysis on homogeneous-heterogeneous mechanism in Carreau fluid flow
Khan, Imad; Rehman, Khalil Ur; Malik, M. Y.; Shafquatullah
2018-03-01
In this article magnetohydrodynamic Carreau fluid flow towards stretching cylinder is considered in the presence of homogeneous-heterogeneous reactions effect. The flow model is structured by utilizing theoretical grounds. For the numerical solution a shooting method along with Runge-Kutta algorithm is executed. The outcomes are provided through graphs. It is observed that the Carreau fluid concentration shows decline values via positive iterations of homogeneous-heterogeneous reaction parameters towards both shear thinning and thickening case. The present work is certified through comparison with already existing literature in a limiting sense.
International Nuclear Information System (INIS)
Muslim, G.A.; Ali, A.; Tariq, G.F.
1998-01-01
This paper deals with a mathematical model developed for carrying out trajectories and performance analysis of aerodynamic bodies in flight. The model caters for external wind and the earth rotation effects, and simulates three dimensional motion of the powered or un powered vehicles in space,. The resulting system of ordinary differential equations is solved by fourth order Runge Kutta method. The trajectory and performance parameters are computed by a computer Code AERO. The sensitivity analysis of the burnout conditions has also been carried out for the strategic missiles. (author)
On the accuracy and efficiency of finite difference solutions for nonlinear waves
DEFF Research Database (Denmark)
Bingham, Harry B.
2006-01-01
-uniform grid. Time-integration is performed using a fourth-order Runge-Kutta scheme. The linear accuracy, stability and convergence properties of the method are analyzed in two-dimensions, and high-order schemes with a stretched vertical grid are found to be advantageous relative to second-order schemes...... on an even grid. Comparison with highly accurate periodic solutions shows that these conclusions carry over to nonlinear problems. The combination of non-uniform grid spacing in the vertical and fourth-order schemes is suggested as providing an optimal balance between accuracy and complexity for practical...
Steady and transient states of a two-phase counter current flow
International Nuclear Information System (INIS)
Siebert, S.
1984-06-01
The aim of this work is to estimate the efficiency of the counter current exchange between a heavy dispersed phase and a continous light phase in a pulse perforated plate column. From an experimental point, hydraulic measurements (retention ratio, droplet size) and residence time measurements (radioactive tracers). The model will be so applied to the calculation of retention ratios in steady conditions then of tracer concentrations in transient conditions. From a numerical point of view a fixed point type iteration then a method Runge Kutta are then adapted [fr
An Image Encryption Scheme Based on Hyperchaotic Rabinovich and Exponential Chaos Maps
Directory of Open Access Journals (Sweden)
Xiaojun Tong
2015-01-01
Full Text Available This paper proposes a new four-dimensional hyperchaotic map based on the Rabinovich system to realize chaotic encryption in higher dimension and improve the security. The chaotic sequences generated by Runge-Kutta method are combined with the chaotic sequences generated by an exponential chaos map to generate key sequences. The key sequences are used for image encryption. The security test results indicate that the new hyperchaotic system has high security and complexity. The comparison between the new hyperchaotic system and the several low-dimensional chaotic systems shows that the proposed system performs more efficiently.
Directory of Open Access Journals (Sweden)
Khaled S.M.
2018-01-01
Full Text Available In this paper, we re-investigate the problem describing effects of radiation, Joule heating, and viscous dissipation on magnetohydrodynamic Marangoni convection boundary layer over a flat surface with suction/injection. The analytical solution obtained for the reduced system of non-linear-coupled differential equations governing the problem. Laplace transform successfully implemented to get the exact expression for the temperature profile. Furthermore, comparing the current exact results with approximate numerical results obtained using Runge-Kutta-Fehlberg method is introduced. These comparisons declare that the published numerical results agree with the current exact results. In addition, the effects of various parameters on the temperature profile are discussed graphically.
Energy Technology Data Exchange (ETDEWEB)
Perez M, C.; Benitez R, J.S.; Lopez C, R. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)
2003-07-01
The development of a simulator that uses the Runge-Kutta-Fehlberg method to solve the model of the punctual kinetics of a nuclear research reactor type TRIGA. The simulator includes an algorithm of power control of the reactor based on the fuzzy logic, a friendly graphic interface which responds to the different user's petitions and that it shows numerical and graphically the results in real time. The user can modify the demanded power and to visualize the dynamic behavior of the one system. This simulator was developed in Visual Basic under an open architecture with which its will be prove different controllers for its analysis. (Author)
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Rashidi
2008-01-01
Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.
International Nuclear Information System (INIS)
Qin Hong; Guan Xiaoyin
2008-01-01
A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods
International Nuclear Information System (INIS)
Qin, H.; Guan, X.
2008-01-01
A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods.
Study of Penetration Technology
1976-11-01
srecimens fabricated at the AFATL, AISI-01 oil quenched bar stock was used. Three of the projectiles used in the Eglin penetration experiments are shown...in the Mathema- tical Laboratory at Eglin AFB, is essencially a fourth order Runge-Kutta numerical method for solving simultaneous differential...C9G. VEL. X-COMPo (M4/5): d!10. I oil 140. 107. 82. RmCC~kr’ED TIME OF MAXIftjM/MINIM94U COIL VOLTAGE tSI MAX 0040 A 55 *.03J04A 0 0 05ji6 .000634 MIN
有理Runge-Kutta法を用いたSemi-Lagrangian海洋モデルの開発
上原, 克人; Uehara, Katsuto
1997-01-01
A new Semi-Lagrangian scheme using Rational Runge-Kutta method (RKSL scheme)is developed for reduced-gravity ocean model. It is superior to Semi-Implicit/Semi-Lagrangian (SISL) scheme in handling lateral boundaries, whereas it can take longer time-step than usual external Eulerian schemes. To evaluate this new scheme, experiments simulating the mid-depth circulation of the Mediterranean outflow region in the eastern North Atlantic were made by using the RKSL scheme, the SISL scheme, and cente...
Abdoli-Arani, A.; Montazeri, M. M.
2018-04-01
Two special types of metallic waveguide having dielectric cladding and plasma core including the combined circular and elliptical structure are studied. Longitudinal and transverse field components in the different regions are obtained. Applying the boundary conditions, dispersion relations of the electromagnetic waves in the structures are obtained and then plotted. The acceleration of an injected external relativistic electron in the considered waveguides is studied. The obtained differential equations related to electron motion are solved by the fourth-order Runge-Kutta method. Numerical computations are made, and the results are graphically presented.
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
Directory of Open Access Journals (Sweden)
S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
Analytical treatment of gas flows through multilayer insulation, project 1
Lin, J. T.
1972-01-01
A theoretical investigation of gas flow inside a multilayer insulation system was made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was also investigated. It was shown that when the relaxation time is less than the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparisons with experimental data were made.
Function of bunching segment in multi-cell RF gun
International Nuclear Information System (INIS)
Yang Xingfan; Xu Zhou Liu Xisan
2001-01-01
With a bunching segment and a shortened first cell, the 4 + 1/2 cell RF gun produced in CAEP has been proved experimentally to be effective in reducing electron back bombardment. The analysis of the electric field distribution and electron motion in bunching segment of multi-cell RF gun is presented. The electron capture efficiency and electron trajectory with different initial phase are calculated using Runge-Kutta method. The function of the bunching segment is discussed. The calculated parameters of the 4 + 1/2 cell RF gun agree well with the experimental results
Bubble dynamics in a superheated liquid
International Nuclear Information System (INIS)
Sha, W.T.; Shah, V.L.
1977-09-01
The report presents an extensive literature survey on bubble dynamics. Growth of a single spherical bubble moving in a uniformly superheated liquid is considered. Equations of motion and energy are presented in the forms that take into consideration the interaction between the motion and the growth. The fourth-order Runge-Kutta method is used to obtain a simultaneous solution of equations of motion and growth rate, and the solution is compared with available experimental results. Results for liquid sodium are presented for a range of pressures and Jakob numbers
Ordinary and partial differential equation routines in C, C++, Fortran, Java, Maple, and Matlab
Lee, HJ
2003-01-01
This book provides a set of ODE/PDE integration routines in the six most widely used computer languages, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems. This text concisely reviews integration algorithms and then analyzes the widely used Runge-Kutta method. It first presents a complete code before discussing its components in detail, focusing on integration concepts such as error monitoring and control. The format allows readers to understand the basics of ODE/PDE integration, and then calculate sample numerical solutions within the targeted program
Development of a simulator for design and test of power controllers in a TRIGA Mark III reactor
International Nuclear Information System (INIS)
Perez M, C.; Benitez R, J.S.; Lopez C, R.
2003-01-01
The development of a simulator that uses the Runge-Kutta-Fehlberg method to solve the model of the punctual kinetics of a nuclear research reactor type TRIGA. The simulator includes an algorithm of power control of the reactor based on the fuzzy logic, a friendly graphic interface which responds to the different user's petitions and that it shows numerical and graphically the results in real time. The user can modify the demanded power and to visualize the dynamic behavior of the one system. This simulator was developed in Visual Basic under an open architecture with which its will be prove different controllers for its analysis. (Author)
Effect of tunneling injection on the modulation response of quantum dot lasers
Directory of Open Access Journals (Sweden)
Y. Yekta kiya
2014-03-01
Full Text Available In this paper, modulation bandwidth characteristics of InGaAs/GaAs quantum dot (QD laser were theoretically investigated. Simulation was done by using the fourth order Runge-Kutta method. Effect of carrier relaxation life time, temperature and current density on characteristics of tunneling injection QD laser (TIL and conventional QD laser (CL were analyzed. Results showed that tunneling injection in QD laser increases the modulation bandwidth indicating that it is very useful for using in the fiber optic communication systems.
International Nuclear Information System (INIS)
Lopez, Fabio O.; Boutet, Luis I.; Bruno, Hector A.; Gavini, Ricardo M.
2004-01-01
A new methodology is presented to assess the evaluation of the radiological impact to the population, due to the discharges to the environment of liquids effluents of Central Nuclear Embalse (CNE), located in the Province of Cordoba (Argentina). In order to carry out the dose evaluation, a code denominated EDDELIQ was developed, in this code the calculation of the radionuclides concentration in the water lake is made by means of a simple physical model of the type of complete mixture. The physical model is solved numerically by means of Runge Kutta method of second order. (author)
A neuro approach to solve fuzzy Riccati differential equations
Energy Technology Data Exchange (ETDEWEB)
Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)
2015-10-22
There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.
Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.
2014-09-01
Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the
Cavaglieri, Daniele; Bewley, Thomas; Mashayek, Ali
2015-11-01
We present a new code, Diablo 2.0, for the simulation of the incompressible NSE in channel and duct flows with strong grid stretching near walls. The code leverages the fractional step approach with a few twists. New low-storage IMEX (implicit-explicit) Runge-Kutta time-marching schemes are tested which are superior to the traditional and widely-used CN/RKW3 (Crank-Nicolson/Runge-Kutta-Wray) approach; the new schemes tested are L-stable in their implicit component, and offer improved overall order of accuracy and stability with, remarkably, similar computational cost and storage requirements. For duct flow simulations, our new code also introduces a new smoother for the multigrid solver for the pressure Poisson equation. The classic approach, involving alternating-direction zebra relaxation, is replaced by a new scheme, dubbed tweed relaxation, which achieves the same convergence rate with roughly half the computational cost. The code is then tested on the simulation of a shear flow instability in a duct, a classic problem in fluid mechanics which has been the object of extensive numerical modelling for its role as a canonical pathway to energetic turbulence in several fields of science and engineering.
Explicit estimating equations for semiparametric generalized linear latent variable models
Ma, Yanyuan
2010-07-05
We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.
Implicit and explicit processes in social cognition
DEFF Research Database (Denmark)
Frith, Christopher; Frith, Uta
2008-01-01
In this review we consider research on social cognition in which implicit processes can be compared and contrasted with explicit, conscious processes. In each case, their function is distinct, sometimes complementary and sometimes oppositional. We argue that implicit processes in social interaction...... are automatic and are often opposed to conscious strategies. While we are aware of explicit processes in social interaction, we cannot always use them to override implicit processes. Many studies show that implicit processes facilitate the sharing of knowledge, feelings, and actions, and hence, perhaps...
The Role of Explicit and Impelicit Memory in Stutteres
Directory of Open Access Journals (Sweden)
Golavizh Karimi-Javan
2007-07-01
Full Text Available Objective: Stuttering is one of the most common speech disorders. However, its etiology is poorly understood, and is likely to be heterogeneous. Impairment of cognitive functions such as emotional memory and attention is one of the important factors. The aim of this research is to compare explicit and implicit memory between stutterers and normal individuals and also comparison of anxiety and depression between 2 groups. Materials & Methods: This is a case-control and analytical research.The participated individuals in this research were 30 male and female stutterers and the same number as the matched control group. The control group was matched for gender, age, education and bilingualism. The cue recall task performed to investigate explicit memory and the word stem completing task for implicit memory. The anxiety and depression of the individuals were measured by using general Hygiene Questionnaire (GHQ28 in this study. The performance of the individuals was measured based on positive and negative words in explicit and implicit memory and was compared with anxiety and depression score they obtained. Data was analyzed by using independent T-test, paired T-test, U-Man Witney and Willkaxon test. Results: The data indicated that stutterers recognized less emotionally positive words in explicit memory as compared with nonstutterers. Also, stutterers recognized more emotionally negative words as compared with emotionally positive words in explicit and implicit memory tasks (P<0/05. Additionally, stutterers showed more anxiety and depression as compared to nonstutterers. This difference was significant except for depression (P0.05. Conclusion: Taking into consideration the role of cognitive functions including emotional memory in motor speech programming and the difference in the function of positive versus negative emotional memories between stutterers and nonstutterers in this research, the role of emotional memory can be considered as an important
Modular invariants from simple currents. An explicit proof
International Nuclear Information System (INIS)
Schellekens, A.N.; Yankielowicz, S.
1989-01-01
In a previous paper an orbifold construction was used to demonstrate that the existence of primary fields with simple fusion rules in a conformal field theory implies the existence of non-diagonal modular invariant partition functions. Here we present a direct and explicit proof of modular invariance, which also covers a few cases that could not be obtained with the orbifold method. We also give a very simple general formula for the modular matrix M. (orig.)
Explicit solutions for exit-only radioactive decay chains
International Nuclear Information System (INIS)
Yuan, Ding; Kernan, Warnick
2007-01-01
In this study, we extended Bateman's [Proc. Cambridge Philos. Soc. 15, 423 (1910)] original work for solving radioactive decay chains and explicitly derived analytic solutions for generic exit-only radioactive decay problems under given initial conditions. Instead of using the conventional Laplace transform for solving Bateman's equations, we used a much simpler algebraic approach. Finally, we discuss methods of breaking down certain classes of large decay chains into collections of simpler chains for easy handling
Energy Technology Data Exchange (ETDEWEB)
López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es
2017-03-15
Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.
Wakif, Abderrahim; Boulahia, Zoubair; Sehaqui, Rachid
2018-06-01
The main aim of the present analysis is to examine the electroconvection phenomenon that takes place in a dielectric nanofluid under the influence of a perpendicularly applied alternating electric field. In this investigation, we assume that the nanofluid has a Newtonian rheological behavior and verifies the Buongiorno's mathematical model, in which the effects of thermophoretic and Brownian diffusions are incorporated explicitly in the governing equations. Moreover, the nanofluid layer is taken to be confined horizontally between two parallel plate electrodes, heated from below and cooled from above. In a fast pulse electric field, the onset of electroconvection is due principally to the buoyancy forces and the dielectrophoretic forces. Within the framework of the Oberbeck-Boussinesq approximation and the linear stability theory, the governing stability equations are solved semi-analytically by means of the power series method for isothermal, no-slip and non-penetrability conditions. In addition, the computational implementation with the impermeability condition implies that there exists no nanoparticles mass flux on the electrodes. On the other hand, the obtained analytical solutions are validated by comparing them to those available in the literature for the limiting case of dielectric fluids. In order to check the accuracy of our semi-analytical results obtained for the case of dielectric nanofluids, we perform further numerical and semi-analytical computations by means of the Runge-Kutta-Fehlberg method, the Chebyshev-Gauss-Lobatto spectral method, the Galerkin weighted residuals technique, the polynomial collocation method and the Wakif-Galerkin weighted residuals technique. In this analysis, the electro-thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical AC electric Rayleigh number Rec , whose value depends on several physical parameters. Furthermore, the effects of various pertinent parameters on the electro
Antichrist, Explicit Sex, Anxiety, and Care
DEFF Research Database (Denmark)
Grodal, Torben Kragh
2015-01-01
The article analyzes how von Trier's Antichrist uses explicit sex to discuss the relation between fear of human embodiment and a longing for care and spiritual intimacy. It discusses how lyrical episodes contrasts descriptions of embodied degradation and experiences of being imprisoned in the body....
EXPLICIT PLANNING FOR PARAGRAPH WRITING CLASS
Directory of Open Access Journals (Sweden)
Lestari Setyowati
2017-11-01
Full Text Available The purpose of the study is to improve the students writing ability for paragraph writing class. The subjects of the study were 37 students of English Education Study Program who joined the paragraph writing class. The design of the study was Classroom Action Research with two cycles. Cycle 1 consisted of three meetings, and cycle 2 consisted of two meetings. The types of explicit planning used in the action research were word listing and word mapping with phrases and sentence for detail. The instruments used were direct writing test, observation, and documentation of students’ reflective essay. To score the students’ writing, two raters were asked to rate the composition by using Jacobs ESL Composition profile scoring rubric. The finding shows that the use of explicit planning was able to improve the students’ paragraph writing performance, indicated with the achievement of the criteria of success. The students’ mean improved from cycle 1 (74.62 to cycle2 (76.78. Although explicit planning instruction was able to help the students to write better, data from their self-reflection essay showed that many of the students preferred to use free writing instead of explicit planning instruction.
Orchestrating Semiotic Resources in Explicit Strategy Instruction
Shanahan, Lynn E.; Flury-Kashmanian, Caroline
2014-01-01
Research and pedagogical information provided to teachers on implementing explicit strategy instruction has primarily focused on teachers' speech, with limited attention to other modes of communication, such as gesture and artefacts. This interpretive case study investigates two teachers' use of different semiotic resources when introducing…
Explicit Instruction Elements in Core Reading Programs
Child, Angela R.
2012-01-01
Classroom teachers are provided instructional recommendations for teaching reading from their adopted core reading programs (CRPs). Explicit instruction elements or what is also called instructional moves, including direct explanation, modeling, guided practice, independent practice, discussion, feedback, and monitoring, were examined within CRP…
Sleep Enhances Explicit Recollection in Recognition Memory
Drosopoulos, Spyridon; Wagner, Ullrich; Born, Jan
2005-01-01
Recognition memory is considered to be supported by two different memory processes, i.e., the explicit recollection of information about a previous event and an implicit process of recognition based on a contextual sense of familiarity. Both types of memory supposedly rely on distinct memory systems. Sleep is known to enhance the consolidation of…
Implicit and explicit prejudice and interracial interaction
Dovidio, J.F.; Kawakami, K.L.; Gaertner, S.L.
2002-01-01
The present research examined how implicit racial associations and explicit racial attitudes of Whites relate to behaviors and impressions in interracial interactions, Specifically, the authors examined how response latency and self-report measures predicted bias and perceptions of bias in verbal
Explicit Covariance Matrix for Particle Measurement Precision
Karimäki, Veikko
1997-01-01
We derive explicit and precise formulae for 3 by 3 error matrix of the particle transverse momentum, direction and impact parameter. The error matrix elements are expressed as functions of up to fourth order statistical moments of the measured coordinates. The formulae are valid for any curvature and track length in case of negligible multiple scattering.
Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan
1992-01-01
Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.
Newman, James C., III
1995-01-01
The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary problems are evaluated. These are namely the structured-overlapped and the unstructured grid schemes. Both methods use a cell centered, finite volume, upwind approach. The structured-overlapped algorithm uses an approximately factored, alternating direction implicit scheme to perform the time integration, whereas, the unstructured algorithm uses an explicit Runge-Kutta method. To examine the accuracy, efficiency, and limitations of each scheme, they are applied to the same steady complex multicomponent configurations and unsteady moving boundary problems. The steady complex cases consist of computing the subsonic flow about a two-dimensional high-lift multielement airfoil and the transonic flow about a three-dimensional wing/pylon/finned store assembly. The unsteady moving boundary problems are a forced pitching oscillation of an airfoil in a transonic freestream and a two-dimensional, subsonic airfoil/store separation sequence. Accuracy was accessed through the comparison of computed and experimentally measured pressure coefficient data on several of the wing/pylon/finned store assembly's components and at numerous angles-of-attack for the pitching airfoil. From this study, it was found that both the structured-overlapped and the unstructured grid schemes yielded flow solutions of
The shallow water equations in Lagrangian coordinates
International Nuclear Information System (INIS)
Mead, J.L.
2004-01-01
Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. We apply numerical methods traditionally used to solve differential equations in Eulerian coordinates, to solve the shallow water equations in Lagrangian coordinates. The difficulty with solving in Lagrangian coordinates is that the transformation from Eulerian coordinates results in solving a highly nonlinear partial differential equation. The non-linearity is mainly due to the Jacobian of the coordinate transformation, which is a precise record of how the particles are rotated and stretched. The inverse Jacobian must be calculated, thus Lagrangian coordinates cannot be used in instances where the Jacobian vanishes. For linear (spatial) flows we give an explicit formula for the Jacobian and describe the two situations where the Lagrangian shallow water equations cannot be used because either the Jacobian vanishes or the shallow water assumption is violated. We also prove that linear (in space) steady state solutions of the Lagrangian shallow water equations have Jacobian equal to one. In the situations where the shallow water equations can be solved in Lagrangian coordinates, accurate numerical solutions are found with finite differences, the Chebyshev pseudospectral method, and the fourth order Runge-Kutta method. The numerical results shown here emphasize the need for high order temporal approximations for long time integrations
Finding all flux vacua in an explicit example
Energy Technology Data Exchange (ETDEWEB)
Martinez-Pedrera, Danny; Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Mehta, Dhagash [Syracuse Univ., NY (United States). Dept. of Physics; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2012-12-15
We explicitly construct all supersymmetric flux vacua of a particular Calabi-Yau compactification of type IIB string theory for a small number of flux carrying cycles and a given D3-brane tadpole. The analysis is performed in the large complex structure region by using the polynomial homotopy continuation method, which allows to find all stationary points of the polynomial equations that characterize the supersymmetric vacuum solutions. The number of vacua as a function of the D3 tadpole is in agreement with statistical studies in the literature. We calculate the available tuning of the cosmological constant from fluxes and extrapolate to scenarios with a larger number of flux carrying cycles. We also verify the range of scales for the moduli and gravitino masses recently found for a single explicit flux choice giving a Kaehler uplifted de Sitter vacuum in the same construction.
Parallel alternating direction preconditioner for isogeometric simulations of explicit dynamics
Łoś, Marcin
2015-04-27
In this paper we present a parallel implementation of the alternating direction preconditioner for isogeometric simulations of explicit dynamics. The Alternating Direction Implicit (ADI) algorithm, belongs to the category of matrix-splitting iterative methods, was proposed almost six decades ago for solving parabolic and elliptic partial differential equations, see [1–4]. The new version of this algorithm has been recently developed for isogeometric simulations of two dimensional explicit dynamics [5] and steady-state diffusion equations with orthotropic heterogenous coefficients [6]. In this paper we present a parallel version of the alternating direction implicit algorithm for three dimensional simulations. The algorithm has been incorporated as a part of PETIGA an isogeometric framework [7] build on top of PETSc [8]. We show the scalability of the parallel algorithm on STAMPEDE linux cluster up to 10,000 processors, as well as the convergence rate of the PCG solver with ADI algorithm as preconditioner.
Exact error estimation for solutions of nuclide chain equations
International Nuclear Information System (INIS)
Tachihara, Hidekazu; Sekimoto, Hiroshi
1999-01-01
The exact solution of nuclide chain equations within arbitrary figures is obtained for a linear chain by employing the Bateman method in the multiple-precision arithmetic. The exact error estimation of major calculation methods for a nuclide chain equation is done by using this exact solution as a standard. The Bateman, finite difference, Runge-Kutta and matrix exponential methods are investigated. The present study confirms the following. The original Bateman method has very low accuracy in some cases, because of large-scale cancellations. The revised Bateman method by Siewers reduces the occurrence of cancellations and thereby shows high accuracy. In the time difference method as the finite difference and Runge-Kutta methods, the solutions are mainly affected by the truncation errors in the early decay time, and afterward by the round-off errors. Even though the variable time mesh is employed to suppress the accumulation of round-off errors, it appears to be nonpractical. Judging from these estimations, the matrix exponential method is the best among all the methods except the Bateman method whose calculation process for a linear chain is not identical with that for a general one. (author)
2.5-D poroelastic wave modelling in double porosity media
Liu, Xu; Greenhalgh, Stewart; Wang, Yanghua
2011-09-01
To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as a way to represent the sum of the convolution integrals for both the solid particle velocity and the macroscopic fluid flux in the governing equations. By application of the memory equations, the field quantities at every time step need not be stored. However, this approximation allows just two Zener relaxation times to represent the very complex double porosity and dual permeability attenuation mechanism, and thus reduce the difficulty. The 2.5-D governing equations are numerically solved by a time-splitting method for the non-stiff parts and an explicit fourth-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. The 2.5-D solution has the advantage of producing a 3-D wavefield (point source) for a 2-D model but is much more computationally efficient than the full 3-D solution. As an illustrative example, we firstly show the computed 2.5-D wavefields in a homogeneous single porosity model for which we reformulated an analytic solution. Results for a two-layer, water-saturated double porosity model and a laterally heterogeneous double porosity structure are also presented.
Depletion benchmarks calculation of random media using explicit modeling approach of RMC
International Nuclear Information System (INIS)
Liu, Shichang; She, Ding; Liang, Jin-gang; Wang, Kan
2016-01-01
Highlights: • Explicit modeling of RMC is applied to depletion benchmark for HTGR fuel element. • Explicit modeling can provide detailed burnup distribution and burnup heterogeneity. • The results would serve as a supplement for the HTGR fuel depletion benchmark. • The method of adjacent burnup regions combination is proposed for full-core problems. • The combination method can reduce memory footprint, keeping the computing accuracy. - Abstract: Monte Carlo method plays an important role in accurate simulation of random media, owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. Three stochastic geometry modeling methods including Random Lattice Method, Chord Length Sampling and explicit modeling approach with mesh acceleration technique, have been implemented in RMC to simulate the particle transport in the dispersed fuels, in which the explicit modeling method is regarded as the best choice. In this paper, the explicit modeling method is applied to the depletion benchmark for HTGR fuel element, and the method of combination of adjacent burnup regions has been proposed and investigated. The results show that the explicit modeling can provide detailed burnup distribution of individual TRISO particles, and this work would serve as a supplement for the HTGR fuel depletion benchmark calculations. The combination of adjacent burnup regions can effectively reduce the memory footprint while keeping the computational accuracy.
Al Jarro, Ahmed; Salem, Mohamed; Bagci, Hakan; Benson, Trevor; Sewell, Phillip D.; Vuković, Ana
2012-01-01
An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.
Al Jarro, Ahmed
2012-11-01
An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.
Explicit K-symplectic algorithms for charged particle dynamics
International Nuclear Information System (INIS)
He, Yang; Zhou, Zhaoqi; Sun, Yajuan; Liu, Jian; Qin, Hong
2017-01-01
We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.
Explicit K-symplectic algorithms for charged particle dynamics
Energy Technology Data Exchange (ETDEWEB)
He, Yang [School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 (China); Zhou, Zhaoqi [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China); Sun, Yajuan, E-mail: sunyj@lsec.cc.ac.cn [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Liu, Jian [Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 (China); Qin, Hong [Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States)
2017-02-12
We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.
Efficacy of an explicit handwriting program.
Kaiser, Marie-Laure; Albaret, Jean-Michel; Doudin, Pierre-André
2011-04-01
The aim of this study was to investigate the effects of an explicit handwriting program introduced during the first grade of elementary school. Grade 1 children (N=23) with an age range of 6.1 to 7.4 yr. (15 girls, 8 boys) were administered an additional handwriting program of two weekly sessions of 45 min. over six weeks. Another group of 19 Grade 1 children (11 girls, 8 boys) received only the regular handwriting program of one weekly session. The Concise Assessment Scale for Children's Handwriting was administered to measure the changes in quality and speed of handwriting. The children given the explicit program showed better quality and speed of handwriting than did the control group. Their handwriting was more regular, with fewer ambiguous letters and fewer incorrect relative heights.
International Nuclear Information System (INIS)
Zhang, Ruili; Tang, Yifa; Zhu, Beibei; Liu, Jian; Xiao, Jianyuan; Qin, Hong
2014-01-01
The gyrocenter dynamics of charged particles in time-independent magnetic fields is a non-canonical Hamiltonian system. The canonical description of the gyrocenter has both theoretical and practical importance. We provide a general procedure of the gyrocenter canonicalization, which is expressed by the series of a small variable ϵ depending only on the parallel velocity u and can be expressed in a recursive manner. We prove that the truncation of the series to any given order generates a set of exact canonical coordinates for a system, whose Lagrangian approximates to that of the original gyrocenter system in the same order. If flux surfaces exist for the magnetic field, the series stops simply at the second order and an exact canonical form of the gyrocenter system is obtained. With the canonicalization schemes, the canonical symplectic simulation of gyrocenter dynamics is realized for the first time. The canonical symplectic algorithm has the advantage of good conservation properties and long-term numerical accuracy, while avoiding numerical instability. It is worth mentioning that explicitly expressing the canonical Hamiltonian in new coordinates is usually difficult and impractical. We give an iteration procedure that is easy to implement in the original coordinates associated with the coordinate transformation. This is crucial for modern large-scale simulation studies in plasma physics. The dynamics of gyrocenters in the dipole magnetic field and in the toroidal geometry are simulated using the canonical symplectic algorithm by comparison with the higher-order non symplectic Runge-Kutta scheme. The overwhelming superiorities of the symplectic method for the gyrocenter system are evidently exhibited
Implicit and explicit attitudes among students
Félix Neto
2009-01-01
Mental processing and mental experience is not the same thing. The former is the operation of the mind; the latter is the subjective life that emerges from these operations. In social evaluation, implicit and explicit attitudes express this distinction. https://implicit.harvard.edu/ was created to provide experience with the Implicit Association Test (IAT) a procedure designed to measure social knowledge that may operate outside of awareness. In this paper we examined the relationships betwee...
Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul
In this article, one and two-dimensional hydrodynamical models of semiconductor devices are numerically investigated. The models treat the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. Mathematically, the governing equations form a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the kinetic flux-vector splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct splitting of macroscopic flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the splitting scheme based on the NT central scheme. The effects of various parameters such as low field mobility, device length, lattice temperature and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations. A two dimensional simulation is also performed by KFVS method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.
Krysko, V. A.; Awrejcewicz, J.; Krylova, E. Yu; Papkova, I. V.; Krysko, A. V.
2018-06-01
Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.
A mixed implicit/explicit procedure for soil-structure interaction
International Nuclear Information System (INIS)
Kunar, R.R.
1982-01-01
This paper describes an efficient method for the solution of dynamic soil-structure interaction problems. The method which combines implicit and explicit time integration procedures is ideally suited to problems in which the structure is considered linear and the soil non-linear. The equations relating to the linear structures are integrated using an unconditionally stable implicit scheme while the non-linear soil is treated explicitly. The explicit method is ideally suited to non-linear calculations as there is no need for iterative techniques. The structural equations can also be integrated explicitly, but this generally requires a time step that is much smaller than that for the soil. By using an unconditionally stable implicit algorithm for the structure, the complete analysis can be performed using the time step for the soil. The proposed procedure leads to economical solutions with the soil non-linearities handled accurately and efficiently. (orig.)
Suslow, Thomas; Donges, Uta-Susan
2017-01-01
Alexithymia represents a multifaceted personality construct defined by difficulties in recognizing and verbalizing emotions and externally oriented thinking. According to clinical observations, experience of negative affects is exacerbated and experience of positive affects is decreased in alexithymia. Findings from research based on self-report indicate that all alexithymia facets are negatively associated with the experience of positive affects, whereas difficulties identifying and describing feelings are related to heightened negative affect. Implicit affectivity, which can be measured using indirect assessment methods, relates to processes of the impulsive system. The aim of the present study was to examine, for the first time, the relations between alexithymia components and implicit and explicit positive and negative affectivity in healthy adults. The 20-item Toronto Alexithymia Scale, the Implicit Positive and Negative Affect Test and the Positive and Negative Affect Schedule (PANAS) were administered to two hundred and forty-one healthy individuals along with measures of depression and trait anxiety. Difficulties identifying feelings were correlated with explicit negative trait affect, depressive mood and trait anxiety. Difficulties describing feelings showed smaller but also significant correlations with depressive mood and trait anxiety but were not correlated with explicit state or trait affect as assessed by the PANAS. Externally oriented thinking was not significantly correlated with any of the implicit and explicit affect measures. According to our findings, an externally oriented, concrete way of thinking appears to be generally unrelated to dispositions to develop positive or negative affects. Difficulties identifying feelings seem to be associated with increased conscious negative affects but not with a heightened disposition to develop negative affects at an automatic response level.
Directory of Open Access Journals (Sweden)
Thomas Suslow
2017-10-01
Full Text Available Alexithymia represents a multifaceted personality construct defined by difficulties in recognizing and verbalizing emotions and externally oriented thinking. According to clinical observations, experience of negative affects is exacerbated and experience of positive affects is decreased in alexithymia. Findings from research based on self-report indicate that all alexithymia facets are negatively associated with the experience of positive affects, whereas difficulties identifying and describing feelings are related to heightened negative affect. Implicit affectivity, which can be measured using indirect assessment methods, relates to processes of the impulsive system. The aim of the present study was to examine, for the first time, the relations between alexithymia components and implicit and explicit positive and negative affectivity in healthy adults. The 20-item Toronto Alexithymia Scale, the Implicit Positive and Negative Affect Test and the Positive and Negative Affect Schedule (PANAS were administered to two hundred and forty-one healthy individuals along with measures of depression and trait anxiety. Difficulties identifying feelings were correlated with explicit negative trait affect, depressive mood and trait anxiety. Difficulties describing feelings showed smaller but also significant correlations with depressive mood and trait anxiety but were not correlated with explicit state or trait affect as assessed by the PANAS. Externally oriented thinking was not significantly correlated with any of the implicit and explicit affect measures. According to our findings, an externally oriented, concrete way of thinking appears to be generally unrelated to dispositions to develop positive or negative affects. Difficulties identifying feelings seem to be associated with increased conscious negative affects but not with a heightened disposition to develop negative affects at an automatic response level.
Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning
Bradley, Ben K.
Motivated by the growing space catalog and the demands for precise orbit determination with shorter latency for science and reconnaissance missions, this research improves the computational performance of orbit propagation through more efficient and precise numerical integration and frame transformation implementations. Propagation of satellite orbits is required for astrodynamics applications including mission design, orbit determination in support of operations and payload data analysis, and conjunction assessment. Each of these applications has somewhat different requirements in terms of accuracy, precision, latency, and computational load. This dissertation develops procedures to achieve various levels of accuracy while minimizing computational cost for diverse orbit determination applications. This is done by addressing two aspects of orbit determination: (1) numerical integration used for orbit propagation and (2) precise frame transformations necessary for force model evaluation and station coordinate rotations. This dissertation describes a recently developed method for numerical integration, dubbed Bandlimited Collocation Implicit Runge-Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. It requires significantly fewer force function evaluations than explicit Runge-Kutta schemes and approaches the efficiency of the 8th-order Gauss-Jackson multistep method. Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit propagation, orbit determination, and analyzing geoscience data from satellite missions. This dissertation provides simplifications to the Celestial Intermediate Origin (CIO) transformation scheme and Earth orientation parameter (EOP) storage for use in positioning and
Study of the acceleration of nuclide burnup calculation using GPU with CUDA
International Nuclear Information System (INIS)
Okui, S.; Ohoka, Y.; Tatsumi, M.
2009-01-01
The computation costs of neutronics calculation code become higher as physics models and methods are complicated. The degree of them in neutronics calculation tends to be limited due to available computing power. In order to open a door to the new world, use of GPU for general purpose computing, called GPGPU, has been studied [1]. GPU has multi-threads computing mechanism enabled with multi-processors which realize mush higher performance than CPUs. NVIDIA recently released the CUDA language for general purpose computation which is a C-like programming language. It is relatively easy to learn compared to the conventional ones used for GPGPU, such as OpenGL or CG. Therefore application of GPU to the numerical calculation became much easier. In this paper, we tried to accelerate nuclide burnup calculation, which is important to predict nuclides time dependence in the core, using GPU with CUDA. We chose the 4.-order Runge-Kutta method to solve the nuclide burnup equation. The nuclide burnup calculation and the 4.-order Runge-Kutta method were suitable to the first step of introduction CUDA into numerical calculation because these consist of simple operations of matrices and vectors of single precision where actual codes were written in the C++ language. Our experimental results showed that nuclide burnup calculations with GPU have possibility of speedup by factor of 100 compared to that with CPU. (authors)
International Nuclear Information System (INIS)
Hamm, L.L.; Van Brunt, V.
1982-08-01
A comparison of implicit Runge-Kutta and orthogonal collocation methods is made for the numerical solution to the ordinary differential equation which describes the high-pressure vapor-liquid equilibria of a binary system. The systems of interest are limited to binary solubility systems where one of the components is supercritical and exists as a noncondensable gas in the pure state. Of the two methods - implicit Runge-Kuta and orthogonal collocation - this paper attempts to present some preliminary but not necessarily conclusive results that the implicit Runge-Kutta method is superior for the solution to the ordinary differential equation utilized in the thermodynamic consistency testing of binary solubility systems. Due to the extreme nonlinearity of thermodynamic properties in the region near the critical locus, an extended cubic spline fitting technique is devised for correlating the P-x data. The least-squares criterion is employed in smoothing the experimental data. Even though the derivation is presented specifically for the correlation of P-x data, the technique could easily be applied to any thermodynamic data by changing the endpoint requirements. The volumetric behavior of the systems must be given or predicted in order to perform thermodynamic consistency tests. A general procedure is developed for predicting the volumetric behavior required and some indication as to the expected limit of accuracy is given
Implicit and explicit timing in oculomotor control.
Directory of Open Access Journals (Sweden)
Ilhame Ameqrane
Full Text Available The passage of time can be estimated either explicitly, e.g. before leaving home in the morning, or implicitly, e.g. when catching a flying ball. In the present study, the latency of saccadic eye movements was used to evaluate differences between implicit and explicit timing. Humans were required to make a saccade between a central and a peripheral position on a computer screen. The delay between the extinction of a central target and the appearance of an eccentric target was the independent variable that could take one out of four different values (400, 900, 1400 or 1900 ms. In target trials, the delay period lasted for one of the four durations randomly. At the end of the delay, a saccade was initiated by the appearance of an eccentric target. Cue&target trials were similar to target trials but the duration of the delay was visually cued. In probe trials, the duration of the upcoming delay was cued, but there was no eccentric target and subjects had to internally generate a saccade at the estimated end of the delay. In target and cue&target trials, the mean and variance of latency distributions decreased as delay duration increased. In cue&target trials latencies were shorter. In probe trials, the variance increased with increasing delay duration and scalar variability was observed. The major differences in saccadic latency distributions were observed between visually-guided (target and cue&target trials and internally-generated saccades (probe trials. In target and cue&target trials the timing of the response was implicit. In probe trials, the timing of the response was internally-generated and explicitly based on the duration of the visual cue. Scalar timing was observed only during probe trials. This study supports the hypothesis that there is no ubiquitous timing system in the brain but independent timing processes active depending on task demands.
Explicit field realizations of W algebras
International Nuclear Information System (INIS)
Wei Shaowen; Liu Yuxiao; Ren Jirong; Zhang Lijie
2009-01-01
The fact that certain nonlinear W 2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W 2,s algebras from linear W 1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W 1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W 2,s algebras are presented. The results show that all these realizations are Romans-type realizations.
Sexually explicit media use and relationship satisfaction
DEFF Research Database (Denmark)
Veit, Maria; Stulhofer, Aleksandar; Hald, Gert Martin
2017-01-01
Using a cross-sectional questionnaire design and a sample of 2284 coupled Croatian adults, this study investigated the association between Sexually Explicit Media (SEM) use and relationship satisfaction. Further, possible moderation of emotional intimacy on the relationship between SEM use...... and relationship satisfaction was investigated. Controlling for sociodemographic, psychosexual and relationship variables, no significant association between SEM use and relationship satisfaction was found. However, among men, a moderating effect of emotional intimacy was found. Thus, higher SEM use was found...... to be significantly associated with lower relationship satisfaction only among men who reported lower levels of emotional intimacy with their partner....
Explicit field realizations of W algebras
Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong
2009-01-01
The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$ algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct the explicit field realizations of linear $W_{1,2,s}$ algebras with double-scalar and double-spinor, respectively. Then, after a change of basis, the realizations of $W_{2,s}$ algebras are presented. The results show that all these realizations are Romans-type realiz...
Explicit MDS Codes with Complementary Duals
DEFF Research Database (Denmark)
Beelen, Duals Peter; Jin, Lingfei
2018-01-01
In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have been extensively studied in literature....... On the other hand, MDS codes form an optimal family of classical codes which have wide applications in both theory and practice. The main purpose of this paper is to give an explicit construction of several classes of LCD MDS codes, using tools from algebraic function fields. We exemplify this construction...
Research on transient thermal process of a friction brake during repetitive cycles of operation
Slavchev, Yanko; Dimitrov, Lubomir; Dimitrov, Yavor
2017-12-01
Simplified models are used in the classical engineering analyses of the friction brake heating temperature during repetitive cycles of operation to determine basically the maximum and minimum brake temperatures. The objective of the present work is to broaden and complement the possibilities for research through a model that is based on the classical scheme of the Newton's law of cooling and improves the studies by adding a disturbance function for a corresponding braking process. A general case of braking in non-periodic repetitive mode is considered, for which a piecewise function is defined to apply pulse thermal loads to the system. Cases with rectangular and triangular waveforms are presented. Periodic repetitive braking process is also studied using a periodic rectangular waveform until a steady thermal state is achieved. Different numerical methods such as the Euler's method, the classical fourth order Runge-Kutta (RK4) and the Runge-Kutta-Fehlberg 4-5 (RKF45) are used to solve the non-linear differential equation of the model. The constructed model allows during pre-engineering calculations to be determined effectively the time for reaching the steady thermal state of the brake, to be simulated actual braking modes in vehicles and material handling machines, and to be accounted for the thermal impact when performing fatigue calculations.
Jain, Madhu; Meena, Rakesh Kumar
2018-03-01
Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the servers. The server returns back to render repair job when the pre-specified workload of failed machines is build up. The first (second) repairman turns on only when the work load of N1 (N2) failed machines is accumulated in the system. The both servers may go for vacation in case when all the machines are in good condition and there are no pending repair jobs for the repairmen. Runge-Kutta method is implemented to solve the set of governing equations used to formulate the Markov model. Various system metrics including the mean queue length, machine availability, throughput, etc., are derived to determine the performance of the machining system. To provide the computational tractability of the present investigation, a numerical illustration is provided. A cost function is also constructed to determine the optimal repair rate of the server by minimizing the expected cost incurred on the system. The hybrid soft computing method is considered to develop the adaptive neuro-fuzzy inference system (ANFIS). The validation of the numerical results obtained by Runge-Kutta approach is also facilitated by computational results generated by ANFIS.
Explicit signal to noise ratio in reproducing kernel Hilbert spaces
DEFF Research Database (Denmark)
Gomez-Chova, Luis; Nielsen, Allan Aasbjerg; Camps-Valls, Gustavo
2011-01-01
This paper introduces a nonlinear feature extraction method based on kernels for remote sensing data analysis. The proposed approach is based on the minimum noise fraction (MNF) transform, which maximizes the signal variance while also minimizing the estimated noise variance. We here propose...... an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted...
Guzel Isayevna Gumerova; Elmira Shamilevna Shaimieva
2015-01-01
Objective to define the notion of ldquohightech businessrdquo to elaborate classification of hightech businesses to elaborate the business model for hightech business management. Methods general scientific methods of theoretical and empirical cognition. Results the research presents a business model of hightech businesses management basing on the trends of explicit and explicit knowledge market with the dominating implicit knowledge market classification of hightech business...
Explicit symplectic algorithms based on generating functions for charged particle dynamics
Zhang, Ruili; Qin, Hong; Tang, Yifa; Liu, Jian; He, Yang; Xiao, Jianyuan
2016-07-01
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of H (x ,p ) =pif (x ) or H (x ,p ) =xig (p ) . Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.
Implicit and Explicit Memory Bias in Opiate Dependent, Abstinent and Normal Individuals
Directory of Open Access Journals (Sweden)
Jafar Hasani
2013-07-01
Full Text Available Objective: The aim of current research was to assess implicit and explicit memory bias to drug related stimuli in opiate Dependent, abstinent and normal Individuals. Method: Three groups including opiate Dependent, abstinent and normal Individuals (n=25 were selected by available sampling method. After matching on the base of age, education level and type of substance use all participants assessed by recognition task (explicit memory bias and stem completion task (implicit memory bias. Results: The analysis of data showed that opiate dependent and abstinent groups in comparison with normal individual had implicit memory bias, whereas in explicit memory only opiate dependent individuals showed bias. Conclusion: The identification of explicit and implicit memory governing addiction may have practical implications in diagnosis, treatment and prevention of substance abuse.
Spatially explicit modelling of cholera epidemics
Finger, F.; Bertuzzo, E.; Mari, L.; Knox, A. C.; Gatto, M.; Rinaldo, A.
2013-12-01
Epidemiological models can provide crucial understanding about the dynamics of infectious diseases. Possible applications range from real-time forecasting and allocation of health care resources to testing alternative intervention mechanisms such as vaccines, antibiotics or the improvement of sanitary conditions. We apply a spatially explicit model to the cholera epidemic that struck Haiti in October 2010 and is still ongoing. The dynamics of susceptibles as well as symptomatic and asymptomatic infectives are modelled at the scale of local human communities. Dissemination of Vibrio cholerae through hydrological transport and human mobility along the road network is explicitly taken into account, as well as the effect of rainfall as a driver of increasing disease incidence. The model is calibrated using a dataset of reported cholera cases. We further model the long term impact of several types of interventions on the disease dynamics by varying parameters appropriately. Key epidemiological mechanisms and parameters which affect the efficiency of treatments such as antibiotics are identified. Our results lead to conclusions about the influence of different intervention strategies on the overall epidemiological dynamics.
Energy Technology Data Exchange (ETDEWEB)
Khan, Masood [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hashim, E-mail: hashim_alik@yahoo.com [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hussain, M. [Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad 44000 (Pakistan); Azam, M. [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan)
2016-08-15
This paper presents a study of the magnetohydrodynamic (MHD) boundary layer flow of a non-Newtonian Carreau fluid over a convectively heated surface. The analysis of heat transfer is further performed in the presence of non-linear thermal radiation. The appropriate transformations are employed to bring the governing equations into dimensionless form. The numerical solutions of the partially coupled non-linear ordinary differential equations are obtained by using the Runge-Kutta Fehlberg integration scheme. The influence of non-dimensional governing parameters on the velocity, temperature, local skin friction coefficient and local Nusselt number is studied and discussed with the help of graphs and tables. Results proved that there is significant decrease in the velocity and the corresponding momentum boundary layer thickness with the growth in the magnetic parameter. However, a quite the opposite is true for the temperature and the corresponding thermal boundary layer thickness. - Highlights: • We investigated the Magnetohydrodynamic flow of Carreau constitutive fluid model. • Impact of non-linear thermal radiation is further taken into account. • Runge-Kutta Fehlberg method is employed to obtain the numerical solutions. • Fluid velocity is higher in case of hydromagnetic flow in comparison with hydrodynamic flow. • The local Nusselt number is a decreasing function of the thermal radiation parameter.
Explicit Building Block Multiobjective Evolutionary Computation: Methods and Applications
2005-06-16
Ciencia , Tecnologia , Inovaçao do Quadro Comunitário de Apoio III de Fundaçao para a Ciencia e Tecnologia ...Phenotype Function C on n ec te d D is co n n ec te d S y m m et ri c S ca la b le S ol u ti on T y p e( s) O b je ct iv es S id e C on st ra in ts G...ni=1(xi + 1√n ) 2 ) Ptrue concave, number of decision vars VL3:MOP 3 Max(F), where F = (f1(x, y ), f2(x, y )) −π ≤ x, y ≤ π
Implicit and explicit interethnic attitudes and ethnic discrimination in hiring
Blommaert, E.C.C.A.; Tubergen, F.A. van; Coenders, M.T.A.
2012-01-01
We study effects of explicit and implicit interethnic attitudes on ethnic discrimination in hiring. Unlike explicit attitudes, implicit attitudes are characterised by reduced controllability, awareness or intention. Effects of implicit interethnic attitudes on ethnic discrimination in the labour
Explicit estimating equations for semiparametric generalized linear latent variable models
Ma, Yanyuan; Genton, Marc G.
2010-01-01
which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n
A General Symbolic PDE Solver Generator: Beyond Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1 arbitrary number of dependent variables, (2 arbitrary dimensionality, and (3 arbitrary geometry, as well as (4 developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.
Developmental Differences in Implicit and Explicit Memory Performance.
Perez, Lori A.; Peynircioglu, Zehra F.; Blaxton, Teresa A.
1998-01-01
Compared perceptual and conceptual implicit and explicit memory performance of preschool, elementary, and college students. Found that conceptual explicit memory improved with age. Perceptual explicit memory and implicit memory showed no developmental change. Perceptual processing during study led to better performance than conceptual processing…
Narcissistic Traits and Explicit Self-Esteem: The Moderating Role of Implicit Self-view
Directory of Open Access Journals (Sweden)
Rossella Di Pierro
2016-11-01
Full Text Available Objective: Whilst the relationship between narcissism and self-esteem has been studied for a long time, findings are still controversial. The majority of studies investigated narcissistic grandiosity, neglecting the existence of vulnerable manifestations of narcissism. Moreover, recent studies have shown that grandiosity traits are not always associated with inflated explicit self-esteem. The aim of the present study is to investigate the relationship between narcissistic traits and explicit self-esteem, distinguishing between grandiosity and vulnerability. Moreover, we consider the role of implicit self-esteem in qualifying these associations.Method: Narcissistic traits, explicit and implicit self-esteem measures were assessed among 120 university students (55.8% women, Mage = 22.55, SD = 3.03.Results: Results showed different patterns of association between narcissistic traits and explicit self-esteem, depending on phenotypic manifestations of narcissism. Narcissistic vulnerability was linked to low explicit self-evaluations regardless of one’s levels of implicit self-esteem. On the other hand, the link between narcissistic grandiosity and explicit self-esteem was qualified by levels of implicit self-views, such that grandiosity was significantly associated with inflated explicit self-evaluations only at either high or medium levels of implicit self-views.Discussion: These findings showed that the relationship between narcissistic traits and explicit self-esteem is not univocal, highlighting the importance of distinguishing between narcissistic grandiosity and narcissistic vulnerability. Finally, the study suggested that both researchers and clinicians should consider the relevant role of implicit self-views in conditioning self-esteem levels reported explicitly by individuals with grandiose narcissistic traits.
Narcissistic Traits and Explicit Self-Esteem: The Moderating Role of Implicit Self-View
Di Pierro, Rossella; Mattavelli, Simone; Gallucci, Marcello
2016-01-01
Objective: Whilst the relationship between narcissism and self-esteem has been studied for a long time, findings are still controversial. The majority of studies investigated narcissistic grandiosity (NG), neglecting the existence of vulnerable manifestations of narcissism. Moreover, recent studies have shown that grandiosity traits are not always associated with inflated explicit self-esteem. The aim of the present study is to investigate the relationship between narcissistic traits and explicit self-esteem, distinguishing between grandiosity and vulnerability. Moreover, we consider the role of implicit self-esteem in qualifying these associations. Method: Narcissistic traits, explicit and implicit self-esteem measures were assessed among 120 university students (55.8% women, Mage = 22.55, SD = 3.03). Results: Results showed different patterns of association between narcissistic traits and explicit self-esteem, depending on phenotypic manifestations of narcissism. Narcissistic vulnerability (NV) was linked to low explicit self-evaluations regardless of one’s levels of implicit self-esteem. On the other hand, the link between NG and explicit self-esteem was qualified by levels of implicit self-views, such that grandiosity was significantly associated with inflated explicit self-evaluations only at either high or medium levels of implicit self-views. Discussion: These findings showed that the relationship between narcissistic traits and explicit self-esteem is not univocal, highlighting the importance of distinguishing between NG and NV. Finally, the study suggested that both researchers and clinicians should consider the relevant role of implicit self-views in conditioning self-esteem levels reported explicitly by individuals with grandiose narcissistic traits. PMID:27920739
Narcissistic Traits and Explicit Self-Esteem: The Moderating Role of Implicit Self-View.
Di Pierro, Rossella; Mattavelli, Simone; Gallucci, Marcello
2016-01-01
Objective: Whilst the relationship between narcissism and self-esteem has been studied for a long time, findings are still controversial. The majority of studies investigated narcissistic grandiosity (NG), neglecting the existence of vulnerable manifestations of narcissism. Moreover, recent studies have shown that grandiosity traits are not always associated with inflated explicit self-esteem. The aim of the present study is to investigate the relationship between narcissistic traits and explicit self-esteem, distinguishing between grandiosity and vulnerability. Moreover, we consider the role of implicit self-esteem in qualifying these associations. Method: Narcissistic traits, explicit and implicit self-esteem measures were assessed among 120 university students (55.8% women, M age = 22.55, SD = 3.03). Results: Results showed different patterns of association between narcissistic traits and explicit self-esteem, depending on phenotypic manifestations of narcissism. Narcissistic vulnerability (NV) was linked to low explicit self-evaluations regardless of one's levels of implicit self-esteem. On the other hand, the link between NG and explicit self-esteem was qualified by levels of implicit self-views, such that grandiosity was significantly associated with inflated explicit self-evaluations only at either high or medium levels of implicit self-views. Discussion: These findings showed that the relationship between narcissistic traits and explicit self-esteem is not univocal, highlighting the importance of distinguishing between NG and NV. Finally, the study suggested that both researchers and clinicians should consider the relevant role of implicit self-views in conditioning self-esteem levels reported explicitly by individuals with grandiose narcissistic traits.
Directory of Open Access Journals (Sweden)
Wilasinee Peerajit
2017-12-01
Full Text Available This paper proposes the explicit formulas for the derivation of exact formulas from Average Run Lengths (ARLs using integral equation on CUSUM control chart when observations are long memory processes with exponential white noise. The authors compared efficiency in terms of the percentage of absolute difference to a similar method to verify the accuracy of the ARLs between the values obtained by the explicit formulas and numerical integral equation (NIE method. The explicit formulas were based on Banach fixed point theorem which was used to guarantee the existence and uniqueness of the solution for ARFIMA(p,d,q. Results showed that the two methods are similar in good agreement with the percentage of absolute difference at less than 0.23%. Therefore, the explicit formulas are an efficient alternative for implementation in real applications because the computational CPU time for ARLs from the explicit formulas are 1 second preferable over the NIE method.
Reporting transparency: making the ethical mandate explicit.
Nicholls, Stuart G; Langan, Sinéad M; Benchimol, Eric I; Moher, David
2016-03-16
Improving the transparency and quality of reporting in biomedical research is considered ethically important; yet, this is often based on practical reasons such as the facilitation of peer review. Surprisingly, there has been little explicit discussion regarding the ethical obligations that underpin reporting guidelines. In this commentary, we suggest a number of ethical drivers for the improved reporting of research. These ethical drivers relate to researcher integrity as well as to the benefits derived from improved reporting such as the fair use of resources, minimizing risk of harms, and maximizing benefits. Despite their undoubted benefit to reporting completeness, questions remain regarding the extent to which reporting guidelines can influence processes beyond publication, including researcher integrity or the uptake of scientific research findings into policy or practice. Thus, we consider investigation on the effects of reporting guidelines an important step in providing evidence of their benefits.
Integrating remote sensing and spatially explicit epidemiological modeling
Finger, Flavio; Knox, Allyn; Bertuzzo, Enrico; Mari, Lorenzo; Bompangue, Didier; Gatto, Marino; Rinaldo, Andrea
2015-04-01
Spatially explicit epidemiological models are a crucial tool for the prediction of epidemiological patterns in time and space as well as for the allocation of health care resources. In addition they can provide valuable information about epidemiological processes and allow for the identification of environmental drivers of the disease spread. Most epidemiological models rely on environmental data as inputs. They can either be measured in the field by the means of conventional instruments or using remote sensing techniques to measure suitable proxies of the variables of interest. The later benefit from several advantages over conventional methods, including data availability, which can be an issue especially in developing, and spatial as well as temporal resolution of the data, which is particularly crucial for spatially explicit models. Here we present the case study of a spatially explicit, semi-mechanistic model applied to recurring cholera outbreaks in the Lake Kivu area (Democratic Republic of the Congo). The model describes the cholera incidence in eight health zones on the shore of the lake. Remotely sensed datasets of chlorophyll a concentration in the lake, precipitation and indices of global climate anomalies are used as environmental drivers. Human mobility and its effect on the disease spread is also taken into account. Several model configurations are tested on a data set of reported cases. The best models, accounting for different environmental drivers, and selected using the Akaike information criterion, are formally compared via cross validation. The best performing model accounts for seasonality, El Niño Southern Oscillation, precipitation and human mobility.
Academic Publishing: Making the Implicit Explicit
Directory of Open Access Journals (Sweden)
Cecile Badenhorst
2016-07-01
Full Text Available For doctoral students, publishing in peer-reviewed journals is a task many face with anxiety and trepidation. The world of publishing, from choosing a journal, negotiating with editors and navigating reviewers’ responses is a bewildering place. Looking in from the outside, it seems that successful and productive academic writers have knowledge that is inaccessible to novice scholars. While there is a growing literature on writing for scholarly publication, many of these publications promote writing and publishing as a straightforward activity that anyone can achieve if they follow the rules. We argue that the specific and situated contexts in which academic writers negotiate publishing practices is more complicated and messy. In this paper, we attempt to make explicit our publishing processes to highlight the complex nature of publishing. We use autoethnographic narratives to provide discussion points and insights into the challenges of publishing peer reviewed articles. One narrative is by a doctoral student at the beginning of her publishing career, who expresses her desires, concerns and anxieties about writing for publication. The other narrative focuses on the publishing practices of a more experienced academic writer. Both are international scholars working in the Canadian context. The purpose of this paper is to explore academic publishing through the juxtaposition of these two narratives to make explicit some of the more implicit processes. Four themes emerge from these narratives. To publish successfully, academic writers need: (1 to be discourse analysts; (2 to have a critical competence; (3 to have writing fluency; and (4 to be emotionally intelligent.
El-Amin, Mohamed
2012-01-01
The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cellcentered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.
Environmental context effects in conceptual explicit and implicit memory.
Parker, Andrew; Dagnall, Neil; Coyle, Anne-Marie
2007-05-01
Previous research has found environmental context effects for both conceptual explicit and conceptual implicit memory (Parker, Gellatly, & Waterman, 1999). The research presented here challenges these findings on methodological grounds. Experiment 1 assessed the effects of context change on category-exemplar generation (conceptual implicit memory test) and category-cued recall (conceptual explicit memory test). Experiment 2 assessed the effects of context change on word association (conceptual implicit memory test) and word associate cued recall (conceptual explicit memory test). In both experiments, study-test changes in environmental context were found to influence performance only on tests of explicit memory. It is concluded that when retrieval cues across explicit and implicit tests are matched, and the probability of explicit contamination is reduced, then only conceptual explicit test performance is reduced by study-test changes in environmental context.
Implicit and explicit ethnocentrism: revisiting the ideologies of prejudice.
Cunningham, William A; Nezlek, John B; Banaji, Mahzarin R
2004-10-01
Two studies investigated relationships among individual differences in implicit and explicit prejudice, right-wing ideology, and rigidity in thinking. The first study examined these relationships focusing on White Americans' prejudice toward Black Americans. The second study provided the first test of implicit ethnocentrism and its relationship to explicit ethnocentrism by studying the relationship between attitudes toward five social groups. Factor analyses found support for both implicit and explicit ethnocentrism. In both studies, mean explicit attitudes toward out groups were positive, whereas implicit attitudes were negative, suggesting that implicit and explicit prejudices are distinct; however, in both studies, implicit and explicit attitudes were related (r = .37, .47). Latent variable modeling indicates a simple structure within this ethnocentric system, with variables organized in order of specificity. These results lead to the conclusion that (a) implicit ethnocentrism exists and (b) it is related to and distinct from explicit ethnocentrism.
Optimizing Environmental Flow Operation Rules based on Explicit IHA Constraints
Dongnan, L.; Wan, W.; Zhao, J.
2017-12-01
Multi-objective operation of reservoirs are increasingly asked to consider the environmental flow to support ecosystem health. Indicators of Hydrologic Alteration (IHA) is widely used to describe environmental flow regimes, but few studies have explicitly formulated it into optimization models and thus is difficult to direct reservoir release. In an attempt to incorporate the benefit of environmental flow into economic achievement, a two-objective reservoir optimization model is developed and all 33 hydrologic parameters of IHA are explicitly formulated into constraints. The benefit of economic is defined by Hydropower Production (HP) while the benefit of environmental flow is transformed into Eco-Index (EI) that combined 5 of the 33 IHA parameters chosen by principal component analysis method. Five scenarios (A to E) with different constraints are tested and solved by nonlinear programming. The case study of Jing Hong reservoir, located in the upstream of Mekong basin, China, shows: 1. A Pareto frontier is formed by maximizing on only HP objective in scenario A and on only EI objective in scenario B. 2. Scenario D using IHA parameters as constraints obtains the optimal benefits of both economic and ecological. 3. A sensitive weight coefficient is found in scenario E, but the trade-offs between HP and EI objectives are not within the Pareto frontier. 4. When the fraction of reservoir utilizable capacity reaches 0.8, both HP and EI capture acceptable values. At last, to make this modelmore conveniently applied to everyday practice, a simplified operation rule curve is extracted.
Implicit and explicit categorization of natural scenes.
Codispoti, Maurizio; Ferrari, Vera; De Cesarei, Andrea; Cardinale, Rossella
2006-01-01
Event-related potential (ERP) studies have consistently found that emotionally arousing (pleasant and unpleasant) pictures elicit a larger late positive potential (LPP) than neutral pictures in a window from 400 to 800 ms after picture onset. In addition, an early ERP component has been reported to vary with emotional arousal in a window from about 150 to 300 ms with affective, compared to neutral stimuli, prompting significantly less positivity over occipito-temporal sites. Similar early and late ERP components have been found in explicit categorization tasks, suggesting that selective attention to target features results in similar cortical changes. Several studies have shown that the affective modulation of the LPP persisted even when the same pictures are repeated several times, when they are presented as distractors, or when participants are engaged in a competing task. These results indicate that categorization of affective stimuli is an obligatory process. On the other hand, perceptual factors (e.g., stimulus size) seem to affect the early ERP component but not the affective modulation of the LPP. Although early and late ERP components vary with stimulus relevance, given that they are differentially affected by stimulus and task manipulations, they appear to index different facets of picture processing.
Explicit logic circuits discriminate neural states.
Directory of Open Access Journals (Sweden)
Lane Yoder
Full Text Available The magnitude and apparent complexity of the brain's connectivity have left explicit networks largely unexplored. As a result, the relationship between the organization of synaptic connections and how the brain processes information is poorly understood. A recently proposed retinal network that produces neural correlates of color vision is refined and extended here to a family of general logic circuits. For any combination of high and low activity in any set of neurons, one of the logic circuits can receive input from the neurons and activate a single output neuron whenever the input neurons have the given activity state. The strength of the output neuron's response is a measure of the difference between the smallest of the high inputs and the largest of the low inputs. The networks generate correlates of known psychophysical phenomena. These results follow directly from the most cost-effective architectures for specific logic circuits and the minimal cellular capabilities of excitation and inhibition. The networks function dynamically, making their operation consistent with the speed of most brain functions. The networks show that well-known psychophysical phenomena do not require extraordinarily complex brain structures, and that a single network architecture can produce apparently disparate phenomena in different sensory systems.
Explicit information reduces discounting behavior in monkeys
Directory of Open Access Journals (Sweden)
John ePearson
2010-12-01
Full Text Available Animals are notoriously impulsive in common laboratory experiments, preferring smaller, sooner rewards to larger, delayed rewards even when this reduces average reward rates. By contrast, the same animals often engage in natural behaviors that require extreme patience, such as food caching, stalking prey, and traveling long distances to high quality food sites. One possible explanation for this discrepancy is that standard laboratory delay discounting tasks artificially inflate impulsivity by subverting animals’ common learning strategies. To test this idea, we examined choices made by rhesus macaques in two variants of a standard delay discounting task. In the conventional variant, post-reward delays were uncued and adjusted to render total trial length constant; in the second, all delays were cued explicitly. We found that measured discounting was significantly reduced in the cued task, with discount rates well below those reported in studies using the standard uncued design. When monkeys had complete information, their decisions were more consistent with a strategy of reward rate maximization. These results indicate that monkeys, and perhaps other animals, are more patient than is normally assumed, and that laboratory measures of delay discounting may overstate impulsivity.
Comparing Explicit and Implicit Learning of Emotional and Non-Emotional Words in Autistic Children
Directory of Open Access Journals (Sweden)
Vahid Nejati
2013-02-01
Full Text Available Background: Explicit and implicit memories have different cerebral origins and learning approaches. Defective emotional words processing in children with autism may affect the memory allocated to such words. The aim of this study was comparing two types of (explicit and implicit memories during processing the two types of (emotional and non-emotional words in autistic children and their healthy counterparts. Materials and Methods: The present cross sectional study was conducted on 14 autistic children, who had referred to Autism Medical Treatment Center on Tehran, and 14 healthy children in kindergartens and schools across Tehran. For the explicit memory, a list of words was presented to the subjects of our study and they were asked to repeat the words they heard one time immediately and one time with delay. For implicit memory, the subjects were asked to identify the heard words among the presented words. Statistical analysis was performed using two-way analysis of variance. Results: The results showed that the normal children have higher efficiency in explicit and implicit memory than the children with autism (p<0.01. The two-way analysis of memory type and word type showed that the former affects memory significantly (p<0.05 while word type had no significant effect. Conclusion: Autistic children suffer from impaired memory. This defect is higher in implicit memory than in the explicit memory. It is recommended to apply rehabilitation, training, learning approaches and also explicit memory for interventions of autistic children.
International Nuclear Information System (INIS)
Oezis, Turgut; Aslan, Imail
2009-01-01
With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G'/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered. (general)
Explicit integration with GPU acceleration for large kinetic networks
International Nuclear Information System (INIS)
Brock, Benjamin; Belt, Andrew; Billings, Jay Jay; Guidry, Mike
2015-01-01
We demonstrate the first implementation of recently-developed fast explicit kinetic integration algorithms on modern graphics processing unit (GPU) accelerators. Taking as a generic test case a Type Ia supernova explosion with an extremely stiff thermonuclear network having 150 isotopic species and 1604 reactions coupled to hydrodynamics using operator splitting, we demonstrate the capability to solve of order 100 realistic kinetic networks in parallel in the same time that standard implicit methods can solve a single such network on a CPU. This orders-of-magnitude decrease in computation time for solving systems of realistic kinetic networks implies that important coupled, multiphysics problems in various scientific and technical fields that were intractable, or could be simulated only with highly schematic kinetic networks, are now computationally feasible.
Philosophical Reflections made explicit as a Tool for Mathematical Reasoning
DEFF Research Database (Denmark)
Frølund, Sune; Andresen, Mette
2009-01-01
A new construct, ‘multidiciplinarity', is prescribed in the curricula of Danish Upper Secondary Schools by governmental regulations since 2006. Multidisciplinarity offers a good chance to introduce philosophical tools or methods in mathematics with the aim to improve the students' learning...... of both subjects, and to study the students' reactions and signs of progressive mathematizing. Based on realistic mathematics education (RME) which is rooted in Hans Freudenthal's idea of mathematics as a human activity, we decided to centre our work on the concept of reflection and to build a model...... for making students reflections in the mathematics class explicit to themselves. In our paper, we present a combination of two stratifications of reflections which were developed recently in works by other authors. The paper outlines our model and exemplifies its use on the teaching of mathematical models...
Spatially explicit modeling in ecology: A review
DeAngelis, Donald L.; Yurek, Simeon
2017-01-01
The use of spatially explicit models (SEMs) in ecology has grown enormously in the past two decades. One major advancement has been that fine-scale details of landscapes, and of spatially dependent biological processes, such as dispersal and invasion, can now be simulated with great precision, due to improvements in computer technology. Many areas of modeling have shifted toward a focus on capturing these fine-scale details, to improve mechanistic understanding of ecosystems. However, spatially implicit models (SIMs) have played a dominant role in ecology, and arguments have been made that SIMs, which account for the effects of space without specifying spatial positions, have an advantage of being simpler and more broadly applicable, perhaps contributing more to understanding. We address this debate by comparing SEMs and SIMs in examples from the past few decades of modeling research. We argue that, although SIMs have been the dominant approach in the incorporation of space in theoretical ecology, SEMs have unique advantages for addressing pragmatic questions concerning species populations or communities in specific places, because local conditions, such as spatial heterogeneities, organism behaviors, and other contingencies, produce dynamics and patterns that usually cannot be incorporated into simpler SIMs. SEMs are also able to describe mechanisms at the local scale that can create amplifying positive feedbacks at that scale, creating emergent patterns at larger scales, and therefore are important to basic ecological theory. We review the use of SEMs at the level of populations, interacting populations, food webs, and ecosystems and argue that SEMs are not only essential in pragmatic issues, but must play a role in the understanding of causal relationships on landscapes.
Towards a theoretical foundation for explicitation and implicitation
De Metsenaere, Hinde; Vandepitte, Sonia
2017-01-01
Explicitation and implicitation are two translation studies concepts that have given rise to a vast array of studies. These studies are, however, often difficult to compare, primarily because explicitation and implicitation have been interpreted differently, not rarely intuitively, by many translation studies researchers. This is due to the fact that the underlying concepts of explicitness and implicitness have not yet been satisfactorily defined for translation studies purposes. It is there...
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-07-26
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
Chinese Undergraduates' Explicit and Implicit Attitudes toward Persons with Disabilities
Chen, Shuang; Ma, Li; Zhang, Jian-Xin
2011-01-01
The present study is aimed at examining implicit and explicit attitudes toward persons with disabilities among Chinese college students. The "Implicit Association Test" was used to measure their implicit attitudes, whereas their explicit attitudes toward persons with disabilities were measured by using a scale of three items.…
From Explicit to Symbolic Types for Communication Protocols in CCS
DEFF Research Database (Denmark)
Nielson, Hanne Riis; Nielson, Flemming; Kreiker, Jörg
2012-01-01
We study communication protocols having several rounds and expressed in value passing CCS. We develop a type-based analysis for providing an explicit record of all communications and show the usual subject reduction result. Since the explicit records can be infinitely large, we also develop a type...
The Ms. Stereotype Revisited: Implicit and Explicit Facets
Malcolmson, Kelly A.; Sinclair, Lisa
2007-01-01
Implicit and explicit stereotypes toward the title Ms. were examined. Participants read a short description of a target person whose title of address varied (Ms., Mrs., Miss, Mr.). They then rated the person on agentic and communal traits and completed an Implicit Association Test. Replicating earlier research (Dion, 1987), at an explicit level,…
Age and time effects on implicit and explicit learning
Verneau, M.; Kamp, J. van der; Savelsbergh, G.J.P.; Looze, M.P. de
2014-01-01
Study Context: It has been proposed that effects of aging are more pronounced for explicit than for implicit motor learning. The authors evaluated this claim by comparing the efficacy of explicit and implicit learning of a movement sequence in young and older adults, and by testing the resilience
Age and Time Effects on Implicit and Explicit Learning
Verneau, M.M.N.; van der Kamp, J.; Savelsbergh, G.J.P.; de Looze, M.P.
2014-01-01
Study Context: It has been proposed that effects of aging are more pronounced for explicit than for implicit motor learning. The authors evaluated this claim by comparing the efficacy of explicit and implicit learning of a movement sequence in young and older adults, and by testing the resilience
Explicitly solvable complex Chebyshev approximation problems related to sine polynomials
Freund, Roland
1989-01-01
Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.
Implicit versus explicit : An ACT-R learning perspective
Taatgen, N.A.
1999-01-01
Dienes & Perner propose a theory of implicit and explicit knowledge that is not entirely complete. It does not address many of the empirical issues, nor does it explain the difference between implicit and explicit learning. It does, however, provide a possible unified explanation, as opposed to the