LED-based Photometric Stereo: Modeling, Calibration and Numerical Solutions
DEFF Research Database (Denmark)
Quéau, Yvain; Durix, Bastien; Wu, Tao
2018-01-01
We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in pr...
Numerical solution of dynamic equilibrium models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
2013-01-01
We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations...... of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel...... solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households....
Numerical Solution of a Model Equation of Price Formation
Chernogorova, T.; Vulkov, L.
2009-10-01
The paper [2] is devoted to the effect of reconciling the classical Black-Sholes theory of option pricing and hedging with various phenomena observed in the markets such as the influence of trading and hedging on the dynamics of an asset. Here we will discuss the numerical solution of initial boundary-value problems to a model equation of the theory. The lack of regularity in the solution as a result from Dirac delta coefficient reduces the accuracy in the numerical computations. First, we apply the finite volume method to discretize the differential problem. Second, we implement a technique of local regularization introduced by A-K. Tornberg and B. Engquist [7] for handling this equation. We derived the numerical regularization process into two steps: the Dirac delta function is regularized and then the regularized differential equation is discretized by difference schemes. Using the discrete maximum principle a priori bounds are obtained for the difference equations that imply stability and convergence of difference schemes for the problem under consideration. Numerical experiments are discussed.
Numerical solution of a model for a superconductor field problem
International Nuclear Information System (INIS)
Alsop, L.E.; Goodman, A.S.; Gustavson, F.G.; Miranker, W.L.
1979-01-01
A model of a magnetic field problem occurring in connection with Josephson junction devices is derived, and numerical solutions are obtained. The model is of mathematical interest, because the magnetic vector potential satisfies inhomogeneous Helmholtz equations in part of the region, i.e., the superconductors, and the Laplace equation elsewhere. Moreover, the inhomogeneities are the guage constants for the potential, which are different for each superconductor, and their magnitudes are proportional to the currents flowing in the superconductors. These constants are directly related to the self and mutual inductances of the superconducting elements in the device. The numerical solution is obtained by the iterative use of a fast Poisson solver. Chebyshev acceleration is used to reduce the number of iterations required to obtain a solution. A typical problem involves solving 100,000 simultaneous equations, which the algorithm used with this model does in 20 iterations, requiring three minutes of CPU time on an IBM VM/370/168. Excellent agreement is obtained between calculated and observed values for the inductances
Numerical solution of High-kappa model of superconductivity
Energy Technology Data Exchange (ETDEWEB)
Karamikhova, R. [Univ. of Texas, Arlington, TX (United States)
1996-12-31
We present formulation and finite element approximations of High-kappa model of superconductivity which is valid in the high {kappa}, high magnetic field setting and accounts for applied magnetic field and current. Major part of this work deals with steady-state and dynamic computational experiments which illustrate our theoretical results numerically. In our experiments we use Galerkin discretization in space along with Backward-Euler and Crank-Nicolson schemes in time. We show that for moderate values of {kappa}, steady states of the model system, computed using the High-kappa model, are virtually identical with results computed using the full Ginzburg-Landau (G-L) equations. We illustrate numerically optimal rates of convergence in space and time for the L{sup 2} and H{sup 1} norms of the error in the High-kappa solution. Finally, our numerical approximations demonstrate some well-known experimentally observed properties of high-temperature superconductors, such as appearance of vortices, effects of increasing the applied magnetic field and the sample size, and the effect of applied constant current.
Gómez-Aguilar, J. F.
2018-03-01
In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.
Improved numerical solutions for chaotic-cancer-model
Directory of Open Access Journals (Sweden)
Muhammad Yasir
2017-01-01
Full Text Available In biological sciences, dynamical system of cancer model is well known due to its sensitivity and chaoticity. Present work provides detailed computational study of cancer model by counterbalancing its sensitive dependency on initial conditions and parameter values. Cancer chaotic model is discretized into a system of nonlinear equations that are solved using the well-known Successive-Over-Relaxation (SOR method with a proven convergence. This technique enables to solve large systems and provides more accurate approximation which is illustrated through tables, time history maps and phase portraits with detailed analysis.
Projection methods for the numerical solution of Markov chain models
Saad, Youcef
1989-01-01
Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.
Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.
2007-01-01
Abstract: The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci. 35 (1997) 793-802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous
Numerical Modeling for the Solute Uptake from Groundwater by Plants-Plant Uptake Package
El-Sayed, Amr A.
2006-01-01
A numerical model is presented to describe solute transport in groundwater coupled to sorption by plant roots, translocation into plant stems, and finally evapotranspiration. The conceptual model takes into account both Root Concentration Factor, RCF, and Transpiration Stream Concentration Factor, TSCF for chemicals which are a function of Kow. A similar technique used to simulate the solute transport in groundwater to simulate sorption and plant uptake is used. The mathematical equation is s...
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
Directory of Open Access Journals (Sweden)
Roman Cherniha
2016-06-01
Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.
Numerical Modeling Tools for the Prediction of Solution Migration Applicable to Mining Site
International Nuclear Information System (INIS)
Martell, M.; Vaughn, P.
1999-01-01
Mining has always had an important influence on cultures and traditions of communities around the globe and throughout history. Today, because mining legislation places heavy emphasis on environmental protection, there is great interest in having a comprehensive understanding of ancient mining and mining sites. Multi-disciplinary approaches (i.e., Pb isotopes as tracers) are being used to explore the distribution of metals in natural environments. Another successful approach is to model solution migration numerically. A proven method to simulate solution migration in natural rock salt has been applied to project through time for 10,000 years the system performance and solution concentrations surrounding a proposed nuclear waste repository. This capability is readily adaptable to simulate solution migration around mining
Numerical solution of continuous-time DSGE models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We...... then use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary differential equations by standard methods and fix-point iteration. Analytical solutions are provided as a benchmark from which our numerical method can be used to explore broader...... classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We find that, even for non-linear policy functions, the maximum (absolute) error is very...
International Nuclear Information System (INIS)
Milioli, F.E.
1985-01-01
In this research work a numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities of a Boussinesq fluid is presented. The conservation equations are written in a general curvilinear coordinate system which matches the irregular boundaries of the domain. The nonorthogonal system is generated by a suitable system of elliptic equations. The momentum and continuity equations are transformed from the Cartesian system to the general curvilinear system keeping the Cartesian velocity components as the dependent variables in the transformed domain. Finite difference equations are obtained for the contravariant velocity components in the transformed domain. The numerical calculations are performed in a fixed rectangular domain and both the Cartesian and the contravariant velocity components take part in the solutiomn procedure. The dependent variables are arranged on the grid in a staggered manner. The numerical model is tested by solving the driven flow in a square cavity with a moving side using a nonorthogoanl grid. The natural convenction in a square cavity, using an orthogonal and a nonorthogonal grid, is also solved for the model test. Also, the solution for the buoyancy flow between a square cylinder placed inside a circular cylinder is presented. The results of the test problems are compared with those available in the specialized literature. Finally, in order to show the generality of the model, the natural convection problem inside a very irregular cavity is presented. (Author) [pt
An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere
Swidinsky, Andrei; Liu, Lifei
2017-11-01
We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.
Zhu, Shichen; Yu, Xiaoyue; Xiong, Shanbai; Liu, Ru; Gu, Zhipeng; You, Juan; Yin, Tao; Hu, Yang
2017-09-01
The elaboration of the rheological behaviors of alginate dialdehyde (ADA) crosslinked collagen solutions, along with the quantitative analysis via numerical models contribute to the controllable design of ADA crosslinked solution system's fluid mechanics performance during manufacturing process for collagen biomaterials. In the present work, steady shear flow, dynamical viscoelasticity, creep-recovery, thixotropy tests were performed to characterize the rheological behaviors of the collagen solutions incorporating of ADA from the different aspects and fitted with corresponding numerical models. It was found that pseudoplastic properties of all samples enhanced with increasing amounts of ADA, which was confirmed by the parameters calculated from the Ostwald-de Waele model, Carreau and Cross model, for instance, the non-Newtonian index (n) decreased from 0.786 to 0.201 and a great increase by 280 times in value of viscosity index (K) was obtained from Ostwald-de Waele model. The forth-mode Leonov model was selected to fit all dynamic modulus-frequency curves due to its higher fitting precision (R 2 >0.99). It could be found that the values of correlation shear viscosity (η k ) increased and the values of relaxation time (θ k ) decreased with increasing ADA at the fixed k value, suggesting that the incorporation of ADA accelerated the transformation of the collagen solutions from liquid-like to gel-like state due to more formation of CN linkages between aldehyde groups and lysine residues. Also, the curves of creep and recovery phase of the native and crosslinked collagen solutions were simulated well using Burger model and a semi-empirical model, respectively. The ability to resist to deformation and elasticity strengthened for the samples with higher amounts of ADA, accompanied with the important fact that compliance value (J 50 ) decreased from 56.317Pa -1 to 2.135Pa -1 and the recovery percentage (R creep ) increased from 2.651% to 28.217%. Finally, it was found
On the formulation of environmental fugacity models and their numerical solutions.
Bates, Michael L; Bigot, Marie; Cropp, Roger A; Engwirda, Darren; Friedman, Carey L; Hawker, Darryl W
2016-09-01
Multimedia models based on chemical fugacity, solved numerically, play an important role in investigating and quantifying the environmental fate of chemicals such as persistent organic pollutants. These models have been used extensively in studying the local and global distribution of chemicals in the environment. The present study describes potential sources of error that may arise from the formulation and numerical solution of environmental fugacity models. The authors derive a general fugacity equation for the rate of change of mass in an arbitrary volume (e.g., an environmental phase). Deriving this general equation makes clear several assumptions that are often not articulated but can be important for successfully applying multimedia fugacity models. It shows that the homogeneity of fugacity and fugacity capacity in a volume (the homogeneity assumption) is fundamental to formulating discretized fugacity models. It also shows that when using the fugacity rather than mass as the state-variable, correction terms may be necessary to accommodate environmental factors such as varying phase temperatures and volume. Neglecting these can lead to conservation errors. The authors illustrate the manifestation of these errors using heuristic multimedia fugacity models. The authors also show that there are easily avoided errors that can arise in mass state-variable models if variables are not updated appropriately in the numerical integration scheme. Environ Toxicol Chem 2016;35:2182-2191. © 2016 SETAC. © 2016 SETAC.
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-01-01
Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904
Numerical modeling of solute transport in deformable unsaturated layered soil
Directory of Open Access Journals (Sweden)
Sheng Wu
2017-07-01
Full Text Available The effect of soil stratification was studied through numerical investigation based on the coupled model of solute transport in deformable unsaturated soil. The theoretical model implied two-way coupled excess pore pressure and soil deformation based on Biot's consolidation theory as well as a one-way coupled volatile pollutant concentration field developed from the advection-diffusion theory. Embedded in the model, the degree of saturation, fluid compressibility, self-weight of the soil matrix, porosity variance, longitudinal dispersion, and linear sorption were computed. Based on simulation results of a proposed three-layer landfill model using the finite element method, the multi-layer effects are discussed with regard to the hydraulic conductivity, shear modulus, degree of saturation, molecular diffusion coefficient, and thickness of each layer. Generally speaking, contaminants spread faster in a stratified field with a soft and highly permeable top layer; soil parameters of the top layer are more critical than the lower layers but controlling soil thicknesses will alter the results. This numerical investigation showed noticeable impacts of stratified soil properties on solute migration results, demonstrating the importance of correctly modeling layered soil instead of simply assuming the averaged properties across the soil profile.
Turchi, Patrice E. A.; Fattebert, Jean-Luc; Dorr, Milo R.; Wickett, Michael E.; Belak, James F.
2011-03-01
We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in alloys using physical parameters from thermodynamic (CALPHAD) and kinetic databases. The coupled system of PFM equations includes a local order parameter, a quaternion representation of local crystal orientation and a species composition parameter. Time evolution of microstructures and alloy composition is obtained using an implicit time integration of the system. Physical parameters in databases can be obtained either through experiment or first-principles calculations. Application to coring studies and microstructure evolution of Au-Ni will be presented. Prepared by LLNL under Contract DE-AC52-07NA27344
A Numerical Algorithm for the Solution of a Phase-Field Model of Polycrystalline Materials
Energy Technology Data Exchange (ETDEWEB)
Dorr, M R; Fattebert, J; Wickett, M E; Belak, J F; Turchi, P A
2008-12-04
We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H; Miller, Cass T
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Code and Solution Verification of 3D Numerical Modeling of Flow in the Gust Erosion Chamber
Yuen, A.; Bombardelli, F. A.
2014-12-01
Erosion microcosms are devices commonly used to investigate the erosion and transport characteristics of sediments at the bed of rivers, lakes, or estuaries. In order to understand the results these devices provide, the bed shear stress and flow field need to be accurately described. In this research, the UMCES Gust Erosion Microcosm System (U-GEMS) is numerically modeled using Finite Volume Method. The primary aims are to simulate the bed shear stress distribution at the surface of the sediment core/bottom of the microcosm, and to validate the U-GEMS produces uniform bed shear stress at the bottom of the microcosm. The mathematical model equations are solved by on a Cartesian non-uniform grid. Multiple numerical runs were developed with different input conditions and configurations. Prior to developing the U-GEMS model, the General Moving Objects (GMO) model and different momentum algorithms in the code were verified. Code verification of these solvers was done via simulating the flow inside the top wall driven square cavity on different mesh sizes to obtain order of convergence. The GMO model was used to simulate the top wall in the top wall driven square cavity as well as the rotating disk in the U-GEMS. Components simulated with the GMO model were rigid bodies that could have any type of motion. In addition cross-verification was conducted as results were compared with numerical results by Ghia et al. (1982), and good agreement was found. Next, CFD results were validated by simulating the flow within the conventional microcosm system without suction and injection. Good agreement was found when the experimental results by Khalili et al. (2008) were compared. After the ability of the CFD solver was proved through the above code verification steps. The model was utilized to simulate the U-GEMS. The solution was verified via classic mesh convergence study on four consecutive mesh sizes, in addition to that Grid Convergence Index (GCI) was calculated and based on
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
Directory of Open Access Journals (Sweden)
De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
An Integrated Numerical Hydrodynamic Shallow Flow-Solute Transport Model for Urban Area
Alias, N. A.; Mohd Sidek, L.
2016-03-01
The rapidly changing on land profiles in the some urban areas in Malaysia led to the increasing of flood risk. Extensive developments on densely populated area and urbanization worsen the flood scenario. An early warning system is really important and the popular method is by numerically simulating the river and flood flows. There are lots of two-dimensional (2D) flood model predicting the flood level but in some circumstances, still it is difficult to resolve the river reach in a 2D manner. A systematic early warning system requires a precisely prediction of flow depth. Hence a reliable one-dimensional (1D) model that provides accurate description of the flow is essential. Research also aims to resolve some of raised issues such as the fate of pollutant in river reach by developing the integrated hydrodynamic shallow flow-solute transport model. Presented in this paper are results on flow prediction for Sungai Penchala and the convection-diffusion of solute transports simulated by the developed model.
Atlabachew, Abunu; Shu, Longcang; Wu, Peipeng; Zhang, Yongjie; Xu, Yang
2018-03-01
This laboratory study improves the understanding of the impacts of horizontal hydraulic gradient, artificial recharge, and groundwater pumping on solute transport through aquifers. Nine experiments and numerical simulations were carried out using a sand tank. The variable-density groundwater flow and sodium chloride transport were simulated using the three-dimensional numerical model SEAWAT. Numerical modelling results successfully reproduced heads and concentrations observed in the sand tank. A higher horizontal hydraulic gradient enhanced the migration of sodium chloride, particularly in the groundwater flow direction. The application of constant artificial recharge increased the spread of the sodium chloride plume in both the longitudinal and lateral directions. In addition, groundwater pumping accelerated spreading of the sodium chloride plume towards the pumping well. Both higher hydraulic gradient and pumping rate generated oval-shaped plumes in the horizontal plane. However, the artificial recharge process produced stretched plumes. These effects of artificial recharge and groundwater pumping were greater under higher hydraulic gradient. The concentration breakthrough curves indicated that emerging solutions never attained the concentration of the originally injected solution. This is probably because of sorption of sodium chloride onto the silica sand and/or the exchange of sodium chloride between the mobile and immobile liquid domains. The fingering and protruding plume shapes in the numerical models constitute instability zones produced by buoyancy-driven flow. Overall, the results have substantiated the influences of hydraulic gradient, boundary condition, artificial recharge, pumping rate and density differences on solute transport through a homogeneous unconfined aquifer. The implications of these findings are important for managing liquid wastes.
Uncoupled continuous-time random walk model: Analytical and numerical solutions
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
An efficient numerical target strength prediction model: Validation against analysis solutions
Fillinger, L.; Nijhof, M.J.J.; Jong, C.A.F. de
2014-01-01
A decade ago, TNO developed RASP (Rapid Acoustic Signature Prediction), a numerical model for the prediction of the target strength of immersed underwater objects. The model is based on Kirchhoff diffraction theory. It is currently being improved to model refraction, angle dependent reflection and
Energy Technology Data Exchange (ETDEWEB)
Gustafsson, Lars-Goeran; Sassner, Mona (DHI Sverige AB, Stockholm (Sweden)); Bosson, Emma (Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden))
2008-12-15
The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site investigations at two different locations in Sweden, referred to as the Forsmark and Laxemar areas, with the objective of siting a final repository for high-level radioactive waste. Data from the site investigations are used in a variety of modelling activities. This report presents model development and results of numerical transport modelling based on the numerical flow modelling of surface water and near-surface groundwater at the Forsmark site. The numerical modelling was performed using the modelling tool MIKE SHE and is based on the site data and conceptual model of the Forsmark areas. This report presents solute transport applications based on both particle tracking simulations and advection-dispersion calculations. The MIKE SHE model is the basis for the transport modelling presented in this report. Simulation cases relevant for the transport from a deep geological repository have been studied, but also the pattern of near surface recharge and discharge areas. When the main part of the modelling work presented in this report was carried out, the flow modelling of the Forsmark site was not finalised. Thus, the focus of this work is to describe the sensitivity to different transport parameters, and not to point out specific areas as discharge areas from a future repository (this is to be done later, within the framework of the safety assessment). In the last chapter, however, results based on simulations with the re-calibrated MIKE SHE flow model are presented. The results from the MIKE SHE water movement calculations were used by cycling the calculated transient flow field for a selected one-year period as many times as needed to achieve the desired simulation period. The solute source was located either in the bedrock or on top of the model. In total, 15 different transport simulation cases were studied. Five of the simulations were particle tracking simulations, whereas the rest
Numerical methods problems and solutions
Jain, MK
2004-01-01
About the Book: Is an outline series containing brief text of numerical solution of transcendental and polynomial equations, system of linear algebraic equations and eigenvalue problems, interpolation and approximation, differentiation and integration, ordinary differential equations and complete solutions to about 300 problems. Most of these problems are given as unsolved problems in the authors earlier book. User friendly Turbo Pascal programs for commonly used numerical methods are given in the Appendix. This book can be used as a text/help book both by teachers and students. Contents:
A comparison of numerical methods for the solution of continuous-time DSGE models
DEFF Research Database (Denmark)
Parra-Alvarez, Juan Carlos
This paper evaluates the accuracy of a set of techniques that approximate the solution of continuous-time DSGE models. Using the neoclassical growth model I compare linear-quadratic, perturbation and projection methods. All techniques are applied to the HJB equation and the optimality conditions...... parameters of the model and suggest the use of projection methods when a high degree of accuracy is required....
Numerical solution of atmospheric boundary layer flow
Energy Technology Data Exchange (ETDEWEB)
Benes, L.; Kozel, K. [Czech Technical Univ. (Czech Republic). Dept. of Technical Mathematics; Sladek, I. [Czech Technical Univ. (Czech Republic). Dept. of Mathematics
2000-07-01
The work deals with numerical solution of the 3D viscous turbulent steady flows in the atmospheric boundary layer including pollution propagation. The theoretical model consists of a system of Navier-Stokes equations for incompressible flows (continuity and momentum equations) and two equations for concentration and potential temperature in conservative form. Turbulent flow is considered using an algebraic model of turbulence. Numerical solution is based on artificial compressibility method. Numerically is realized using by the finite volume method and multistage Runge-Kutta scheme. The work presents 3D flow for high Re{proportional_to}10{sup 7}-10{sup 8} over a hill or a system of hills. (orig.)
International Nuclear Information System (INIS)
Koeppel, T.; Harvey, M.
1984-06-01
A new numerical method is applied to solving the equations of motion of the Friedberg-Lee Soliton model for both ground and spherically symmetric excited states. General results have been obtained over a wide range of parameters. Critical coupling constants and critical particle numbers have been determined below which soliton solutions cease to exist. The static properties of the proton are considered to show that as presently formulated the model fails to fit all experimental data for any set of parameters
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
Directory of Open Access Journals (Sweden)
Nowak Tomasz Karol
2014-06-01
Full Text Available This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Czech Academy of Sciences Publication Activity Database
Pokorný, Vladislav; Žonda, M.; Kauch, Anna; Janiš, Václav
2017-01-01
Roč. 131, č. 4 (2017), s. 1042-1044 ISSN 0587-4246 R&D Projects: GA ČR GA15-14259S Institutional support: RVO:68378271 Keywords : Anderson model * parquet equations * numerical renormalization group Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Condensed matter physics (including formerly solid state physics, supercond.) Impact factor: 0.469, year: 2016
A numerical solution model of the rewetting of a nuclear fuel rod
International Nuclear Information System (INIS)
Braz Filho, F.A.
1984-01-01
The study of thermal behaviour of a nuclear reactor fuel rod during the reflooding phase of the loss-of-coolant accident (LOCA) is presented. A mathematical model and a numerical scheme were proposed in order to solve the bidimensional heat conduction equation in cylindrical coordinates. The phenomenon of reflooding is not completely understood. One of the main difficulties is to estimate the heat transfer coefficient (h). For this reason two different models were elaborated: in the first three regions are considered and in each region h is considered constant; in the second the h profile is adjusted according to the boiling curve. The three region model yields satisfactory results at high and low mass flows while the 'boiling curve' model yields reasonable at low flows. (Author) [pt
International Nuclear Information System (INIS)
Velloso, P.A.; Galeao, A.C.
1989-05-01
This paper deals with nonlinear vibrations of pipes subjected to non-conservative loads. Periodic solutions of these problems are determined using a variational approach based on Hamilton's Principle combined with a Fourier series expansion to describe the displacement field time dependence. A finite element model which utilizes Hemite's cubic interpolation for both axial and transversal displacement amplitudes is used. This model is applied to the problem of a pipe subjected to a tangential and a normal follower force. The numerical results obtained with this model are compared with the corespondent solutions determined using a total lagrangian description for the Principle of Virtual Work, coupled with Newmark's step-by-step integration procedure. It is shown that for small to moderate displacement amplitudes the one-term Fourier series approximation compares fairly well with the predicted solution. For large displacements as least a two-term approximation should be utilized [pt
Numerical transducer modelling
DEFF Research Database (Denmark)
Cutanda, Vicente
1999-01-01
Numerical modelling is of importance for the design, improvement and study of acoustic transducers such as microphones and accelerometers. Techniques like the boundary element method and the finite element method are the most common supplement to the traditional empirical and analytical approaches...... errors and instabilities in the computations of numerical solutions. An investigation to deal with this narrow-gap problem has been carried out....
Digital Repository Service at National Institute of Oceanography (India)
Unnikrishnan, A.S.; Manoj, N.T.
developed most of the above models. This is a good approximation to simulate horizontal distribution of active and passive variables. The future challenge lies in developing capability to simulate the distribution in the vertical....
Automatic validation of numerical solutions
DEFF Research Database (Denmark)
Stauning, Ole
1997-01-01
, using this method has been developed. (ADIODES is an abbreviation of `` Automatic Differentiation Interval Ordinary Differential Equation Solver''). ADIODES is used to prove existence and uniqueness of periodic solutions to specific ordinary differential equations occuring in dynamical systems theory....... These proofs of existence and uniqueness are difficult or impossible to obtain using other known methods. Also, a method for solving boundary value problems is described. Finally a method for enclosing solutions to a class of integral equations is described. This method is based on the mean value enclosure...... of an integral operator and uses interval Bernstein polynomials for enclosing the solution. Two numerical examples are given, using two orders of approximation and using different numbers of discretization points....
Directory of Open Access Journals (Sweden)
C. L. Chang
2004-03-01
Full Text Available We study a family of diffusion models for compounded risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models in which the dividend payments are paid from the risk reserves. After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. Based on the behavior of the total income flow, asymptotic and numerical methods are used to solve the special class of diffusion equations which govern the conditional ruin probability over finite time.
Zhou, X.; Nenna, F. A.; Aydin, A.
2009-12-01
Pressure solution seams (PSSs) are closing mode structures of localized dissolution that form perpendicular to the greatest compressive stress. Their formation mechanism is known to be intragranular pressure solution (IPS) and involves a physicochemical process resulting in a volume reduction. It is generally accepted that pressure solution occurs through three steps: 1) dissolution of solid material, 2) diffusion of dissolved material, and 3) precipitation of dissolved material. Since the earliest studies it has been inferred that these seams grow laterally due to additional dissolution at the tip, and by thickening as dissolution progresses at the seam boundary. However, the processes and conditions required for this growth to occur, and the effect of neighboring seams upon each other, are not well known. We present new observations that constrain the processes by which PSSs initiate and grow in low porosity clastic rocks from County Cork, Ireland. Microprobe and optical microscope images show that solution seams initiate as IPS at grain to grain contacts of quartz minerals. As quartz dissolves, clay remains as a residue along the grain contacts as well as filling the adjacent pore spaces to form incipient PSSs of more than one grain boundary and associated pores in between them. Further growth of PSSs occurs by lateral and transverse linkage and coalescence of neighboring segments of incipient PSSs and results in lengthening and thickening of the seam, respectively. Multiple PSS segments are observed to concentrate in thin tabular zones that appear as single macroscopic PSSs visible to the eye in hand samples, thereby providing an indication for the role of PSSs interaction in their growth process. Here, we use a finite element (FE) model to investigate the stress distribution associated with a localized volume reduction structure (LVRS), which is an idealized PSS in the form of a high aspect ratio elliptical body within a linear elastic medium. The accuracy of
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...... ? and how do boundary value approximations affect the overall order of the method. Knowledge of a reliable order and error estimate enables us to determine (near-)optimal step sizes to meet a prescribed error tolerance, and possibly to extrapolate to get (higher order and) better accuracy at a minimal...
DEFF Research Database (Denmark)
Lee, Jonghyun; Rolle, Massimo; Kitanidis, Peter K.
2017-01-01
and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process...... parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection...... investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion and mass transfer limitations, i.e., the exchange of mass between the permeable matrix and the low permeability inclusions. We illustrate the physical...
An Efficient and Robust Numerical Solution of the Full-Order Multiscale Model of Lithium-Ion Battery
Directory of Open Access Journals (Sweden)
Michal Beneš
2018-01-01
Full Text Available We propose a novel and efficient numerical approach for solving the pseudo two-dimensional multiscale model of the Li-ion cell dynamics based on first principles, describing the ion diffusion through the electrolyte and the porous electrodes, electric potential distribution, and Butler-Volmer kinetics. The numerical solution is obtained by the finite difference discretization of the diffusion equations combined with an original iterative scheme for solving the integral formulation of the laws of electrochemical interactions. We demonstrate that our implementation is fast and stable over the expected lifetime of the cell. In contrast to some simplified models, it provides physically consistent results for a wide range of applied currents including high loads. The algorithm forms a solid basis for simulations of cells and battery packs in hybrid electric vehicles, with possible straightforward extensions by aging and heat effects.
Amarti, Z.; Nurkholipah, N. S.; Anggriani, N.; Supriatna, A. K.
2018-03-01
Predicting the future of population number is among the important factors that affect the consideration in preparing a good management for the population. This has been done by various known method, one among them is by developing a mathematical model describing the growth of the population. The model usually takes form in a differential equation or a system of differential equations, depending on the complexity of the underlying properties of the population. The most widely used growth models currently are those having a sigmoid solution of time series, including the Verhulst logistic equation and the Gompertz equation. In this paper we consider the Allee effect of the Verhulst’s logistic population model. The Allee effect is a phenomenon in biology showing a high correlation between population size or density and the mean individual fitness of the population. The method used to derive the solution is the Runge-Kutta numerical scheme, since it is in general regarded as one among the good numerical scheme which is relatively easy to implement. Further exploration is done via the fuzzy theoretical approach to accommodate the impreciseness of the initial values and parameters in the model.
Directory of Open Access Journals (Sweden)
A. Mushtaq
2016-01-01
Full Text Available Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i the shooting method and (ii the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.
Numerical Solution of Diffusion Models in Biomedical Imaging on Multicore Processors
Directory of Open Access Journals (Sweden)
Luisa D'Amore
2011-01-01
Full Text Available In this paper, we consider nonlinear partial differential equations (PDEs of diffusion/advection type underlying most problems in image analysis. As case study, we address the segmentation of medical structures. We perform a comparative study of numerical algorithms arising from using the semi-implicit and the fully implicit discretization schemes. Comparison criteria take into account both the accuracy and the efficiency of the algorithms. As measure of accuracy, we consider the Hausdorff distance and the residuals of numerical solvers, while as measure of efficiency we consider convergence history, execution time, speedup, and parallel efficiency. This analysis is carried out in a multicore-based parallel computing environment.
A mathematical model and numerical solution of interface problems for steady state heat conduction
Directory of Open Access Journals (Sweden)
Z. Muradoglu Seyidmamedov
2006-01-01
(isolation Ωδ tends to zero. For each case, the local truncation errors of the used conservative finite difference scheme are estimated on the nonuniform grid. A fast direct solver has been applied for the interface problems with piecewise constant but discontinuous coefficient k=k(x. The presented numerical results illustrate high accuracy and show applicability of the given approach.
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.
Difference schemes for numerical solutions of lagging models of heat conduction
Cabrera Sánchez, Jesús; Castro López, María Ángeles; Rodríguez Mateo, Francisco; Martín Alustiza, José Antonio
2013-01-01
Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the...
Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.
2012-10-01
A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.
International Nuclear Information System (INIS)
Yudov, Y.V.
2001-01-01
The functional part of the KORSAR computer code is based on the computational unit for the reactor system thermal-hydraulics and other thermal power systems with water cooling. The two-phase flow dynamics of the thermal-hydraulic network is modelled by KORSAR in one-dimensional two-fluid (non-equilibrium and nonhomogeneous) approximation with the same pressure of both phases. Each phase is characterized by parameters averaged over the channel sections, and described by the conservation equations for mass, energy and momentum. The KORSAR computer code relies upon a novel approach to mathematical modelling of two-phase dispersed-annular flows. This approach allows a two-fluid model to differentiate the effects of the liquid film and droplets in the gas core on the flow characteristics. A semi-implicit numerical scheme has been chosen for deriving discrete analogs the conservation equations in KORSAR. In the semi-implicit numerical scheme, solution of finite-difference equations is reduced to the problem of determining the pressure field at a new time level. For the one-channel case, the pressure field is found from the solution of a system of linear algebraic equations by using the tri-diagonal matrix method. In the branched network calculation, the matrix of coefficients in the equations describing the pressure field is no longer tri-diagonal but has a sparseness structure. In this case, the system of linear equations for the pressure field can be solved with any of the known classical methods. Such an approach is implemented in the existing best-estimate thermal-hydraulic computer codes (TRAC, RELAP5, etc.) For the KORSAR computer code, we have developed a new non-iterative method for calculating the pressure field in the network of any topology. This method is based on the tri-diagonal matrix method and performs well when solving the thermal-hydraulic network problems. (author)
Numerical solution of multiband k.p model for tunnelling in type-II heterostructures
Directory of Open Access Journals (Sweden)
A.E. Botha
2010-01-01
Full Text Available A new and very general method was developed for calculating the charge and spin-resolved electron tunnelling in type-II heterojunctions. Starting from a multiband k.p description of the bulk energy-band structure, a multiband k.p Riccati equation was derived. The reflection and transmission coefficients were obtained for each channel by integrating the Riccati equation over the entire heterostructure. Numerical instability was reduced through this method, in which the multichannel log-derivative of the envelope function matrix, rather than the envelope function itself, was propagated. As an example, a six-band k.p Hamiltonian was used to calculate the current-voltage characteristics of a 10-nm wide InAs/ GaSb/InAs single quantum well device which exhibited negative differential resistance at room temperature. The calculated current as a function of applied (bias voltage was found to be in semiquantitative agreement with the experiment, a result which indicated that inelastic transport mechanisms do not contribute significantly to the valley currents measured in this particular device.
Modeling of gravity-imbibition and gravity-drainage processes: Analytic and numerical solutions
DEFF Research Database (Denmark)
Bech, N.; Jensen, O.K.; Nielsen, B.
1991-01-01
A matrix/fracture exchange model for a fractured reservoir simulator is described. Oil/water imbibition is obtained from a diffusion equation with water saturation as the dependent variable. Gas/oil gravity drainage and imbibition are calculated by taking into account the vertical saturation...... distribution in the matrix blocks....
Numerical Solution of the Contact Problem. Application to a Simple Model of the Human Hip Joint
Czech Academy of Sciences Publication Activity Database
Bartoš, M.; Kestřánek, Zdeněk
1995-01-01
Roč. 63, 1/3 (1995), s. 439-447 ISSN 0377-0427. [Modelling'94. Prague, 29.08.1994-02.09.1994] R&D Projects: GA ČR GA308/95/0304 Grant - others:COPERNICUS(XE) 94-00820 Keywords : contact problem * finite element method * mathematical programming Impact factor: 0.373, year: 1995
International Nuclear Information System (INIS)
Bodvarsson, G.S.; Lippmann, M.J.
1980-01-01
The computer program CCC (conduction-convection-consolidation), developed at Lawrence Berkeley Laboratory, solves numerically the heat and mass flow equations for a fully saturated medium, and computes one-dimensional consolidation of the simulated systems. The model employs the Integrated Finite Difference Method (IFDM) in discretizing the saturated medium and formulating the governing equations. The sets of equations are solved either by an iterative solution technique (old version) or an efficient sparse solver (new version). The deformation of the medium is calculated using the one-dimensional consolidation theory of Terzaghi. In this paper, the numerical code is described, validation examples given and areas of application discussed. Several example problems involving flow through fractured media are also presented
Energy Technology Data Exchange (ETDEWEB)
Prinja, A.K.
1998-09-01
In this work, it has been shown that, for the given sets of parameters (transport coefficients), the Tangent-Predictor (TP) continuation method, which was used in the coarsest grid, works remarkably well. The problems in finding an initial guess that resides well within Newton`s method radius of convergence are alleviated by correcting the initial guess by the predictor step of the TP method. The TP method works well also in neutral gas puffing and impurity simulations. The neutral gas puffing simulation is performed by systematically increasing the fraction of puffing rate according to the TP method until it reaches a desired condition. Similarly, the impurity simulation characterized by using the fraction of impurity density as the continuation parameter, is carried out in line with the TP method. Both methods show, as expected, a better performance than the classical embedding (CE) method. The convergence criteria {epsilon} is set to be 10{sup {minus}9} based on the fact that lower value of {epsilon} does not alter the solution significantly. Correspondingly, the number of Newton`s iterations in the corrector step of the TP method decrease substantially, an extra point in terms of code speed. The success of the TP method enlarges the possibility of including other sets of parameters (operations and physics). With the availability of the converged coarsest grid solution, the next forward step to the multigrid cycle becomes possible. The multigrid method shows that the memory storage problems that plagued the application of Newton`s method on fine grids, are of no concern. An important result that needs to be noted here is the performance of the FFCD model. The FFCD model is relatively simple and is based on the overall results the model has shown to predict different divertor plasma parameters. The FFCD model treats exactly the implementation of the deep penetration of energetic neutrals emerging from the divertor plate. The resulting ionization profiles are
International Nuclear Information System (INIS)
Prinja, A.K.
1998-01-01
In this work, it has been shown that, for the given sets of parameters (transport coefficients), the Tangent-Predictor (TP) continuation method, which was used in the coarsest grid, works remarkably well. The problems in finding an initial guess that resides well within Newton's method radius of convergence are alleviated by correcting the initial guess by the predictor step of the TP method. The TP method works well also in neutral gas puffing and impurity simulations. The neutral gas puffing simulation is performed by systematically increasing the fraction of puffing rate according to the TP method until it reaches a desired condition. Similarly, the impurity simulation characterized by using the fraction of impurity density as the continuation parameter, is carried out in line with the TP method. Both methods show, as expected, a better performance than the classical embedding (CE) method. The convergence criteria ε is set to be 10 -9 based on the fact that lower value of ε does not alter the solution significantly. Correspondingly, the number of Newton's iterations in the corrector step of the TP method decrease substantially, an extra point in terms of code speed. The success of the TP method enlarges the possibility of including other sets of parameters (operations and physics). With the availability of the converged coarsest grid solution, the next forward step to the multigrid cycle becomes possible. The multigrid method shows that the memory storage problems that plagued the application of Newton's method on fine grids, are of no concern. An important result that needs to be noted here is the performance of the FFCD model. The FFCD model is relatively simple and is based on the overall results the model has shown to predict different divertor plasma parameters. The FFCD model treats exactly the implementation of the deep penetration of energetic neutrals emerging from the divertor plate. The resulting ionization profiles are relatively smooth as a
Numerical solution methods for viscoelastic orthotropic materials
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1988-01-01
Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
. Among the special features of this book can be mentioned the presentation of a practical approach to reliable estimates of the global error, including warning signals if the reliability is questionable. The technique is generally applicable for estimating the discretization error in numerical...
Numerical Modelling of Streams
DEFF Research Database (Denmark)
Vestergaard, Kristian
In recent years there has been a sharp increase in the use of numerical water quality models. Numeric water quality modeling can be divided into three steps: Hydrodynamic modeling for the determination of stream flow and water levels. Modelling of transport and dispersion of a conservative...
A Well-Posed Two Phase Flow Model and its Numerical Solutions for Reactor Thermal-Fluids Analysis
Energy Technology Data Exchange (ETDEWEB)
Kadioglu, Samet Y. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Berry, Ray [Idaho National Lab. (INL), Idaho Falls, ID (United States); Martineau, Richard [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2016-08-01
A 7-equation two-phase flow model and its numerical implementation is presented for reactor thermal-fluids applications. The equation system is well-posed and treats both phases as compressible flows. The numerical discretization of the equation system is based on the finite element formalism. The numerical algorithm is implemented in the next generation RELAP-7 code (Idaho National Laboratory (INL)’s thermal-fluids code) built on top of an other INL’s product, the massively parallel multi-implicit multi-physics object oriented code environment (MOOSE). Some preliminary thermal-fluids computations are presented.
Numerical experiments modelling turbulent flows
Trefilík, Jiří; Kozel, Karel; Příhoda, Jaromír
2014-03-01
The work aims at investigation of the possibilities of modelling transonic flows mainly in external aerodynamics. New results are presented and compared with reference data and previously achieved results. For the turbulent flow simulations two modifications of the basic k - ω model are employed: SST and TNT. The numerical solution was achieved by using the MacCormack scheme on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability.
Numerical experiments modelling turbulent flows
Directory of Open Access Journals (Sweden)
Trefilík Jiří
2014-03-01
Full Text Available The work aims at investigation of the possibilities of modelling transonic flows mainly in external aerodynamics. New results are presented and compared with reference data and previously achieved results. For the turbulent flow simulations two modifications of the basic k – ω model are employed: SST and TNT. The numerical solution was achieved by using the MacCormack scheme on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability.
Hozman, J.; Tichý, T.
2017-12-01
Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.
Analysis of numerical solutions for Bateman equations
International Nuclear Information System (INIS)
Loch, Guilherme G.; Bevilacqua, Joyce S.
2013-01-01
The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)
International Nuclear Information System (INIS)
Cunha Furtado, F. da; Galeao, A.C.N.R.
1984-01-01
A numerical procedure for the integration of the incompressible Navier-Stokes equations, when expressed in terms of a stream function equation and a vorticity transport equation, is presented. This procedure comprises: the variational formulation of the equations, the construction of the approximation spaces by the finite element method and the discretization via the Galerkin method. For the stationary problems, the system of non-linear algebraic equations resulting from the discretization is solved by the Newton-Raphson algorithm. Finally, for the transient problems, the solution of the non-linear ordinary differential equations resulting from the spatial discretization is accomplished through a Crank-Nicolson scheme. (Author) [pt
Zhuravlev, A. K.; Anokhin, A. O.; Irkhin, V. Yu.
2018-02-01
Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s-d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.
International Nuclear Information System (INIS)
Ravetto, P.; Sumini, M.; Ganapol, B.D.
1988-01-01
In an attempt to better understand the influence of prompt and delayed neutrons on nuclear reactor dynamics, a continuous slowing down model based on Fermi age theory was developed several years ago. This model was easily incorporated into the one-group diffusion equation and provided a realistic physical picture of how delayed and prompt neutrons slow down and simultaneously diffuse throughout a medium. The model allows for different slowing down times for each delayed neutron group as well as for prompt neutrons and for spectral differences between the two typed of neutrons. Because of its generality, this model serves not only a a useful predictive tool to anticipate reactor transients, but also as an excellent educational tool to demonstrate the effect of delayed neutrons in reactor kinetics. However, because of numerical complications, the slowing down model could not be developed to its full potential. In particular, the major limitation was the inversion of the Laplace transform, which relied on a knowledge of the poles associated with the resulting transformed flux. For this reason, only one group of delayed neutrons and times longer than the slowing down times could be considered. As is shown, the new inversion procedure removes the short time limitation as well as allows for any number of delayed neutron groups. The inversion technique is versatile and is useful in teaching numerical methods in nuclear science
Numerical Solution of Laminar Incompressible Generalized Newtonian Fluids Flow
Keslerová, R.; Kozel, K.
2009-09-01
This paper deals with the numerical solution of laminar viscous incompressible flows for generalized Newtonian (Newtonian and non-Newtonian) fluids in the branching channel. The mathematical model is the generalized system of Navier-Stokes equations. The right hand side of this system is defined by power-law model. The finite volume method combined with an artificial compressibility method is used for spatial discretization. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Numerical solution is divided into two parts, steady and unsteady. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. For unsteady solution a dual-time stepping method is considered. Numerical results for flows in two dimensional and three dimensional branching channel are presented.
Underdown, C. G.; Boutt, D. F.; Hynek, S. A.; Munk, L. A.
2017-12-01
Importance of transience in managed groundwater systems is generally determined by timeframe of management decisions. Watersheds with management times shorter than the aquifer (watershed) response time, or the time it takes a watershed to recover from a change in hydrologic state, would not include the new state and are treated as steady-state. However, these watersheds will experience transient response between hydrologic states. Watershed response time is a function of length. Therefore flat, regional watersheds characteristic of the Great Basin have long response times. Defining watershed extents as the area in which the water budget is balanced means inputs equal outputs. Steady-state budgets in the Great Basin have been balanced by extending watershed boundaries to include more area for recharge; however, the length and age of requisite flow paths are poorly constrained and often unrealistic. Inclusion of stored water in hydrologic budget calculations permits water balance within smaller contributing areas. As groundwater flow path lengths, depths, and locations differ between steady-state and transient systems, so do solute transport mechanisms. To observe how transience affects response time and solute transport, a refined (transient) version of the USGS steady-state groundwater flow model of the Great Basin is evaluated. This model is used to assess transient changes in contributing area for Clayton Valley, a lithium-brine producing endorheic basin in southwestern Nevada. Model runs of various recharge, discharge and storage bounds are created from conceptual models based upon historical climate data. Comparing results of the refined model to USGS groundwater observations allows for model validation and comparison against the USGS steady-state model. The transient contributing area to Clayton Valley is 85% smaller than that calculated from the steady-state solution, however several long flow paths important to both water and solute budgets at Clayton Valley
Numerical solution of large sparse linear systems
International Nuclear Information System (INIS)
Meurant, Gerard; Golub, Gene.
1982-02-01
This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr
International Nuclear Information System (INIS)
Ren Zhihao; Kong Xiangyin; Tsai Chiungwen; Ruan Jialei; Li Jinggang; Ma Zhongying; Yan Jianxing; Ma Yinxiang
2015-01-01
A system transient thermal-hydraulic analysis code for PWRs named GINKGO is being developed as part of the indigenous effort of China General Nuclear Power Corp. (CGN) to develop a full-spectrum software package for reactor design and safety analysis. Implemented using the Object-Oriented programming technology, GINKGO is designed to be used for simulating all PWR transients except LBLOCA. The primary physical models and key algorithms applied in GINKGO and also the preliminary validation with the phenomena cases are introduced in the paper. To account for reactor coolant transients, the separated phase model under thermal equilibrium is used in the code. The three governing mixture balance equations augmented with Chexal-Lellouche drift-flux model to determine phase velocities are solved at each time step. Thermal equilibrium between the vapor and liquid phases is assumed with the exception of the upper head volume and pressurizer. And two-region non-equilibrium model and multi-region non-equilibrium model are available for the pressurizer simulation. The reactor point kinetics model with six groups of delayed neutrons, the partial derivative approximation of the DNBR model and decay heat model are combined to give a full description for the reactor core. The additional component model, engineered safety system model and models for other auxiliary systems in GINKGO demonstrate a complete capability for PWR safety analysis and thermal-hydraulic design. A fully implicit solution algorithm involving pressure search is applied in GINKGO to improve the stability of the solution method, especially when two-phase conditions with unequal phase velocities exist. Different phenomena cases are set up to demonstrate the capability of GINKGO used in different boundary conditions, steady state achievement, reverse and branch flow, etc. The GINKGO code uses the C/C++ programming language to take advantage of the language's inherent Object Oriented characteristic and to
Higher-order numerical solutions using cubic splines
Rubin, S. G.; Khosla, P. K.
1976-01-01
A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.
He, Qiaolin
2011-06-01
In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.
DEFF Research Database (Denmark)
Henriquez, Vicente Cutanda
This thesis describes the development of a numerical model of the propagation of sound waves in fluids with viscous and thermal losses, with application to the simulation of acoustic transducers, in particular condenser microphones for measurement. The theoretical basis is presented, numerical...... tools and implementation techniques are described and performance tests are carried out. The equations that govern the motion of fluids with losses and the corresponding boundary conditions are reduced to a form that is tractable for the Boundary Element Method (BEM) by adopting some hypotheses...... that are allowable in this case: linear variations, absence of flow, harmonic time variation, thermodynamical equilibrium and physical dimensions much larger than the molecular mean free path. A formulation of the BEM is also developed with an improvement designed to cope with the numerical difficulty associated...
Numerical solution of inviscid and viscous flow around the profile
Slouka, Martin; Kozel, Karel; Prihoda, Jaromir
2015-05-01
This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox's k-ω model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution and compared with experimental measurements for 8% DCA profile.
Numerical solution of inviscid and viscous flow around the profile
Directory of Open Access Journals (Sweden)
Slouka Martin
2015-01-01
Full Text Available This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox’s k-ω model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution and compared with experimental measurements for 8% DCA profile.
Directory of Open Access Journals (Sweden)
2015-12-01
Full Text Available Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
Numerical Modeling of Airblast.
1987-06-01
can be found in Appendix A. TASK 2.4 The 3--D FCT code was used to study the late time cloud rise geometry from multiple nulear explosions...code was used to study the possiblity of using distributed chemical charges in array geometries. Numerous chemical energy release models where employed...relief of the blast energy at the edges of the DECA charge). Later, it was realized that the edge effects are small at the time when most of the blast
Numerical solutions of the Vlasov equation
International Nuclear Information System (INIS)
Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi
1985-01-01
A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)
International Nuclear Information System (INIS)
Lauber, Philipp
2013-01-01
of the plasma modes that are responsible for the transport of energetic particles. Furthermore, the fast particle distribution function itself can also be measured with much greater confidence. Therefore, the new physics accessible due to a more comprehensive model and numerical implementation can be directly verified and validated with experimental data
numerical and numerical and experimental modeling of the static
African Journals Online (AJOL)
eobe
Keywords: model experiment; numerical analysis; flat shell strips; and reinforced concrete thin-walled sections. 1. INTRODUCTION ..... Note that um, un are obtained from the solution of the beam vibration differential equation and. Ym, Yn are functions of µm, .... the Data Acquisition System. 3.3 The Finite Strip Models of the ...
Numerical solutions of diffusive logistic equation
International Nuclear Information System (INIS)
Afrouzi, G.A.; Khademloo, S.
2007-01-01
In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years
Numerical models for differential problems
Quarteroni, Alfio
2017-01-01
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, an...
Sensitivity analysis of numerical solutions for environmental fluid problems
International Nuclear Information System (INIS)
Tanaka, Nobuatsu; Motoyama, Yasunori
2003-01-01
In this study, we present a new numerical method to quantitatively analyze the error of numerical solutions by using the sensitivity analysis. If a reference case of typical parameters is one calculated with the method, no additional calculation is required to estimate the results of the other numerical parameters such as more detailed solutions. Furthermore, we can estimate the strict solution from the sensitivity analysis results and can quantitatively evaluate the reliability of the numerical solution by calculating the numerical error. (author)
Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.
2018-02-01
A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.
Numerical solution of Newtonian fluids flow through the branching channel
Keslerová, R.; Kozel, K.; Louda, P.
2012-09-01
In this paper the laminar viscous incompressible flow for Newtonian fluids in the branching channel with two outlets is considered. The governing system of equations is based on the system of balance laws for mass and momentum. Steady numerical solution of the described model is based on cell-centered finite volume method using explicit Runge-Kutta time integration. Steady state solution is achieved for t → ∞. In this case the artificial compressibility method can be applied. Channels considered in presented calculations are of constant square or circular cross-sections. The numerical results of Newtonian fluids flow are presented.
Numerical solution of the differential equation for simulation of the ...
African Journals Online (AJOL)
The Euler's method is used to approximate the solutions of the ODEs. According to the RMSE, the simulation results were good agreement with the field collection data. Therefore, the numerical methods can be the technical tool for solving the severity of rice blast disease. Keywords: EPIRICE model, Khao Dawk Mali 105, ...
Kavka, P.; Jeřábek, J.; Strouhal, L.
2016-12-01
The contribution presents a numerical model SMODERP that is used for calculation and prediction of surface runoff and soil erosion from agricultural land. The physically based model includes the processes of infiltration (Phillips equation), surface runoff routing (kinematic wave based equation), surface retention, surface roughness and vegetation impact on runoff. The model is being developed at the Department of Irrigation, Drainage and Landscape Engineering, Civil Engineering Faculty, CTU in Prague. 2D version of the model was introduced in last years. The script uses ArcGIS system tools for data preparation. The physical relations are implemented through Python scripts. The main computing part is stand alone in numpy arrays. Flow direction is calculated by Steepest Descent algorithm and in multiple flow algorithm. Sheet flow is described by modified kinematic wave equation. Parameters for five different soil textures were calibrated on the set of hundred measurements performed on the laboratory and filed rainfall simulators. Spatially distributed models enable to estimate not only surface runoff but also flow in the rills. Development of the rills is based on critical shear stress and critical velocity. For modelling of the rills a specific sub model was created. This sub model uses Manning formula for flow estimation. Flow in the ditches and streams are also computed. Numerical stability of the model is controled by Courant criterion. Spatial scale is fixed. Time step is dynamic and depends on the actual discharge. The model is used in the framework of the project "Variability of Short-term Precipitation and Runoff in Small Czech Drainage Basins and its Influence on Water Resources Management". Main goal of the project is to elaborate a methodology and online utility for deriving short-term design precipitation series, which could be utilized by a broad community of scientists, state administration as well as design planners. The methodology will account for
Numerical solution of highly oscillatory ordinary differential equations
Petzold, Linda R.; Jay, Laurent O.; Yen, Jeng
One of the most difficult problems in the numerical solution of ordinary differential equations (ODEs) and in differential-algebraic equations (DAEs) is the development of methods for dealing with highly oscillatory systems. These types of systems arise, for example, in vehicle simulation when modelling the suspension system or tyres, in models for contact and impact, in flexible body simulation from vibrations in the structural model, in molecular dynamics, in orbital mechanics, and in circuit simulation. Standard numerical methods can require a huge number of time-steps to track the oscillations, and even with small stepsizes they can alter the dynamics, unless the method is chosen very carefully.
CSIR Research Space (South Africa)
Shatalov, M
2011-07-01
Full Text Available to a system of ordinary differential equations. For checking of accuracy of the numerical solution we chose special initial conditions, namely we assume that initial longitudinal displacements of the rod are proportional to one of eigenfunction...
Performance analysis of numeric solutions applied to biokinetics of radionuclides
International Nuclear Information System (INIS)
Mingatos, Danielle dos Santos; Bevilacqua, Joyce da Silva
2013-01-01
Biokinetics models for radionuclides applied to dosimetry problems are constantly reviewed by ICRP. The radionuclide trajectory could be represented by compartmental models, assuming constant transfer rates between compartments. A better understanding of physiological or biochemical phenomena, improve the comprehension of radionuclide behavior in the human body and, in general, more complex compartmental models are proposed, increasing the difficulty of obtaining the analytical solution for the system of first order differential equations. Even with constant transfer rates numerical solutions must be carefully implemented because of almost singular characteristic of the matrix of coefficients. In this work we compare numerical methods with different strategies for ICRP-78 models for Thorium-228 and Uranium-234. The impact of uncertainty in the parameters of the equations is also estimated for local and global truncation errors. (author)
Energy Technology Data Exchange (ETDEWEB)
Molinero Huguet, J.
2001-07-01
This work deals with numerical modeling of groundwater flow, solute transport and chemical reactions through fractured media. These models have been developed within the framework of research activities founded by ENRESA , the Spanish Company for Nuclear Waste Management. This project is the result of a collaborative agreement between ENRESA and his equivalent Swedish Company (SKB) through the research project Task Force 5 of the Aspo Underground Laboratory. One of the objectives of this project is to assess quantitatively th hydrogeological and hydrochemical impact produced by the construction of a Deep Geological Repository in fractured granites. This is important because the new conditions altered construction impact will constitute the initial conditions for the repository closure stage. A second goo l of this work deals with testing the ability of current numerical tools to cope simultaneously with the complex hydrogeological and hydrochemical settlings, which are expected to take place in actual nuclear waste underground repositories constructed in crystalline fractured bed racks. This study has been undertaken through the performance of numerical models, which have subsequently been applied to simulate the hydrogeological and hydrochemical behavior of a granite massif, at a kilo metrical scale, during construction of the Aspo Hard Rock Underground Laboratory (Sweden). The Aspo Hard Rock Laboratory is a prototype, full-scale underground facility launched and operated by SKB. The main aim of the laboratory is to provide an opportunity for research, development and demonstration in a realistic rock environment down to the depth planned for the future deep repository. The framework of this underground facility provides a unique opportunity to attempt the objectives of the present dissertation. (Author)
International Nuclear Information System (INIS)
Molinero Huguet, J.
2001-06-01
This work deals with numerical modeling of groundwater flow, solute transport and chemical reactions through fractured media. These models have been developed within the framework of research activities founded by ENRESA , the Spanish Company for Nuclear Waste Management. This project is the result of a collaborative agreement between ENRESA and his equivalent Swedish Company (SKB) through the research project Task Force 5 of the Aspo Underground Laboratory. One of the objectives of this project is to assess quantitatively th hydrogeological and hydrochemical impact produced by the construction of a Deep Geological Repository in fractured granites. This is important because the new conditions altered construction impact will constitute the initial conditions for the repository closure stage. A second goo l of this work deals with testing the ability of current numerical tools to cope simultaneously with the complex hydrogeological and hydrochemical settlings, which are expected to take place in actual nuclear waste underground repositories constructed in crystalline fractured bed racks. This study has been undertaken through the performance of numerical models, which have subsequently been applied to simulate the hydrogeological and hydrochemical behavior of a granite massif, at a kilo metrical scale, during construction of the Aspo Hard Rock Underground Laboratory (Sweden). The Aspo Hard Rock Laboratory is a prototype, full-scale underground facility launched and operated by SKB. The main aim of the laboratory is to provide an opportunity for research, development and demonstration in a realistic rock environment down to the depth planned for the future deep repository. The framework of this underground facility provides a unique opportunity to attempt the objectives of the present dissertation. (Author)
Numerical Modeling of Ablation Heat Transfer
Ewing, Mark E.; Laker, Travis S.; Walker, David T.
2013-01-01
A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.
Numerical Modeling of Microelectrochemical Systems
DEFF Research Database (Denmark)
Adesokan, Bolaji James
for the reactants in the bulk electrolyte that are traveling waves. The first paper presents the mathematical model which describes an electrochemical system and simulates an electroanalytical technique called cyclic voltammetry. The model is governed by a system of advection–diffusion equations with a nonlinear...... reaction term at the boundary. We investigate the effect of flow rates, scan rates, and concentration on the cyclic voltammetry. We establish that high flow rates lead to the reduced hysteresis in the cyclic voltammetry curves and increasing scan rates lead to more pronounced current peaks. The final part...... of the paper shows that the response current in a cyclic voltammetry increases proportionally to the electrolyte concentration. In the second paper we present an experiment of an electrochemical system in a microfluidc system and compare the result to the numerical solutions. We investigate how the position...
Numerical modeling of foam flows
International Nuclear Information System (INIS)
Cheddadi, Ibrahim
2010-01-01
Liquid foam flows are involved in numerous applications, e.g. food and cosmetics industries, oil extraction, nuclear decontamination. Moreover, their study leads to fundamental knowledge: as it is easier to manipulate and analyse, foam is used as a model material to understand the flow of emulsions, polymers, pastes, or cell aggregates, all of which display both solid and liquid behaviour. Systematic experiments performed by Francois Graner et al. provide precise data that emphasize the non Newtonian properties of the foam. Meanwhile, Pierre Saramito proposed a visco-elasto-plastic continuous tensorial model, akin to predict the behaviour of the foam. The goal of this thesis is to understand this complex behaviour, using these two elements. We have built and validated a resolution algorithm based on a bidimensional finite elements methods. The numerical solutions are in excellent agreement with the spatial distribution of all measured quantities, and confirm the predictive capabilities of the model. The dominant parameters have been identified and we evidenced the fact that the viscous, elastic, and plastic contributions to the flow have to be treated simultaneously in a tensorial formalism. We provide a substantial contribution to the understanding of foams and open the path to realistic simulations of complex VEP flows for industrial applications. (author)
Numerical solution of a reaction-diffusion equation
International Nuclear Information System (INIS)
Moyano, Edgardo A.; Scarpettini, Alberto F.
2000-01-01
The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)
Sensitivity of solutions computed through the Asymptotic Numerical Method
Charpentier, Isabelle
2008-10-01
The Asymptotic Numerical Method (ANM) allows one to compute solution branches of sufficiently smooth non-linear PDE problems using truncated Taylor expansions. The Diamant approach of the ANM has been proposed for hiding definitively the differentiation aspects to the user. In this Note, this significant improvement in terms of genericity is exploited to compute the sensitivity of ANM solutions with respect to modelling parameters. The differentiation in the parameters is discussed at both the equation and code level to highlight the Automatic Differentiation (AD) purposes. A numerical example proves the interest of such techniques for a generic and efficient implementation of sensitivity computations. To cite this article: I. Charpentier, C. R. Mecanique 336 (2008).
On the Hughes model and numerical aspects
Gomes, Diogo A.
2017-01-05
We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.
Numerical solution of ordinary differential equations
Fox, L
1987-01-01
Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...
Numerical modeling of economic uncertainty
DEFF Research Database (Denmark)
Schjær-Jacobsen, Hans
2007-01-01
Representation and modeling of economic uncertainty is addressed by different modeling methods, namely stochastic variables and probabilities, interval analysis, and fuzzy numbers, in particular triple estimates. Focusing on discounted cash flow analysis numerical results are presented, comparisons...
Numerical solution of plasma fluid equations using locally refined grids
International Nuclear Information System (INIS)
Colella, P.
1997-01-01
This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results
Mathematical and Numerical Modeling in Maritime Geomechanics
Directory of Open Access Journals (Sweden)
Miguel Martín Stickle
2012-04-01
Full Text Available A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,... combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the overning equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism.
Brown, A.; Dahlke, H. E.
2015-12-01
The ability of soil to infiltrate large volumes of water is fundamental to managed aquifer recharge (MAR) when using infiltration basins or agricultural fields. In order to investigate the feasibility of using agricultural fields for MAR we conducted a field experiment designed to not only assess the resilience of alfalfa (Medicago sativa) to large (300 mm), short duration (1.5 hour), repeated irrigation events during the winter but also how crop resilience was influenced by soil water movement. We hypothesized that large irrigation amounts designed for groundwater recharge could cause prolonged saturated conditions in the root-zone and yield loss. Tensiometers were installed at two depths (60 and 150 cm) in a loam soil to monitor the changes in soil matric potential within and below the root-zone following irrigation events in each of five experimental plots (8 x 16 m2). To simulate the individual infiltration events we employed the HYDRUS-1D computational module (Simunek et al., 2005) and compared the finite-water content vadose zone flow method (Ogden et al. 2015) with numerical solutions to the Richards' equation. For both models we assumed a homogenous and isotropic root zone that is initially unsaturated with no water flow. Here we assess the ability of these two models to account for the control volume applied to the plots and to capture sharp changes in matric potential that were observed in the early time after an irrigation pulse. The goodness-of-fit of the models was evaluated using the root mean square error (RMSE) for observed and predicted values of cumulative infiltration over time, wetting front depth over time and water content at observation nodes. For the finite-water content method, the RMSE values and output for observation nodes were similar to that from the HYDRUS-1D solution. This indicates that the finite-water content method may be useful for predicting the fate of large volumes of water applied for MAR. Moreover, both models suggest a
Numerical Solution of Turbulence Problems by Solving Burgers’ Equation
Directory of Open Access Journals (Sweden)
Alicia Cordero
2015-05-01
Full Text Available In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution.
Numerical Solution of the Modified Equal Width Wave Equation
Directory of Open Access Journals (Sweden)
Seydi Battal Gazi Karakoç
2012-01-01
Full Text Available Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws 2 and ∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.
Numerical solution of 3D Stokes problems
International Nuclear Information System (INIS)
Zhou, R.Q.N.
1993-01-01
Preconditions conjugate gradient algorithms for solving 3D Stokes problems by stable piecewise discontinuous pressure finite elements are presented. The emphasis is on the preconditioning schemes and their numerical implementation for use with Hermitian-based discontinuous pressure elements. For the piecewise constant discontinuous pressure elements, a variant implementation of the preconditioner proposed by Cahouet and Chabard for the continuous pressure elements is employed. For the piecewise linear discontinuous pressure elements, a new preconditioner is presented. Numerical examples are presented for the cubic lid driven cavity problem with two representative elements (i.e., the Q2-P0 and the Q2-P1 brick elements). Numerical results show that the preconditioning schemes are very effective in reducing the number of pressure iterations at very reasonable costs. It is also shown that they are insensitive to the mesh Reynolds number, except for nearly steady flows (R em → 0), and are almost independent of mesh sizes. It is demonstrated that the schemes performed reasonably well on nonuniform meshes. 15 refs., 6 figs., 1 tab
NUMERICAL SOLUTIONS OF SOME PARAMETRIC EFFECTS DUE ...
African Journals Online (AJOL)
Dr A.B.Ahmed
ABSTRACT. The analytical solutions for the scattering of electromagnetic waves from an infinite circular cylinder and refractive index are programmed in FORTRAN (Barber and Hill, 1990). The resulting quantities include the scattering coefficients, the scattering amplitudes and the intensities. The range of variable input.
Numerical solution to nonlinear Tricomi equation using WENO schemes
Directory of Open Access Journals (Sweden)
Adrian Sescu
2010-09-01
Full Text Available Nonlinear Tricomi equation is a hybrid (hyperbolic-elliptic second order partial differential equation, modelling the sonic boom focusing. In this paper, the Tricomi equation is transformed into a hyperbolic system of first order equations, in conservation law form. On the upper boundary, a new mixed boundary condition for the acoustic pressure is used to avoid the inclusion of the Dirac function in the numerical solution. Weighted Essentially Non-Oscillatory (WENO schemes are used for the spatial discretization, and the time marching is carried out using the second order accurate Runge-Kutta total-variation diminishing (TVD scheme.
Bio-based lubricants for numerical solution of elastohydrodynamic lubrication
Cupu, Dedi Rosa Putra; Sheriff, Jamaluddin Md; Osman, Kahar
2012-06-01
This paper presents a programming code to provide numerical solution of elastohydrodynamic lubrication problem in line contacts which is modeled through an infinite cylinder on a plane to represent the application of roller bearing. In this simulation, vegetable oils will be used as bio-based lubricants. Temperature is assumed to be constant at 40°C. The results show that the EHL pressure for all vegetable oils was increasing from inlet flow until the center, then decrease a bit and rise to the peak pressure. The shapes of EHL film thickness for all tested vegetable oils are almost flat at contact region.
Numerical solution of ordinary differential equations
Lapidus, Leon
1971-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
On numerical solution of Burgers' equation by homotopy analysis method
International Nuclear Information System (INIS)
Inc, Mustafa
2008-01-01
In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions
Numerical solution of Euler and Navier-Stokes equations for 2D transonic problems
Hulek, T.; Hunek, M.; Kozel, K.
1992-12-01
The present contribution is a numerical solution of Euler and Navier-Stokes equations for 2D transonic flow problems using several different numerical methods. The time marching cell centered and cell vertex finite volume methods were used for both flow models. Various explicit multistage Runge-Kutta methods (RK methods) were applied for inviscid flows and these methods were also used for numerical solution of incompressible and compressinble Navier-Stokes equations.
Solution of Milne problem by Laplace transformation with numerical inversion
International Nuclear Information System (INIS)
Campos Velho, H.F. de.
1987-12-01
The Milne problem for monoenergetic neutrons, by Laplace Transform of the neutron transport integral equation with numerical inversion of the transformed solution by gaussian quadrature, using the fatorization of the dispersion function. The resulted is solved compared its analitical solution. (author) [pt
Numerical solution of electrostatic problems of the accelerator project VICKSI
International Nuclear Information System (INIS)
Janetzki, U.
1975-03-01
In this work, the numerical solution to a few of the electrostatic problems is dealt with which have occured within the framework of the heavy ion accelerator project VICKSI. By means of these selected examples, the versatile applicability of the numerical method is to be demonstrated, and simultaneously assistance is given for the solution of similar problems. The numerical process for solving ion-optics problems consists generally of two steps. In the first step, the potential distribution for a given boundary value problem is iteratively calculated for the Laplace equation, and then the image characteristics of the electostatic lense are investigated using the Raytrace method. (orig./LH) [de
Numerical solution of non-linear diffusion problems
International Nuclear Information System (INIS)
Carmen, A. del; Ferreri, J.C.
1998-01-01
This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs
Fundamentals of Numerical Modelling of Casting Processes
DEFF Research Database (Denmark)
Hattel, Jesper Henri; Pryds, Nini; Thorborg, Jesper
Fundamentals of Numerical Modelling of Casting Processes comprises a thorough presentation of the basic phenomena that need to be addressed in numerical simulation of casting processes. The main philosophy of the book is to present the topics in view of their physical meaning, whenever possible......, rather than relying strictly on mathematical formalism. The book, aimed both at the researcher and the practicing engineer, as well as the student, is naturally divided into four parts. Part I (Chapters 1-3) introduces the fundamentals of modelling in a 1-dimensional framework. Part II (Chapter 4......) presents the most important aspects of solidification theory related to modelling. Part III (Chapter 5) describes the fluid flow phenomena and in part IV (Chapter 6) the stress-strain analysis is addressed. For all parts, both numerical formulations as well as some important analytical solutions...
Directory of Open Access Journals (Sweden)
Gernot Pulverer
2010-01-01
Full Text Available In this paper, we investigate the singular Sturm-Liouville problem u′′=λg(u, u′(0=0, βu′(1+αu(1=A, where λ is a nonnegative parameter, β≥0, α>0, and A>0. We discuss the existence of multiple positive solutions and show that for certain values of λ, there also exist solutions that vanish on a subinterval [0,ρ]⊂[0,1, the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for g(u=1/u and for some model problems from the class of singular differential equations (ϕ(u′′+f(t,u′=λg(t,u,u′ discussed in Agarwal et al. (2007. For the numerical simulation, the collocation method implemented in our MATLAB code bvpsuite has been applied.
Numerical models as interactive art
Donchyts, G.; Baart, F.; van de Pas, B.; Joling, A.
2017-12-01
We capture our understanding of the environment in advanced computer models. We use these numerical models to simulate the growth of deltas, meandering rivers, dune erosion, river floodings, effects of interventions. If presented with care, models can help understand the complexity of our environment and show the beautiful patterns of nature. While the topics are relevant and appealing to the general public the use of numerical models has been limited to technical users. Not many people have appreciations for the pluriform of options, esoteric user interfaces, manual editing of configuration files and extensive jargon. The models are static, you can start them, but then you have to wait, usually hours or more, for the results to become available, not something that you could imagine resulting in an immersive, interactive experience for the general public. How can we go beyond just using results? How can we adapt existing numerical models so they can be used in an interactive environment? How can we touch them and feel them? Here we show how we adapted existing models (Delft3D, Lisflood, XBeach) and reused them in as the basis for interactive exhibitions in museums with an educative goal. We present our structured approach which consists of combining a story, inspiration, a canvas, colors, shapes and interactive elements. We show how the progression from simple presentation forms to interactive art installations.
Numerical approximation of random periodic solutions of stochastic differential equations
Feng, Chunrong; Liu, Yu; Zhao, Huaizhong
2017-10-01
In this paper, we discuss the numerical approximation of random periodic solutions of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the pull-back flow when the starting time tends to -∞ along the multiple integrals of the period. As the random periodic solution is not explicitly constructible, it is useful to study the numerical approximation. We discretise the SDE using the Euler-Maruyama scheme and modified Milstein scheme. Subsequently, we obtain the existence of the random periodic solution as the limit of the pull-back of the discretised SDE. We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of √{Δ t} in the mean square sense in Euler-Maruyama method and Δ t in the Milstein method. We also obtain the weak convergence result for the approximation of the periodic measure.
Numerical modelling in material physics
International Nuclear Information System (INIS)
Proville, L.
2004-12-01
The author first briefly presents his past research activities: investigation of a dislocation sliding in solid solution by molecular dynamics, modelling of metal film growth by phase field and Monte Carlo kinetics, phase field model for surface self-organisation, phase field model for the Al 3 Zr alloy, calculation of anharmonic photons, mobility of bipolarons in superconductors. Then, he more precisely reports the mesoscopic modelling in phase field, and some atomistic modelling (dislocation sliding, Monte Carlo simulation of metal surface growth, anharmonic network optical spectrum modelling)
Numerical solution of the Fokker--Planck equations for a multi-species plasma
International Nuclear Information System (INIS)
Killeen, J.; Mirin, A.A.
1977-01-01
Two numerical models used for studying collisional multispecies plasmas are described. The mathematical model is the Boltzmann kinetic equation with Fokker-Planck collision terms. A one-dimensional code and a two-dimensional code, used for the solution of the time-dependent Fokker-Planck equations for ion and electron distribution functions in velocity space, are described. The required equations and boundary conditions are derived and numerical techniques for their solution are given
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Mathematical modelling and numerical simulation of casting processes
DEFF Research Database (Denmark)
Hattel, Jesper Henri
1998-01-01
The control volume method applied to numerical modelling of castning. Analytical solutions based on the error function.Riemann-temperature. Modelling of release of latent heat with the enthalpy method....
Numerical solution of Lord-Shulman thermopiezoelectricity dynamical problem
Stelmashchuk, Vitaliy; Shynkarenko, Heorhiy
2018-01-01
Using Lord-Shulman hypothesis we formulate the initial boundary value problem and its corresponding variational problem of a generalized linear thermopiezoelectricity in terms of the displacement, electrical potential, temperature increment and heat flux, which describes the dynamic behavior of the coupled mechanic, electric and heat waves in pyroelectric materials. We construct the corresponding energy balance equation and determine input data regularity for the variational problem, which guarantees the existence, uniqueness and stability of its solution in the problem energy norm. Based on these results, we propose a numerical scheme for solving this problem, which includes spatial finite element semi-discretization and one-step recurrent time integration procedures and generalizes the similar one for classic thermopiezoelectricity problem. We give the sufficient conditions on the values of the scheme parameters which guarantee properties of conservatism and unconditional stability of the scheme. The rest of the article is devoted to the analysis of performed numerical experiments with 1D model problem and their results are then compared with the ones obtained by the other researchers.
Constructing exact symmetric informationally complete measurements from numerical solutions
Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne
2018-04-01
Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.
Case studies in the numerical solution of oscillatory integrals
International Nuclear Information System (INIS)
Adam, G.
1992-06-01
A numerical solution of a number of 53,249 test integrals belonging to nine parametric classes was attempted by two computer codes: EAQWOM (Adam and Nobile, IMA Journ. Numer. Anal. (1991) 11, 271-296) and DO1ANF (Mark 13, 1988) from the NAG library software. For the considered test integrals, EAQWOM was found to be superior to DO1ANF as it concerns robustness, reliability, and friendly user information in case of failure. (author). 9 refs, 3 tabs
Efficient numerical solution to vacuum decay with many fields
Energy Technology Data Exchange (ETDEWEB)
Masoumi, Ali; Olum, Ken D.; Shlaer, Benjamin, E-mail: ali@cosmos.phy.tufts.edu, E-mail: kdo@cosmos.phy.tufts.edu, E-mail: shlaer@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2017-01-01
Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.
Numerical models of planetary dynamos
International Nuclear Information System (INIS)
Glatzmaier, G.A.; Roberts, P.H.
1992-01-01
We describe a nonlinear, axisymmetric, spherical-shell model of planetary dynamos. This intermediate-type dynamo model requires a prescribed helicity field (the alpha effect) and a prescribed buoyancy force or thermal wind (the omega effect) and solves for the axisymmetric time-dependent magnetic and velocity fields. Three very different time dependent solutions are obtained from different prescribed sets of alpha and omega fields
Numerical modelling of mine workings.
CSIR Research Space (South Africa)
Lightfoot, N
1999-03-01
Full Text Available List of Tables Table 6-1: The benefits of artificial expertise (expert systems) in comparison to human expertise (after Waterman, 1986)………………………………………………………….22 Table 6-2: Available expert system development tools………………………………….27 9 Glossary... with ‘intelligence’ to help engineers use numerical modelling programs for mine design. This area of the project represented 55 man-days of work. The work concentrated on four potential aspects of user interface development for numerical modelling. The first...
New numerical method for solving the solute transport equation
International Nuclear Information System (INIS)
Ross, B.; Koplik, C.M.
1978-01-01
The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste
Numerical solution of the resistive magnetohydrodynamic boundary layer equations
Energy Technology Data Exchange (ETDEWEB)
Glasser, A.H.; Jardin, S.C.; Tesauro, G.
1984-05-01
Three different techniques are presented for numerical solution of the equations governing the boundary layer of resistive magnetohydrodynamic tearing and interchange instabilities in toroidal geometry. Good agreement among these methods and with analytical results provides confidence in the correctness of the results. Solutions obtained in regimes where analytical methods fail indicate a new scaling for the tearing mode as well as the existence of a new regime of stability.
Numerical solution of the resistive magnetohydrodynamic boundary-layer equations
Energy Technology Data Exchange (ETDEWEB)
Glasser, A.H.; Jardin, S.C.; Tesauro, G.
1983-10-01
Three different techniques are presented for numerical solution of the equations governing the boundary layer of resistive magnetohydrodynamic tearing and interchange instabilities in toroidal geometry. Excellent agreement among these methods and with analytical results provides confidence in the correctness of the results. Solutions obtained in regimes where analytical medthods fail indicate a new scaling for the tearing mode as well as the existence of a new regime of stability.
On the numerical solution of the sine-Gordon equation
International Nuclear Information System (INIS)
Ablowitz, M.J.; Schober, C.; Herbst, B.M.
1996-01-01
In this, the first of two papers on the numerical solution of the sine-Gordon equation, we investigate the numerical behavior of a double discrete, completely integrable discretization of the sine-Gordon equation. For certain initial values, in the vicinity of homoclinic manifolds, this discretization admits an instability in the form of grid scale oscillations. We clarify the nature of the instability through an analytical investigation supported by numerical experiments. In particular, a perturbation analysis of the associated linear spectral problem shows that the initial values used for the numerical experiments lie exponentially close to a homoclinic manifold. This paves the way for the second paper where we use the non-linear spectrum as a basis for comparing different numerical schemes. 21 refs., 11 figs
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
Numerical Solution of Differential Algebraic Equations and Applications
DEFF Research Database (Denmark)
Thomsen, Per Grove
2005-01-01
These lecture notes have been written as part of a special course on the numerical solution of Differential Algebraic Equations and applications . The course was held at IMM in the spring of 2005. The authors of the different chapters have all taken part in the course and the chapters are written...
numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Dr A.B.Ahmed
Fifth order boundary value problems are prevalent in the mathematical stimulations of Viscoelastic flow, heat convection, and in many other fields of science and technology. However, analytic methods of solving these problems are often challenging. Hence, researchers have turned their search light to numerical solution ...
The Numerical Solution of an Abelian Ordinary Differential Equation ...
African Journals Online (AJOL)
In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...
Numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Mamadu-Njoseh polynomials are polynomials constructed in the interval [-1,1] with respect to the weight function () = 2 + 1. This paper aims at applying these polynomials, as trial functions satisfying the boundary conditions, in a numerical approach for the solution of fifth order boundary value problems. For this, these ...
Numerical Solution of Stochastic Nonlinear Fractional Differential Equations
El-Beltagy, Mohamed A.
2015-01-07
Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.
Numerical modeling of sympathetic detonation
Energy Technology Data Exchange (ETDEWEB)
Bowman, A.L.; Kershner, J.D.; Mader, C.L.
1979-11-01
The sympathetic detonation of small cubes of solid rocket propellant was modeled numerically, using the Eulerian reactive hydrodynamic code 2DE with Forest Fire burn rates. The model was applied to cubes of 1 to 3 in., with excellent agreement between calculated and experimental results. The model also was applied to several propellants and to different experimental arrangements. The blast-wave pressures in the air gap and the induced shock pressures in the acceptor were obtained from the model. The correlation between these pressures was coupled with a study of the effect of the length-to-diameter ratio of a donor cylinder and the necessary conditions for detonation of the acceptor to provide a semiquantitative predictive capability.
Numerical model of thyroid counter
Directory of Open Access Journals (Sweden)
Szuchta Maciej
2016-03-01
Full Text Available The aim of this study was to develop a numerical model of spectrometric thyroid counter, which is used for the measurements of internal contamination by in vivo method. The modeled detector is used for a routine internal exposure monitoring procedure in the Radiation Protection Measurements Laboratory of National Centre for Nuclear Research (NCBJ. This procedure may also be used for monitoring of occupationally exposed nuclear medicine personnel. The developed model was prepared using Monte Carlo code FLUKA 2011 ver. 2b.6 Apr-14 and FLAIR ver. 1.2-5 interface. It contains a scintillation NaI(Tl detector, the collimator and the thyroid water phantom with a reference source of iodine 131I. The geometry of the model was designed and a gamma energy spectrum of iodine 131I deposited in the detector was calculated.
Avoiding numerical pitfalls in social force models
Köster, Gerta; Treml, Franz; Gödel, Marion
2013-06-01
The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.
Energy Technology Data Exchange (ETDEWEB)
Nourtier-Mazauric, E.
2003-03-15
This thesis presents a thermodynamic and kinetic model of interactions between a fluid and ideal solid solutions represented by several end-members. The reaction between a solid solution and the aqueous solution results from the competition between the stoichiometric dissolution of the initial solid solution and the co-precipitation of the least soluble solid solution in the fluid at considered time. This model was implemented in ARCHIMEDE, a computer code of reactive transport in porous media, then applied to various examples. In the case of binary solid solutions, a graphical method allowed to determine the compositions of the precipitating solid solutions, with the aid of the end-member chemical potentials. The obtained program could be used to notably model the diagenesis of clayey or carbonated oil reservoirs, or the ground pollutant dispersion. (author)
Simplified method for numerical modeling of fiber lasers.
Shtyrina, O V; Yarutkina, I A; Fedoruk, M P
2014-12-29
A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.
Comprehensive numerical modelling of tokamaks
International Nuclear Information System (INIS)
Cohen, R.H.; Cohen, B.I.; Dubois, P.F.
1991-01-01
We outline a plan for the development of a comprehensive numerical model of tokamaks. The model would consist of a suite of independent, communicating packages describing the various aspects of tokamak performance (core and edge transport coefficients and profiles, heating, fueling, magnetic configuration, etc.) as well as extensive diagnostics. These codes, which may run on different computers, would be flexibly linked by a user-friendly shell which would allow run-time specification of packages and generation of pre- and post-processing functions, including workstation-based visualization of output. One package in particular, the calculation of core transport coefficients via gyrokinetic particle simulation, will become practical on the scale required for comprehensive modelling only with the advent of teraFLOP computers. Incremental effort at LLNL would be focused on gyrokinetic simulation and development of the shell
Numerical Model for Hydrovolcanic Explosions.
Mader, Charles; Gittings, Michael
2007-03-01
A hydrovolcanic explosion is generated by the interaction of hot magma with ground water. It is called Surtseyan after the 1963 explosive eruption off Iceland. The water flashes to steam and expands explosively. Liquid water becomes water gas at constant volume and generates pressures of about 3GPa. The Krakatoa hydrovolcanic explosion was modeled using the full Navier-Stokes AMR Eulerian compressible hydrodynamic code called SAGE [1] which includes the high pressure physics of explosions. The water in the hydrovolcanic explosion was described as liquid water heated by magma to 1100 K. The high temperature water is treated as an explosive with the hot liquid water going to water gas. The BKW [2] steady state detonation state has a peak pressure of 8.9 GPa, a propagation velocity of 5900 meters/sec and the water is compressed to 1.33 g/cc. [1] Numerical Modeling of Water Waves, Second Edition, Charles L. Mader, CRC Press 2004. [2] Numerical Modeling of Explosions and Propellants, Charles L. Mader, CRC Press 1998.
Numerical solution of nonlinear Hammerstein fuzzy functional integral equations
Enkov, Svetoslav; Georgieva, Atanaska; Nikolla, Renato
2016-12-01
In this work we investigate nonlinear Hammerstein fuzzy functional integral equation. Our aim is to provide an efficient iterative method of successive approximations by optimal quadrature formula for classes of fuzzy number-valued functions of Lipschitz type to approximate the solution. We prove the convergence of the method by Banach's fixed point theorem and investigate the numerical stability of the presented method with respect to the choice of the first iteration. Finally, illustrative numerical experiment demonstrate the accuracy and the convergence of the proposed method.
Numerical modelling of barrier discharge
International Nuclear Information System (INIS)
Kozlov, K.V.
1990-01-01
A survey is given of the theory of the barrier discharge in oxygen at atmospheric pressure. The discharge consists of a number of randomly distributed microdischarges of nanosecond duration. This complicated space-time structure must be taken into account in any numerical model of the barrier discharge. In a single discharge channel, three consequent phases can be distinguished; 1) electric breakdown and electron-time-scale processes; 2) ion drift and ion-time-scale processes; 3) slow chemical processes, diffusion of chemical products and heat transfer. The scheme of such a three-phase model is presented and the results of simulation are discussed and compared with experimental data. (J.U.) 9 figs., 15 refs
Solute transport modelling with the variable temporally dependent ...
Indian Academy of Sciences (India)
Pintu Das
2018-02-07
Feb 7, 2018 ... In this present study, analytical and numerical solutions are obtained for solute transport modelling in homogeneous ..... Clay (0.40). Analytical solution. Numerical solution. Figure 3. Comparison of concentration distribution for sinu- soidal velocity pattern for boundary condition c0. 2 1 ю sec wt р. Ю.
Numerical solution of the optimized random phase approximation
International Nuclear Information System (INIS)
Pastore, G.; Matthews, F.; Akinlade, O.; Badirkhan, Z.
1994-06-01
An accurate, efficient and robust numerical method for the solution of the Optimized Random Phase Approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is rigorously proved. The method, hinging on the characterization of the generating functions, significantly improves on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm. (author). 23 refs, 1 fig., 1 tab
High-order numerical solutions using cubic splines
Rubin, S. G.; Khosla, P. K.
1975-01-01
The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
Numerical Modelling Of Pumpkin Balloon Instability
Wakefield, D.
Tensys have been involved in the numerical formfinding and load analysis of architectural stressed membrane structures for 15 years. They have recently broadened this range of activities into the `lighter than air' field with significant involvement in aerostat and heavy-lift hybrid airship design. Since early 2004 they have been investigating pumpkin balloon instability on behalf of the NASA ULDB programme. These studies are undertaken using inTENS, an in-house finite element program suite based upon the Dynamic Relaxation solution method and developed especially for the non-linear analysis and patterning of membrane structures. The paper describes the current state of an investigation that started with a numerical simulation of the lobed cylinder problem first studied by Calladine. The influence of material properties and local geometric deformation on stability is demonstrated. A number of models of complete pumpkin balloons have then been established, including a 64-gore balloon with geometry based upon Julian Nott's Endeavour. This latter clefted dramatically upon initial inflation, a phenomenon that has been reproduced in the numerical model. Ongoing investigations include the introduction of membrane contact modelling into inTENS and correlation studies with the series of large-scale ULDB models currently in preparation.
Numerical modelling of fuel sprays
Energy Technology Data Exchange (ETDEWEB)
Bergstroem, C.
1999-06-01
The way the fuel is introduced into the combustion chamber is one of the most important parameters for the power output and the generation of emissions in the combustion of liquid fuels. The interaction between the turbulent gas flow field and the liquid fuel droplets, the vaporisation of them and the mixing of the gaseous fuel with the ambient air that are vital parameters in the combustion process. The use of numerical calculations is an important tool to better understand these complex interacting phenomena. This thesis reports on the numerical modelling of fuel sprays in non-reacting cases using an own developed spray module. The spray module uses the stochastic parcel method to represent the spray. The module was made in such manner that it could by coupled with different gas flow solver. Results obtained from four different gas flow solvers are presented in the thesis, including the use of two different kinds of turbulence models. In the first part the spray module is coupled with a k-{eta} based 2-D cylindrical gas flow solver. A thorough sensitivity analysis was performed on the spray and gas flow solver parameters, such as grid size dependence and sensitivity to initial values of k-{eta}. The results of the spray module were also compared to results from other spray codes, e.g. the well known KIVA code. In the second part of this thesis the spray was injected into a turbulent and fully developed crossflow studied. The spray module was attached to a LES (Large Eddy Simulation) based flow solvers enabling the study of the complex structures and time dependent phenomena involved in spray in crossflows. It was found that the spray performs an oscillatory motion and that the Strouhal number in the wake was about 0.1. Different spray breakup models were evaluated by comparing with experimental results 66 refs, 56 figs
Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil
Directory of Open Access Journals (Sweden)
Slouka Martin
2016-01-01
Full Text Available This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.
Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil
Slouka, Martin; Kozel, Karel
2016-03-01
This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.
A numerical guide to the solution of the bidomain equations of cardiac electrophysiology
Pathmanathan, Pras
2010-06-01
Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.
Some Numerical Aspects on Crowd Motion - The Hughes Model
Gomes, Diogo A.
2016-01-06
Here, we study a crowd model proposed by R. Hughes in [5] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solution. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two numerical examples.
Directory of Open Access Journals (Sweden)
John F. Moxnes
2014-06-01
Full Text Available There has been increasing interest in numerical simulations of fragmentation of expanding warheads in 3D. Accordingly there is a pressure on developers of leading commercial codes, such as LS-DYNA, AUTODYN and IMPETUS Afea, to implement the reliable fracture models and the efficient solution techniques. The applicability of the Johnson–Cook strength and fracture model is evaluated by comparing the fracture behaviour of an expanding steel casing of a warhead with experiments. The numerical codes and different numerical solution techniques, such as Eulerian, Lagrangian, Smooth particle hydrodynamics (SPH, and the corpuscular models recently implemented in IMPETUS Afea are compared. For the same solution techniques and material models we find that the codes give similar results. The SPH technique and the corpuscular technique are superior to the Eulerian technique and the Lagrangian technique (with erosion when it is applied to materials that have fluid like behaviour such as the explosive and the tracer. The Eulerian technique gives much larger calculation time and both the Lagrangian and Eulerian techniques seem to give less agreement with our measurements. To more correctly simulate the fracture behaviours of the expanding steel casing, we applied that ductility decreases with strain rate. The phenomena may be explained by the realization of adiabatic shear bands. An implemented node splitting algorithm in IMPETUS Afea seems very promising.
Numerical solution of DGLAP equations using Laguerre polynomials expansion and Monte Carlo method.
Ghasempour Nesheli, A; Mirjalili, A; Yazdanpanah, M M
2016-01-01
We investigate the numerical solutions of the DGLAP evolution equations at the LO and NLO approximations, using the Laguerre polynomials expansion. The theoretical framework is based on Furmanski et al.'s articles. What makes the content of this paper different from other works, is that all calculations in the whole stages to extract the evolved parton distributions, are done numerically. The employed techniques to do the numerical solutions, based on Monte Carlo method, has this feature that all the results are obtained in a proper wall clock time by computer. The algorithms are implemented in FORTRAN and the employed coding ideas can be used in other numerical computations as well. Our results for the evolved parton densities are in good agreement with some phenomenological models. They also indicate better behavior with respect to the results of similar numerical calculations.
2nd International Workshop on the Numerical Solution of Markov Chains
1995-01-01
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Numerical solution of 2D and 3D impinging jet flows
Energy Technology Data Exchange (ETDEWEB)
Kozel, K.; Louda, P. (Technical Univ. Prague (Czech Republic). Dept. of Technical Mathematics); Prihoda, J. (Ceska Akademie Ved, Prague (Czech Republic). Inst. of Thermomechanics)
1999-01-01
The work deals with numerical solution of laminar and turbulent incompressible impinging jet flows. Four numerical schemes (two explicit and two implicit) were developed and achieved results were qualitatively compared (isolines of velocity, rate of convergence). For turbulent flows, Reynolds-averaged Navier-Stokes equations were numerically solved by the low-Reynolds number modifications of the k-[epsilon] or by k-[omega] turbulence models. The k-[epsilon] model was used in the form where Dirichlet conditions (zero conditions) for both k and [epsilon] along walls is possible to use. The 2D methods were also extended to 3D problem using a finite-volume approximation. (orig.)
Numerical solution of 2D and 3D impinging jet flows
Energy Technology Data Exchange (ETDEWEB)
Kozel, K.; Louda, P. [Technical Univ. Prague (Czech Republic). Dept. of Technical Mathematics; Prihoda, J. [Ceska Akademie Ved, Prague (Czech Republic). Inst. of Thermomechanics
1999-12-01
The work deals with numerical solution of laminar and turbulent incompressible impinging jet flows. Four numerical schemes (two explicit and two implicit) were developed and achieved results were qualitatively compared (isolines of velocity, rate of convergence). For turbulent flows, Reynolds-averaged Navier-Stokes equations were numerically solved by the low-Reynolds number modifications of the k-{epsilon} or by k-{omega} turbulence models. The k-{epsilon} model was used in the form where Dirichlet conditions (zero conditions) for both k and {epsilon} along walls is possible to use. The 2D methods were also extended to 3D problem using a finite-volume approximation. (orig.)
Random ordinary differential equations and their numerical solution
Han, Xiaoying
2017-01-01
This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor ...
CSR Fields: Direct Numerical Solution of the Maxwell's Equation
International Nuclear Information System (INIS)
Novokhatski, Alexander
2011-01-01
We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in (1). Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in (2). We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields (3).
Experimental and numerical analysis of a knee endoprosthesis numerical model
Directory of Open Access Journals (Sweden)
L. Zach
2016-07-01
Full Text Available The aim of this study is to create and verify a numerical model for a Medin Modular orthopedic knee-joint implant by investigating contact pressure, its distribution and contact surfaces. An experiment using Fuji Prescale pressure sensitive films and a finite element analysis (FEA using Abaqus software were carried out. The experimental data were evaluated using a special designed program and were compared with the results of the analysis. The designed evaluation program had been constructed on the basis of results obtained from a supplementary calibration experiment. The applicability of the numerical model for the real endoprosthesis behavior prediction was proven on the basis of their good correlation.
Conceptual and Numerical Models for UZ Flow and Transport
International Nuclear Information System (INIS)
Liu, H.
2000-01-01
The purpose of this Analysis/Model Report (AMR) is to document the conceptual and numerical models used for modeling of unsaturated zone (UZ) fluid (water and air) flow and solute transport processes. This is in accordance with ''AMR Development Plan for U0030 Conceptual and Numerical Models for Unsaturated Zone (UZ) Flow and Transport Processes, Rev 00''. The conceptual and numerical modeling approaches described in this AMR are used for models of UZ flow and transport in fractured, unsaturated rock under ambient and thermal conditions, which are documented in separate AMRs. This AMR supports the UZ Flow and Transport Process Model Report (PMR), the Near Field Environment PMR, and the following models: Calibrated Properties Model; UZ Flow Models and Submodels; Mountain-Scale Coupled Processes Model; Thermal-Hydrologic-Chemical (THC) Seepage Model; Drift Scale Test (DST) THC Model; Seepage Model for Performance Assessment (PA); and UZ Radionuclide Transport Models
Higher-order numerical solutions using cubic splines. [for partial differential equations
Rubin, S. G.; Khosla, P. K.
1975-01-01
A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-
Numerical solution of singularity-perturbed two-point boundary-value problems
International Nuclear Information System (INIS)
Masenge, R.W.P.
1993-07-01
Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab
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.
Numerical modeling capabilities to predict repository performance
International Nuclear Information System (INIS)
1979-09-01
This report presents a summary of current numerical modeling capabilities that are applicable to the design and performance evaluation of underground repositories for the storage of nuclear waste. The report includes codes that are available in-house, within Golder Associates and Lawrence Livermore Laboratories; as well as those that are generally available within the industry and universities. The first listing of programs are in-house codes in the subject areas of hydrology, solute transport, thermal and mechanical stress analysis, and structural geology. The second listing of programs are divided by subject into the following categories: site selection, structural geology, mine structural design, mine ventilation, hydrology, and mine design/construction/operation. These programs are not specifically designed for use in the design and evaluation of an underground repository for nuclear waste; but several or most of them may be so used
Sensitivity of the solution of the Elder problem to density, velocity and numerical perturbations
Park, Chan-Hee; Aral, Mustafa M.
2007-06-01
In this paper the Elder problem is studied with the purpose of evaluating the inherent instabilities associated with the numerical solution of this problem. Our focus is first on the question of the existence of a unique numerical solution for this problem, and second on the grid density and fluid density requirements necessary for a unique numerical solution. In particular we have investigated the instability issues associated with the numerical solution of the Elder problem from the following perspectives: (i) physical instability issues associated with density differences; (ii) sensitivity of the numerical solution to idealization irregularities; and, (iii) the importance of a precise velocity field calculation and the association of this process with the grid density levels that is necessary to solve the Elder problem accurately. In the study discussed here we have used a finite element Galerkin model we have developed for solving density-dependent flow and transport problems, which will be identified as TechFlow. In our study, the numerical results of Frolkovič and de Schepper [Frolkovič, P. and H. de Schepper, 2001. Numerical modeling of convection dominated transport coupled with density-driven flow in porous media, Adv. Water Resour., 24, 63-72.] were replicated using the grid density employed in their work. We were also successful in duplicating the same result with a less dense grid but with more computational effort based on a global velocity estimation process we have adopted. Our results indicate that the global velocity estimation approach recommended by Yeh [Yeh, G.-T., 1981. On the computation of Darcian velocity and mass balance in finite element modelling of groundwater flow, Water Resour. Res., 17(5), 1529-1534.] allows the use of less dense grids while obtaining the same accuracy that can be achieved with denser grids. We have also observed that the regularity of the elements in the discretization of the solution domain does make a difference
International Nuclear Information System (INIS)
Labik, S.; Pospisil, R.; Malijevsky, A.
1994-01-01
A numerical algorithm for solving the Ornstein-Zernike (OZ) intergal equation of statistical mechanics is described for the class of fluids composed of molecules with axially symmetric interactions. Since the OZ equation is a nonlinear second-kind Fredholm equation whose key feature for the class of problems of interest is the highly computationally intensive nature of the kernel, the general approach employed in this paper is thus potentially useful for similar problems with this characteristic. The algorithm achieves a high degree of computational efficiency by combining iterative linearization of the most complex portion of the kernel with a combination of Newton-Raphson and Picard iteration methods for the resulting approximate equation. This approach makes the algorithm analogous to the approach of the classical Gauss-Newton method for nonlinear regression, and we call our method the GN algorithm. An example calculation is given illustration the use of the algorithm for the hard prolate ellipsoid fluid and its results are compared directly with those of the Picard iteration method. The GN algorithm is four to ten times as fast as the Picard method, and we present evidence that it is the most efficient general method currently available
Numerical modelling approach for mine backfill
Indian Academy of Sciences (India)
... of mine backfill material needs special attention as the numerical model must behave realistically and in accordance with the site conditions. This paper discusses a numerical modelling strategy for modelling mine backfill material. Themodelling strategy is studied using a case study mine from Canadian mining industry.
Criteria for the reliability of numerical approximations to the solution of fluid flow problems
International Nuclear Information System (INIS)
Foias, C.
1986-01-01
The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number N of elements (Galerkin modes, finite-difference cells, finite-elements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the Navier-Stokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations. 56 refs
Numerical solutions of Williamson fluid with pressure dependent viscosity
Directory of Open Access Journals (Sweden)
Iffat Zehra
2015-01-01
Full Text Available In the present paper, we have examined the flow of Williamson fluid in an inclined channel with pressure dependent viscosity. The governing equations of motion for Williamson fluid model under the effects of pressure dependent viscosity and pressure dependent porosity are modeled and then solved numerically by the shooting method with Runge Kutta Fehlberg for two types of geometries i.e., (i Poiseuille flow and (ii Couette flow. Four different cases for pressure dependent viscosity and pressure dependent porosity are assumed and the physical features of pertinent parameters are discussed through graphs.
Directory of Open Access Journals (Sweden)
Andrea Lani
2006-01-01
Full Text Available Object-oriented platforms developed for the numerical solution of PDEs must combine flexibility and reusability, in order to ease the integration of new functionalities and algorithms. While designing similar frameworks, a built-in support for high performance should be provided and enforced transparently, especially in parallel simulations. The paper presents solutions developed to effectively tackle these and other more specific problems (data handling and storage, implementation of physical models and numerical methods that have arisen in the development of COOLFluiD, an environment for PDE solvers. Particular attention is devoted to describe a data storage facility, highly suitable for both serial and parallel computing, and to discuss the application of two design patterns, Perspective and Method-Command-Strategy, that support extensibility and run-time flexibility in the implementation of physical models and generic numerical algorithms respectively.
Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes
Bekbauov, Bakhbergen; Berdyshev, Abdumauvlen; Baishemirov, Zharasbek; Bau, Domenico
2017-12-01
Chemical compositional simulation of enhanced oil recovery and surfactant enhanced aquifer remediation processes is a complex task that involves solving dozens of equations for all grid blocks representing a reservoir. In the present work, we perform a numerical validation of the newly developed mathematical formulation which satisfies the conservation laws of mass and energy and allows applying a sequential solution approach to solve the governing equations separately and implicitly. Through its application to the numerical experiment using a wettability alteration model and comparisons with existing chemical compositional model's numerical results, the new model has proven to be practical, reliable and stable.
Six-dimensional localized black holes: Numerical solutions
International Nuclear Information System (INIS)
Kudoh, Hideaki
2004-01-01
To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six-dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature T≅1/2πl, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes
Digital Repository Service at National Institute of Oceanography (India)
Nakamoto, S.; Kano, M.; PrasannaKumar, S.; Oberhuber, J.M.; Muneyama, K.; Ueyoshi, K.; Subrahmanyam, B.; Nakata, K.; Lai, C.A.; Frouin, R.
and Dickey (1987) demonstrate that the at- tenuation of visible energy and photosynthetically available radiation (PAR) (Morel, 1978) are primarily functions of chlorophyll pigments. iturriaga and Potential Feedback Mechanism 257 Siegel (1989) reported... isoPYcnal coordinate (BPYC) general circulation model (Oberhuber, 1993), Nakamoto et al. (2001) showed that surface chlorophyll pigments in the equatorial Pacific not only influence vertical penetration of solar ra- diation, but also modify...
1977-08-01
To advice the statt-of-che- art in the combustion of granular prope..lents by forwilating a complete theoretical model describ".•j the Important...d~~+W s (-.1 1-3. Where the vector products of W , W/2 , W/ , W/ and W/ vith I arte •iVn as Wl#’. m II -VVW ,÷I&. -Wig I,÷W,4A+. j IS÷ I-P(/. W/r...beginning of the granular propel.ent bed ZL Left boumdary point - •light boundary point Grek S.2 1k (Ip Thermal diffusivity of pellucsp 1 Erosive burning
Numerical treatment of compartment models
International Nuclear Information System (INIS)
Einarsson, B.
1984-11-01
This report describes and interactive program RADIO (Radioactive Decay Information Online) for studying the radioactive decay process, with applications to many ecological problems, but not necessarily involving radioactive processes. Starting with the compartment coefficients and initial values of the various compartments the problem is solved as a system of linear ordinary differential equations. The method of solution is the direct use of matrix exponentials or the backward differences method. A program INVERS is also available for the solution of the inverse problem, that is parameter estimation in a system of linear ordinary differential equations when the solution is available pointwise. The output can be printed on a line printer either from a result file or from the plot file, which of course also can be used to produce graphic output. The plot file is processed by the plotting program VISION or by the auxiliary printing program RADAR. Another file can be used for a later restart from the point of time where the previous computation was aborted or from an arbitrary point of time if the relevant starting information is available. This is useful in order to avoid the manual input of a compartment matrix if it is similar to one used before. When the program RADIO is run the user answers to the question asked by the program. The programs are written in Fortran 77 for the Digital Equipment VAX 11 with graphical presentation on a Tektronix 4010, and are available from the author. (Author)
Earth Radii Used in Numerical Weather Models
2005-09-26
In the development of numerical atmospheric models , many simplifying assumptions are made. One of the simplifying assumptions is that the Earth can...geometric properties within or among spatial reference frames. This paper serves to document the values used for the Earth’s radius by several operational numerical atmospheric models for use in the SRM.
Numerical modelling of rapid solidification
DEFF Research Database (Denmark)
Pryds, Nini; Hattel, Jesper Henri
1997-01-01
A mathematical model of the melt spinning process has been developed based on the control-volume finite-difference method. The model avoids some of the limitations of the previous models, for example including the effect of the wheel in the heat how calculations and the temperature dependence of ...
Numerical modelling of elastic space tethers
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P. L.; Roberts, R. M.
2012-01-01
In this paper the importance of the ill-posedness of the classical, non-dissipative massive tether model on an orbiting tether system is studied numerically. The computations document that via the regularisation of bending resistance a more reliable numerical integrator can be produced. Furthermore......, the numerical experiments of an orbiting tether system show that bending may introduce significant forces in some regions of phase space. Finally, numerical evidence for the existence of an almost invariant slow manifold of the singularly perturbed, regularised, non-dissipative massive tether model is provided...
Numerical solution of fluid-structure interaction in piping systems by Glimm's method
Gomes da Rocha, Rogerio; Bastos de Freitas Rachid, Felipe
2012-01-01
This work presents a numerical procedure for obtaining approximated solutions for one-dimensional fluid-structure interaction (FSI) models, which are used in transient analyses of liquid-filled piping systems. The FSI model considered herein is formed by a system of hyperbolic partial differential equations and describes, simultaneously, pressure waves propagating in the liquid as well as axial, shear and bending waves traveling in the pipe walls. By taking advantage of an operator splitting technique, the flux term is split away from the source one, giving rise to a sequence of simpler problems formed by a set of homogeneous hyperbolic differential equations and by a set of ordinary differential equations in time. The numerical procedure is constructed by advancing in time sequentially through these sets of equations by employing Glimm's method and Gear's stiff method, respectively. To implement Glimm's method, analytical solutions for the associated Riemann problems are presented. The boundary conditions are properly accounted for in Glimm's method by formulating and analytically solving suitable (non-classical) Riemann problems for the pipe's ends. The proposed numerical procedure is used to obtain numerical approximations for the well-known eight-equation FSI model for two closed piping systems, in which transients are generated by the impact of a rod onto one of the ends. The obtained numerical results are compared with experimental data available in the literature and very good agreement is found.
Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.
Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S
2014-09-01
A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies. Copyright © 2014 Elsevier B.V. All rights reserved.
Numerical solution of acoustic scattering by finite perforated elastic plates.
Cavalieri, A V G; Wolf, W R; Jaworski, J W
2016-04-01
We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.
Numerical modelling of torn boudinage
Dabrowski, Marcin; Grasemann, Bernhard
2017-04-01
The seminal text book by J.G. Ramsay outlines the importance of the progressive development of torn boudinage structures because the shape of boudins may vary greatly and is mainly dependent on the viscosity contrast between the more competent layer and the enclosing material and the values of the principal extensions of the finite strain ellipsoid. In this work we demonstrate that another parameter, the initial boudin separation, has a significant influence on the progressive development of the finite boudin shape. We use finite element simulations to study the shape evolution of torn boudins under pure and simple shear. The boudins are initially rectangular and the gaps between them are prescribed. The boudin interfaces are resolved with high-resolution, body-fitting, unstructured computational meshes and a second-order ODE integrator is used to ensure the numerical accuracy of the results. Both the boudins and the host are treated as either linear or non-linear viscous fluids. We neglect any recrystallization processes and the boudin interfaces are considered as fully coherent. We were able to reproduce the typical shape of fish-mouth boudins for a wide range of viscosity ratios between the highly viscous boudins and the host. We have systematically studied the effects due to the boudin-host viscosity ratio and the fluid stress exponents. Our results show that the initial separation can have a profound effect on the final shape of the boudins and we document the formation of hitherto undescribed complex boudin shapes for an initially narrow gap width.
Numerical modelling of reflood processes
International Nuclear Information System (INIS)
Glynn, D.R.; Rhodes, N.; Tatchell, D.G.
1983-01-01
The use of a detailed computer model to investigate the effects of grid size and the choice of wall-to-fluid heat-transfer correlations on the predictions obtained for reflooding of a vertical heated channel is described. The model employs equations for the momentum and enthalpy of vapour and liquid and hence accounts for both thermal non-equilibrium and slip between the phases. Empirical correlations are used to calculate interphase and wall-to-fluid friction and heat-transfer as functions of flow regime and local conditions. The empirical formulae have remained fixed with the exception of the wall-to-fluid heat-transfer correlations. These have been varied according to the practices adopted in other computer codes used to model reflood, namely REFLUX, RELAP and TRAC. Calculations have been performed to predict the CSNI standard problem number 7, and the results are compared with experiment. It is shown that the results are substantially grid-independent, and that the choice of correlation has a significant influence on the general flow behaviour, the rate of quenching and on the maximum cladding temperature predicted by the model. It is concluded that good predictions of reflooding rates can be obtained with particular correlation sets. (author)
Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.
2018-02-01
This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.
Other relevant numerical modelling papers
International Nuclear Information System (INIS)
Chartier, M.
1989-01-01
The ocean modelling is a rapidly evolving science and a large number of results have been published. Several categories of papers are of particular interest for this review: the papers published by the international atomic institutions, such as the NEA (for the CRESP or Subseabed Programs), the IAEA (for example the Safety Series, the Technical Report Series or the TECDOC), and the ICRP, and the papers concerned by more fundamental research, which are published in specific scientific literature. This paper aims to list some of the most relevant publications for the CRESP purposes. It means by no way to be exhaustive, but informative on the incontestable progress recently achieved in that field. One should note that some of these papers are so recent that their final version has not yet been published
Variable time-stepping in the pathwise numerical solution of the chemical Langevin equation
Ilie, Silvana
2012-12-01
Stochastic modeling is essential for an accurate description of the biochemical network dynamics at the level of a single cell. Biochemically reacting systems often evolve on multiple time-scales, thus their stochastic mathematical models manifest stiffness. Stochastic models which, in addition, are stiff and computationally very challenging, therefore the need for developing effective and accurate numerical methods for approximating their solution. An important stochastic model of well-stirred biochemical systems is the chemical Langevin Equation. The chemical Langevin equation is a system of stochastic differential equation with multidimensional non-commutative noise. This model is valid in the regime of large molecular populations, far from the thermodynamic limit. In this paper, we propose a variable time-stepping strategy for the numerical solution of a general chemical Langevin equation, which applies for any level of randomness in the system. Our variable stepsize method allows arbitrary values of the time-step. Numerical results on several models arising in applications show significant improvement in accuracy and efficiency of the proposed adaptive scheme over the existing methods, the strategies based on halving/doubling of the stepsize and the fixed step-size ones.
Numerical solution of an edge flame boundary value problem
Shields, Benjamin; Freund, Jonathan; Pantano, Carlos
2016-11-01
We study edge flames for modeling extinction, reignition, and flame lifting in turbulent non-premixed combustion. An adaptive resolution finite element method is developed for solving a strained laminar edge flame in the intrinsic moving frame of reference of a spatially evolving shear layer. The variable-density zero Mach Navier-Stokes equations are used to solve for both advancing and retreating edge flames. The eigenvalues of the system are determined simultaneously (implicitly) with the scalar fields using a Schur complement strategy. A homotopy transformation over density is used to transition from constant- to variable-density, and pseudo arc-length continuation is used for parametric tracing of solutions. Full details of the edge flames as a function of strain and Lewis numbers will be discussed. This material is based upon work supported [in part] by the Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002374.
Numerical 3-D Modelling of Overflows
DEFF Research Database (Denmark)
Larsen, Torben; Nielsen, L.; Jensen, B.
2008-01-01
The present study uses laboratory experiments to evaluate the reliability of two types of numerical models of sewers systems: - 1-dimensional model based on the extended Saint-Venant equation including the term for curvature of the water surface (the so-called Boussinesq approximation) - 2- and 3......-dimensional so-called Volume of Fluid Models (VOF-models) based on the full Navier-Stokes equations (named NS3 and developed by DHI Water & Environment) As a general conclusion, the two numerical models show excellent results when compared with measurements. However, considerable errors occur when...... inappropriate boundary conditions and grid resolutions are chosen. The paper describes the used physical and numerical models and summarises the results....
The numerical solution of boundary value problems over an infinite domain
International Nuclear Information System (INIS)
Shepherd, M.; Skinner, R.
1976-01-01
A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail
Numerical solution of flame sheet problems with and without multigrid methods
Douglas, Craig C.; Ern, Alexandre
1993-01-01
Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the structure of flames more accurately, we use the vorticity-velocity formulation of the fluid flow equations, as opposed to the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear damped Newton multigrid, using either one way or correction schemes.
Numerical solution of shock and ramp compression for general material properties
Energy Technology Data Exchange (ETDEWEB)
Swift, D C
2009-01-28
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments, without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase transition.
Numerical solution and asymptotic behavior for a nonlocal reaction-diffusion coupled systems
Chin, Pius W. M.
2017-07-01
This paper is considered on a class of nonlocal systems of reaction-diffusion equations with coefficients which are Lipschitz-continuous positive functions. In this model, we are concerned with designing a coupling technique consisting of the non-standard finite difference(NSFD) and finite element method(FEM) both in time and space respectively. We prove theoretically that the schemes designed by the above technique converges optimally in some specified norms for given conditions. Furthermore, we show that the numerical solutions of the said schemes replicates the decaying properties of the exact solutions. Numerical experiments are presented to justify the above theory and some practical studies are carried out for the asymptotic behavior of the schemes under consideration.
Numerical modeling of reinforced foundation pads structures
Ponomarev Andrey Budimirovich; Tat’yannikov Daniil Andreevich
2016-01-01
The wide use of reinforced foundation pads is complicated because of the absence of technical rules and regulations on design of such structures. It is necessary to investigate the main parameters and regularities of such structures operation under loading. For this aim numerical study of the foundation was carried out, the parameters of which were improved by reinforced foundation pad. The numerical modeling of reinforced foundation pads was carried out in the Plaxis 2D for study of the basi...
Comparing numerically exact and modelled static friction
Directory of Open Access Journals (Sweden)
Krengel Dominik
2017-01-01
Full Text Available Currently there exists no mechanically consistent “numerically exact” implementation of static and dynamic Coulomb friction for general soft particle simulations with arbitrary contact situations in two or three dimension, but only along one dimension. We outline a differential-algebraic equation approach for a “numerically exact” computation of friction in two dimensions and compare its application to the Cundall-Strack model in some test cases.
Numerical methods and modelling for engineering
Khoury, Richard
2016-01-01
This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...
Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.
Kumar, Dinesh; Kumar, P; Rai, K N
2017-11-01
This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.
Numerical modelling of the Earth’s ionosphere F region
Ostanin, P. A.; Kulyamin, D. V.; Dymnikov, V. P.
2017-11-01
This paper presents the first version of a new INM RAS Earth’s ionosphere F region dynamical model. A complete set of model equations is formulated taking into account all the key physical processes that form the global state of the ionospheric F region (plasma chemistry, ambipolar diffusion, wind transport, drift across magnetic lines). For the numerical solution, a splitting method based on the physical processes and geometric directions is proposed. The first stage of splitting in a quasi-two-dimensional approximation setting with a projection of ambipolar diffusion on the vertical direction is considered. It is numerically implemented stepwise using various difference schemes for three separate model formulations (taking into account diffusion only along the vertical direction, considering a realistic direction of diffusion along the magnetic field excluding and including a mixed derivative term). The applicability, efficiency, conservation, and monotonicity of these numerical methods are analyzed. The first numerical experiments show convergence of the numerical solution to a stationary vertical profile specific to the F region. The greatest consistency with the observed profiles is obtained in the mid-latitudes. Using the thus constructed model it is shown that the electron density profile is most sensitive to the neutral temperature and ionization level with qualitatively different structures of the corresponding modes of variability.
Advances in numerical modelling of crash dummies
Verhoeve, R.; Kant, R.; Margerie, L.
2001-01-01
Nowadays virtual testing and prototyping are generally accepted methods in crash safety research and design studies. Validated numerical crash dummy models are necessary tools in these methods. Computer models need to be robust, accurate and CPU efficient, where the balance between accuracy and
Amorphous track models: A numerical comparison study
DEFF Research Database (Denmark)
Greilich, Steffen; Grzanka, L.; Bassler, N.
2010-01-01
We present an open-source code library for amorphous track modelling which is suppose to faciliate the application and numerical comparability as well as serve as a frame-work for the implementation of new models. We show an example of using the library indicating the choice of submodels has a si...
Numerical solutions of the N-body problem
International Nuclear Information System (INIS)
Marciniak, A.
1985-01-01
Devoted to the study of numerical methods for solving the general N-body problem and related problems, this volume starts with an overview of the conventional numerical methods for solving the initial value problem. The major part of the book contains original work and features a presentation of special numerical methods conserving the constants of motion in the general N-body problem and methods conserving the Jacobi constant in the problem of motion of N bodies in a rotating frame, as well as an analysis of the applications of both (conventional and special) kinds of methods for solving these problems. For all the methods considered, the author presents algorithms which are easily programmable in any computer language. Moreover, the author compares various methods and presents adequate numerical results. The appendix contains PL/I procedures for all the special methods conserving the constants of motion. 91 refs.; 35 figs.; 41 tabs
Numerical solution of the stochastic parabolic equation with the dependent operator coefficient
Energy Technology Data Exchange (ETDEWEB)
Ashyralyev, Allaberen [Department of Elementary Mathematics Education, Fatih University, 34500, Istanbul (Turkey); Department of Mathematics, ITTU, Ashgabat (Turkmenistan); Okur, Ulker [Institute for Stochastics and Applications, Department of Mathematics, University of Stuttgart, 70569, Stuttgart (Germany)
2015-09-18
In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.
3D Numerical Modeling of Flow in Sedimentation Basin
Directory of Open Access Journals (Sweden)
Harlan Dhemi
2018-01-01
Full Text Available Normal operation sedimentation basin flushing systems require large volumes of water, typically up ten times of the deposited sediment volume for efficient flushing. A complete sediment removal, can only be realized by combination of mechanical removal with drawdown flushing. This operation reaches much longer operation time resulting in water loss and reducing power and energy production of Mini Hydro Power Plant (MHPP. The objective of this study is to improve the flushing system of sedimentation basin based on a numerical approach. Fluid motion is described with non-linear, transient, second-order differential equations. A numerical solution of these equations involves approximating the various terms with algebraic expressions. The resulting equations are then solved to yield an approximate solution to the original problem. The simulation result shows that the 3D numerical modeling of flow in sedimentation basin gives the reasonable result to predict the suspended load movement in the flow.
Numerical FEM modeling in dental implantology
Roateşi, Iulia; Roateşi, Simona
2016-06-01
This paper is devoted to a numerical approach of the stress and displacement calculation of a system made up of dental implant, ceramic crown and surrounding bone. This is the simulation of a clinical situation involving both biological - the bone tissue, and non-biological - the implant and the crown, materials. On the other hand this problem deals with quite fine technical structure details - the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. The authors proposed a three-dimensional numerical model to assess the biomechanical behaviour of this complex structure in order to evaluate its stability by determining the risk zones. A comparison between this numerical analysis and clinical cases is performed and a good agreement is obtained.
Numerical Solution of Problem for Non-Stationary Heat Conduction in Multi-Layer Bodies
Directory of Open Access Journals (Sweden)
R. I. Еsman
2007-01-01
Full Text Available A mathematical model for non-stationary heat conduction of multi-layer bodies has been developed. Dirac’s δ-function is used to take into account phase and chemical transformations in one of the wall layers. While formulating a problem non-linear heat conduction equations have been used with due account of dependence of thermal and physical characteristics on temperature. Solution of the problem is realized with the help of methods of a numerical experiment and computer modeling.
Periodic solutions of nonautonomous differential systems modeling obesity population
International Nuclear Information System (INIS)
Arenas, Abraham J.; Gonzalez-Parra, Gilberto; Jodar, Lucas
2009-01-01
In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.
Periodic solutions of nonautonomous differential systems modeling obesity population
Energy Technology Data Exchange (ETDEWEB)
Arenas, Abraham J. [Departamento de Matematicas y Estadistica, Universidad de Cordoba Monteria (Colombia)], E-mail: aarenas@sinu.unicordoba.edu.co; Gonzalez-Parra, Gilberto [Departamento de Calculo, Universidad de los Andes, Merida (Venezuela, Bolivarian Republic of)], E-mail: gcarlos@ula.ve; Jodar, Lucas [Instituto de Matematica Multidisciplinar, Universidad Politecnica de Valencia Edificio 8G, 2o, 46022 Valencia (Spain)], E-mail: ljodar@imm.upv.es
2009-10-30
In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.
Numerical Solution of Magnetostatic Field of Maglev System
Directory of Open Access Journals (Sweden)
Jaroslav Sobotka
2008-01-01
Full Text Available The paper deals with the design of the levitation and guidance system of the levitation train Transrapid 08 by means of QuickField 5.0 – a 2D program formagnetic electromagnetic fields solutions.
Numerical solution of time dependent neutron transport equation. An application
International Nuclear Information System (INIS)
Barroso, Dalton Ellery Girao
2000-01-01
In this work we show a simple method to solve numerically the time-dependent neutron transport equation which is a simple extension of the numerical methods used to solve the time-independent static transport equation. This is possible because the time-discretized transport equation has the same form as the time-independent transport equation, with only some additional terms. A general outline of the method is given and used to evaluate the neutron flux in a microexplosion calculation of a highly compressed micro fissile system composed by DT-Pu-Be microsphere. (author)
A numerical solution for a closed die forging process
Directory of Open Access Journals (Sweden)
Luca Dorin
2017-01-01
Full Text Available One of the manufacturing processes that can be permanent improved is plastic deformation of metallic materials, as incorporating reserves on the manufacture of products with reduced material and energy consumptions. This paper presents finite element analysis for a closed die forging process, showing the stresses, strains and temperature into deformed part and stresses in the working tools. The analysis of obtained results for different flash dimensions of the working tools has enabled optimization of the forging process studied. To be able to validate the numerical results obtained, experimental tests were conducted. The compared data series show a good agreement between the numerical and experimental data.
From Numeric Models to Granular System Modeling
Directory of Open Access Journals (Sweden)
Witold Pedrycz
2015-03-01
To make this study self-contained, we briefly recall the key concepts of granular computing and demonstrate how this conceptual framework and its algorithmic fundamentals give rise to granular models. We discuss several representative formal setups used in describing and processing information granules including fuzzy sets, rough sets, and interval calculus. Key architectures of models dwell upon relationships among information granules. We demonstrate how information granularity and its optimization can be regarded as an important design asset to be exploited in system modeling and giving rise to granular models. With this regard, an important category of rule-based models along with their granular enrichments is studied in detail.
Feedbacks Between Numerical and Analytical Models in Hydrogeology
Zlotnik, V. A.; Cardenas, M. B.; Toundykov, D.; Cohn, S.
2012-12-01
Hydrogeology is a relatively young discipline which combines elements of Earth science and engineering. Mature fundamental disciplines (e.g., physics, chemistry, fluid mechanics) have centuries-long history of mathematical modeling even prior to discovery of Darcy's law. Thus, in hydrogeology, relatively few classic analytical models (such those by Theis, Polubarinova-Kochina, Philip, Toth, Henry, Dagan, Neuman) were developed by the early 1970's. The advent of computers and practical demands refocused mathematical models towards numerical techniques. With more diverse but less mathematically-oriented training, most hydrogeologists shifted from analytical methods to use of standardized computational software. Spatial variability in internal properties and external boundary conditions and geometry, and the added complexity of chemical and biological processes will remain major challenges for analytical modeling. Possibly, analytical techniques will play a subordinate role to numerical approaches in many applications. On the other hand, the rise of analytical element modeling of groundwater flow is a strong alternative to numerical models when data demand and computational efficiency is considered. The hallmark of analytical models - transparency and accuracy - will remain indispensable for scientific exploration of complex phenomena and for benchmarking numerical models. Therefore, there will always be feedbacks and complementarities between numerical and analytical techniques, as well as a certain ideological schism among various views to modeling. We illustrate the idea of feedbacks by reviewing evolution of Joszef Toth's analytical model of gravity driven flow systems. Toth's (1963) approach was to reduce the flow domain to a rectangle which allowed for closed-form solution of the governing equations. Succeeding numerical finite-element models by Freeze and Witherspoon (1966-1968) explored the effects of geometry and heterogeneity on regional groundwater flow
Numerical modelling approach for mine backfill
Indian Academy of Sciences (India)
Muhammad Zaka Emad
2017-07-24
Jul 24, 2017 ... Abstract. Numerical modelling is broadly used for assessing complex scenarios in underground mines, including mining sequence and blast-induced vibrations from production blasting. Sublevel stoping mining methods with delayed backfill are extensively used to exploit steeply dipping ore bodies by ...
Numerical modelling of multicomponent LNAPL dissolution kinetics ...
Indian Academy of Sciences (India)
Abstract. Characterization of aquifers contaminated by petroleum hydrocarbons is limited by the use of dissolution mass transfer correlations developed for single com- pounds without considering the effects of the mass transfer limitations in presence of other components. A one-dimensional implicit numerical model is ...
A numerical reference model for themomechanical subduction
DEFF Research Database (Denmark)
Quinquis, Matthieu; Chemia, Zurab; Tosi, Nicola
2010-01-01
for thermomechanical subduction. This reference setup will facilitate comparisons of a series of numerical models that focus on different aspects of subduction, such as the effects of elasticity on the stress distribution, the energetic impact of phase transformations or the influence of devolatilization reactions...
Graphical interpretation of numerical model results
International Nuclear Information System (INIS)
Drewes, D.R.
1979-01-01
Computer software has been developed to produce high quality graphical displays of data from a numerical grid model. The code uses an existing graphical display package (DISSPLA) and overcomes some of the problems of both line-printer output and traditional graphics. The software has been designed to be flexible enough to handle arbitrarily placed computation grids and a variety of display requirements
Numerical modeling of eastern connecticut's visual resources
Daniel L. Civco
1979-01-01
A numerical model capable of accurately predicting the preference for landscape photographs of selected points in eastern Connecticut is presented. A function of the social attitudes expressed toward thirty-two salient visual landscape features serves as the independent variable in predicting preferences. A technique for objectively assigning adjectives to landscape...
Numerical modelling approach for mine backfill
Indian Academy of Sciences (India)
Muhammad Zaka Emad
2017-07-24
Jul 24, 2017 ... pulse is applied as a stress history on the CRF stope. Blast wave data obtained from the on-site monitoring are very complex. It requires processing before interpreting and using it for numerical models. Generally, mining compa- nies hire geophysics experts for interpretation of such data. The blast wave ...
Basset force in numerical models of saltation
Czech Academy of Sciences Publication Activity Database
Lukerchenko, Nikolay; Dolanský, Jindřich; Vlasák, Pavel
2012-01-01
Roč. 60, č. 4 (2012), s. 277-287 ISSN 0042-790X R&D Projects: GA ČR GA103/09/1718 Institutional research plan: CEZ:AV0Z20600510 Keywords : basset force * bed load transport * numerical model * particle-bed collision Subject RIV: BK - Fluid Dynamics Impact factor: 0.653, year: 2012
Numerical Methods for Solution of the Extended Linear Quadratic Control Problem
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog
2012-01-01
In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....
Adaptive numerical modeling of dynamic crack propagation
International Nuclear Information System (INIS)
Adouani, H.; Tie, B.; Berdin, C.; Aubry, D.
2006-01-01
We propose an adaptive numerical strategy that aims at developing reliable and efficient numerical tools to model dynamic crack propagation and crack arrest. We use the cohesive zone theory as behavior of interface-type elements to model crack. Since the crack path is generally unknown beforehand, adaptive meshing is proposed to model the dynamic crack propagation. The dynamic study requires the development of specific solvers for time integration. As both geometry and finite element mesh of the studied structure evolve in time during transient analysis, the stability behavior of dynamic solver becomes a major concern. For this purpose, we use the space-time discontinuous Galerkin finite element method, well-known to provide a natural framework to manage meshes that evolve in time. As an important result, we prove that the space-time discontinuous Galerkin solver is unconditionally stable, when the dynamic crack propagation is modeled by the cohesive zone theory, which is highly non-linear. (authors)
Numerical modelling in non linear fracture mechanics
Directory of Open Access Journals (Sweden)
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method
Crevoisier, David; Voltz, Marc
2013-04-01
To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute
Numerical solution of pipe flow problems for generalized Newtonian fluids
International Nuclear Information System (INIS)
Samuelsson, K.
1993-01-01
In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)
Numerical modeling of shock-sensitivity experiments
Energy Technology Data Exchange (ETDEWEB)
Bowman, A.L.; Forest, C.A.; Kershner, J.D.; Mader, C.L.; Pimbley, G.H.
1981-01-01
The Forest Fire rate model of shock initiation of heterogeneous explosives has been used to study several experiments commonly performed to measure the sensitivity of explosives to shock and to study initiation by explosive-formed jets. The minimum priming charge test, the gap test, the shotgun test, sympathetic detonation, and jet initiation have been modeled numerically using the Forest Fire rate in the reactive hydrodynamic codes SIN and 2DE.
Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.
Esmaeeli, Hadi S; Farnam, Yaghoob; Bentz, Dale P; Zavattieri, Pablo D; Weiss, Jason
2017-02-01
This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained.
A numerical solution for a toroidal plasma in equilibrium
International Nuclear Information System (INIS)
Hintz, E.; Sudano, J.P.
1982-01-01
The iterative techniques alternating direction implicit (ADI), sucessive ove-relaxation (SOR) and Gauss-Seidel are applied to a nonlinear elliptical second order differential equation (Grand-Shafranov). This equation was solve with the free boundary conditions plasma-vacuum interface over a rectangular section in cylindrical coordinates R and Z. The current density profile, plasma pressure profile, magnetic and isobaric surfaces are numerically determined for a toroidal plasma in equilibrium. (L.C.) [pt
Numerical Modeling of a Wave Energy Point Absorber
DEFF Research Database (Denmark)
Hernandez, Lorenzo Banos; Frigaard, Peter; Kirkegaard, Poul Henning
2009-01-01
The present study deals with numerical modelling of the Wave Star Energy WSE device. Hereby, linear potential theory is applied via a BEM code on the wave hydrodynamics exciting the floaters. Time and frequency domain solutions of the floater response are determined for regular and irregular seas....... Furthermore, these results are used to estimate the power and the energy absorbed by a single oscillating floater. Finally, a latching control strategy is analysed in open-loop configuration for energy maximization....
NUMERICAL MODELING OF HARDENING OF UNINTERRUPTEDLY-CASTED BRONZE CASTING
Directory of Open Access Journals (Sweden)
E. I. Marukovich
2009-01-01
Full Text Available The three-dimensional numerical model for calculation of thermal fields during solidification of continuously casted bronze casting is developed. Coefficients of heat transfer on borders of calculation areas on the basis of the solution of inverse heat transfer conduction problem are determined. The analysis of thermal fields, depending on loop variables of drawing and the sizes of not cooled zone of crystallizer is curried out.
Numerical solution of the one-dimensional Burgers' equation ...
Indian Academy of Sciences (India)
Abstract. This paper describes two new techniques which give improved exponential finite dif- ference solutions of Burgers' equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers' equa- tion. As the Burgers' equation is ...
Numerical Solution of Hamilton-Jacobi Equations in High Dimension
2012-11-23
high dimension FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA-Universita di Roma P. Aldo Moro, 2 00185 ROMA AH930...solution of Hamilton-Jacobi equations in high dimension AFOSR contract n. FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA
Analysis of the Numerical Solution of the Shallow Water Equations
National Research Council Canada - National Science Library
Hamrick, Thomas
1997-01-01
.... The two schemes are finite difference method (FDM) and the finite element method (FEM). After presenting the shallow water equations in several formulations, some examples will be presented. The use of the Fourier transform to find the solution of a semidiscrete analog of the shallow water equations is also demonstrated.
Numerical modelling of shear socketed piers
Khan, A.
2000-09-01
When a socketed pier embedded in a rock mass is pushed down, the concrete asperities slide over the matching rock asperities. Consequently, the normal stress across the rock-concrete interface increases due to the dilation of the rough contact. The objective of this paper is to model the behaviour of such rough interfaces analytically. A plasticity-based interface model is developed and implemented in a finite element program. Various features of the model such as failure criterion, plastic potential, bond degradation and dilatancy are presented. Interface parameters obtained from laboratory tests are used to simulate the interaction between concrete and rock numerically. A comparison between laboratory observations and numerical predictions is presented.
Numerical Based Linear Model for Dipole Magnets
Energy Technology Data Exchange (ETDEWEB)
Li,Y.; Krinsky, S.; Rehak, M.
2009-05-04
In this paper, we discuss an algorithm for constructing a numerical linear optics model for dipole magnets from a 3D field map. The difference between the numerical model and K. Brown's analytic approach is investigated and clarified. It was found that the optics distortion due to the dipoles' fringe focusing must be properly taken into account to accurately determine the chromaticities. In NSLS-II, there are normal dipoles with 35-mm gap and dipoles for infrared sources with 90-mm gap. This linear model of the dipole magnets is applied to the NSLS-II lattice design to match optics parameters between the DBA cells having dipoles with different gaps.
SOFTWARE SOLUTIONS FOR ARDL MODELS
Directory of Open Access Journals (Sweden)
Nicolae-Marius JULA
2015-07-01
Full Text Available VAR type models can be used only for stationary time series. Causality analyses through econometric models need that series to have the same integrated order. Usually, when constraining the series to comply these restrictions (e.g. by differentiating, economic interpretation of the outcomes may become difficult. Recent solution for mitigating these problems is the use of ARDL (autoregressive distributed lag models. We present implementation in E-Views of these models and we test the impact of exchange rate on consumer price index.
Fikri, Fariz Fahmi; Nuraini, Nuning
2018-03-01
The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.
Numerical and Exact Solution of Buckling Load For Beam on Elastic Foundation
Directory of Open Access Journals (Sweden)
Roland JANČO
2013-06-01
Full Text Available In this paper we will be presented the exact solution of buckling load for supported beam on elastic foundation. Exact solution will be compared with numerical solution by FEM in our code in Matlab. Implementation of buckling to FEM will be presented here.
Numerical analysis of the rebellious voter model
Czech Academy of Sciences Publication Activity Database
Swart, Jan M.; Vrbenský, Karel
2010-01-01
Roč. 140, č. 5 (2010), s. 873-899 ISSN 0022-4715 R&D Projects: GA ČR GA201/09/1931; GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : rebellious voter model * parity conservation * exactly solvable model * coexistence * interface tightness * cancellative systems * Markov chain Monte Carlo Subject RIV: BA - General Mathematics Impact factor: 1.447, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/swart-numerical analysis of the rebellious voter model.pdf
Wind laws for shockless initialization. [numerical forecasting model
Ghil, M.; Shkoller, B.
1976-01-01
A system of diagnostic equations for the velocity field, or wind laws, was derived for each of a number of models of large-scale atmospheric flow. The derivation in each case is mathematically exact and does not involve any physical assumptions not already present in the prognostic equations, such as nondivergence or vanishing of derivatives of the divergence. Therefore, initial states computed by solving these diagnostic equations should be compatible with the type of motion described by the prognostic equations of the model and should not generate initialization shocks when inserted into the model. Numerical solutions of the diagnostic system corresponding to a barotropic model are exhibited. Some problems concerning the possibility of implementing such a system in operational numerical weather prediction are discussed.
The Finite Element Numerical Modelling of 3D Magnetotelluric
Directory of Open Access Journals (Sweden)
Ligang Cao
2014-01-01
Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.
Numerical Modeling of Piezoelectric Transducers Using Physical Parameters
Cappon, H.; Keesman, K.J.
2012-01-01
Design of ultrasonic equipment is frequently facilitated with numerical models. These numerical models, however, need a calibration step, because usually not all characteristics of the materials used are known. Characterization of material properties combined with numerical simulations and
Numerical modelling of mine workings: annual update 1999/2000.
CSIR Research Space (South Africa)
Lightfoot, N
1999-09-01
Full Text Available chapters of the guidebook. In order to download the guidebook a visitor needs to have a password which will issued upon receipt of a nominal charge. 7 2 Updated Edition of Numerical Modelling of Mine Workings Enabling Output 1: Updates to the current... of rock mass ratings. 4.3.3.2 Quadratic model Figure describing the quadratic backfill material model has been corrected. Chapter 5 Solution Methods 5.2 Analytical Methods and 5.3 Computational Methods Use of the words slot, crack and slit...
Experimental study of numerical methods for the solution of gas dynamics problems with shock waves
Godunov, S. K.; Klyuchinskiy, D. V.; Safronov, A. V.; Fortova, S. V.; Shepelev, V. V.
2018-01-01
The work is devoted to some important questions that come with the solution of gas dynamics equations using standard Godunov scheme with the corrections of A V Safronov. The numerical solution is succeeded by intrinsic differential realization of energy conservation law. It has been found experimentally that in all computational cells the entropy nondecreasing is provided. The fact makes it possible to model the entropy rising on shock waves. Besides the experiments described in the paper gives the intrinsic explanation of the reasons for the appearance of the zones with decreased accuracy order in the results. The influence of the computational grid parameters (Courant number) on the plots of grid structures of shock waves is also studied.
Numerical modeling in materials science and engineering
Rappaz, Michel; Deville, Michel
2003-01-01
This book introduces the concepts and methodologies related to the modelling of the complex phenomena occurring in materials processing. After a short reminder of conservation laws and constitutive relationships, the authors introduce the main numerical methods: finite differences, finite volumes and finite elements. These techniques are developed in three main chapters of the book that tackle more specific problems: phase transformation, solid mechanics and fluid flow. The two last chapters treat inverse methods to obtain the boundary conditions or the material properties and stochastic methods for microstructural simulation. This book is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics and for engineering professionals or researchers who want to get acquainted with numerical simulation to model and compute materials processing.
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Meshless Methods for Numerical Solution of Partial Differential Equations
Li, Gang; Jin, Xiaozhong; Alum, N. R.
A popular research topic in numerical methods recently has been the development of meshless methods as alternatives to the traditional finite element, finite volume, and finite difference methods. The traditional methods all require some connectivity knowledge a priori, such as the generation of a mesh, whereas the aim of meshless methods is to sprinkle only a set of points or nodes covering the computational domain, with no connectivity information required among the set of points. Multiphysics and multiscale analysis, which is a common requirement for microsystem technologies such as MEMS and Bio-MEMS, is radically simplified by meshless techniques as we deal with only nodes or points instead of a mesh. Meshless techniques are also appealing because of their potential in adaptive techniques, where a user can simply add more points in a particular region to obtain more accurate results.
Induction and direct resistance heating theory and numerical modeling
Lupi, Sergio; Aliferov, Aleksandr
2015-01-01
This book offers broad, detailed coverage of theoretical developments in induction and direct resistance heating and presents new material on the solution of problems in the application of such heating. The physical basis of induction and conduction heating processes is explained, and electromagnetic phenomena in direct resistance and induction heating of flat workpieces and cylindrical bodies are examined in depth. The calculation of electrical and energetic characteristics of induction and conduction heating systems is then thoroughly reviewed. The final two chapters consider analytical solutions and numerical modeling of problems in the application of induction and direct resistance heating, providing industrial engineers with the knowledge needed in order to use numerical tools in the modern design of installations. Other engineers, scientists, and technologists will find the book to be an invaluable reference that will assist in the efficient utilization of electrical energy.
2-D Flow Numerical Solution for Airfoil and Hovercraft in Ground Effect
1978-12-01
REPRODUCE LEGIBLYo 2-D FLOW NUMERICAL SOLUTION FOR AIRFOIL AND HOVERCRAFT i GROUND EFECT THESIS AFIT/GAE/AA/78D-6 Itzhak Dvir Maj IAF $Approved for public...release; distribution unlimited. ,Li i i -AFIT/GAE/AA/78D-6 ’-~’ 2-D FLOW NUMERICAL SOLUTION FOR AIRFOIL AND HOVERCRAFT IN GROUND EFFECTS i .. THESIS ...Flow Numerical Solution for Airfoil and M.S. Thesis Hovercraft in Ground Effect I .C PERFORMING ORG. RCPOIFT NUM=BER 7. AUTHOR(&) S. CONTRAC’ Or GR
Solute transport modelling with the variable temporally dependent ...
Indian Academy of Sciences (India)
Pintu Das
2018-02-07
Feb 7, 2018 ... Abstract. In this present study, analytical and numerical solutions are obtained for solute transport modelling in homogeneous semi-infinite porous medium. The dispersion coefficient is assumed to be initial dispersion and velocity is assumed to be temporally dependent with initial seepage velocity. Also ...
Advanced Numerical Model for Irradiated Concrete
Energy Technology Data Exchange (ETDEWEB)
Giorla, Alain B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2015-03-01
In this report, we establish a numerical model for concrete exposed to irradiation to address these three critical points. The model accounts for creep in the cement paste and its coupling with damage, temperature and relative humidity. The shift in failure mode with the loading rate is also properly represented. The numerical model for creep has been validated and calibrated against different experiments in the literature [Wittmann, 1970, Le Roy, 1995]. Results from a simplified model are shown to showcase the ability of numerical homogenization to simulate irradiation effects in concrete. In future works, the complete model will be applied to the analysis of the irradiation experiments of Elleuch et al. [1972] and Kelly et al. [1969]. This requires a careful examination of the experimental environmental conditions as in both cases certain critical information are missing, including the relative humidity history. A sensitivity analysis will be conducted to provide lower and upper bounds of the concrete expansion under irradiation, and check if the scatter in the simulated results matches the one found in experiments. The numerical and experimental results will be compared in terms of expansion and loss of mechanical stiffness and strength. Both effects should be captured accordingly by the model to validate it. Once the model has been validated on these two experiments, it can be applied to simulate concrete from nuclear power plants. To do so, the materials used in these concrete must be as well characterized as possible. The main parameters required are the mechanical properties of each constituent in the concrete (aggregates, cement paste), namely the elastic modulus, the creep properties, the tensile and compressive strength, the thermal expansion coefficient, and the drying shrinkage. These can be either measured experimentally, estimated from the initial composition in the case of cement paste, or back-calculated from mechanical tests on concrete. If some
Numerical solution of reinforced concrete beam using arc-length method
Directory of Open Access Journals (Sweden)
Piotr Smarzewski
2016-03-01
Full Text Available This article discusses numerical solution of a reinforced concrete beam. The modelling was conducted with the rules of the finite element method (FEM. In order to verify the correctness of the assumed material’s models: concrete and reinforcing steel, the results obtained with the arc‑length method finite analysis were compared with experimental data. The method had been verified in the beam spatial model, in which concrete crushing at compressive and concrete stiffening at tensile are dominant phenomena. The arc-length method is the only one to offer the possibility of obtaining a complete load‑deflection curve with local and global softening.[b]Keywords[/b]: mechanics of concrete structures, finite element method, reinforced concrete beam, arc‑length algorithm
Features of the Numerical Solution of Thermal Destruction Fuel Pins Problems in the Fast Reactor
Usov, E. V.; Butov, A. A.; Klimonov, I. A.; Chuhno, V. I.; Nikolaenko, A. V.; Zhdanov, V. S.; Pribaturin, N. A.; Strizhov, V. F.
2017-11-01
In this paper the description of the basic equations which can be used for calculation of melting of fuel and cladding of the fast reactor, moving of the melt on a fuel pin surface and its solidification is presented. The special attention is given speed of calculation algorithms and fidelity of the phenomena which are observed at a stage of severe accidents in fast reactors. For check of working capacity of initial models, numerical calculations of Stefan-type problems on front movement of melting/solidification in cylindrical geometry are presented. Comparison with the solutions received by known analytical methods is executed. For validation of the numerical realization of calculation algorithms the analysis is carried out and experiments in which melting of the model fuel pins of fast reactors was studied are chosen. On the basis of the chosen experiments calculation schemes taking into account initial and boundary conditions are prepared and modeling is performed. Modeling results are shown in the present paper. Estimation of calculation error of the basic physical parameters is done by results of the modeling and conclusions are drawn on a correctness of algorithms operation.
Numerical model simulation of atmospheric coolant plumes
International Nuclear Information System (INIS)
Gaillard, P.
1980-01-01
The effect of humid atmospheric coolants on the atmosphere is simulated by means of a three-dimensional numerical model. The atmosphere is defined by its natural vertical profiles of horizontal velocity, temperature, pressure and relative humidity. Effluent discharge is characterised by its vertical velocity and the temperature of air satured with water vapour. The subject of investigation is the area in the vicinity of the point of discharge, with due allowance for the wake effect of the tower and buildings and, where application, wind veer with altitude. The model equations express the conservation relationships for mometum, energy, total mass and water mass, for an incompressible fluid behaving in accordance with the Boussinesq assumptions. Condensation is represented by a simple thermodynamic model, and turbulent fluxes are simulated by introduction of turbulent viscosity and diffusivity data based on in-situ and experimental water model measurements. The three-dimensional problem expressed in terms of the primitive variables (u, v, w, p) is governed by an elliptic equation system which is solved numerically by application of an explicit time-marching algorithm in order to predict the steady-flow velocity distribution, temperature, water vapour concentration and the liquid-water concentration defining the visible plume. Windstill conditions are simulated by a program processing the elliptic equations in an axisymmetrical revolution coordinate system. The calculated visible plumes are compared with plumes observed on site with a view to validate the models [fr
Numerical modelling of methanol liquid pool fires
Prasad, Kuldeep; Li, Chiping; Kailasanath, K.; Ndubizu, Chuka; Ananth, Ramagopal; Tatem, P. A.
1999-12-01
The focus of this paper is on numerical modelling of methanol liquid pool fires. A mathematical model is first developed to describe the evaporation and burning of a two-dimensional or axisymmetric pool containing pure liquid methanol. Then, the complete set of unsteady, compressible Navier-Stokes equations for reactive flows are solved in the gas phase to describe the convection of the fuel gases away from the pool surface, diffusion of the gases into the surrounding air and the oxidation of the fuel into product species. Heat transfer into the liquid pool and the metal container through conduction, convection and radiation are modelled by solving a modified form of the energy equation. Clausius-Clapeyron relationships are invoked to model the evaporation rate of a two-dimensional pool of pure liquid methanol. The governing equations along with appropriate boundary and interface conditions are solved using the flux-corrected transport algorithm. Numerical results exhibit a flame structure that compares well with experimental observations. Temperature profiles and burning rates were found to compare favourably with experimental data from single- and three-compartment laboratory burners. The model predicts a puffing frequency of approximately 12 Hz for a 1 cm diameter methanol pool in the absence of any air co-flow. It is also observed that increasing the air co-flow velocity helps in stabilizing the diffusion flame, by pushing the vortical structures away from the flame region.
Extracting Damping Ratio from Dynamic Data and Numerical Solutions
Casiano, M. J.
2016-01-01
There are many ways to extract damping parameters from data or models. This Technical Memorandum provides a quick reference for some of the more common approaches used in dynamics analysis. Described are six methods of extracting damping from data: the half-power method, logarithmic decrement (decay rate) method, an autocorrelation/power spectral density fitting method, a frequency response fitting method, a random decrement fitting method, and a newly developed half-quadratic gain method. Additionally, state-space models and finite element method modeling tools, such as COMSOL Multiphysics (COMSOL), provide a theoretical damping via complex frequency. Each method has its advantages which are briefly noted. There are also likely many other advanced techniques in extracting damping within the operational modal analysis discipline, where an input excitation is unknown; however, these approaches discussed here are objective, direct, and can be implemented in a consistent manner.
Sendur, Kürşat
2009-04-27
To address the large number of parameters involved in nano-optical problems, a more efficient computational method is necessary. An integral equation based numerical solution is developed when the particles are illuminated with collimated and focused incident beams. The solution procedure uses the method of weighted residuals, in which the integral equation is reduced to a matrix equation and then solved for the unknown electric field distribution. In the solution procedure, the effects of the surrounding medium and boundaries are taken into account using a Green's function formulation. Therefore, there is no additional error due to artificial boundary conditions unlike differential equation based techniques, such as finite difference time domain and finite element method. In this formulation, only the scattering nano-particle is discretized. Such an approach results in a lesser number of unknowns in the resulting matrix equation. The results are compared to the analytical Mie series solution for spherical particles, as well as to the finite element method for rectangular metallic particles. The Richards-Wolf vector field equations are combined with the integral equation based formulation to model the interaction of nanoparticles with linearly and radially polarized incident focused beams.
Numerical modelling of swirling diffusive flames
Directory of Open Access Journals (Sweden)
Parra-Santos Teresa
2016-01-01
Full Text Available Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing in mind the annular jet has swirl number over 0.5, a vortex breakdown appears in the axis of the burner. Besides, the sudden expansion with a ratio of 2 in diameter between nozzle exits and the test chamber produces the boundary layer separation with the corresponding torus shape recirculation. Contrasting the mixing and combustion models, the last one produces the reduction of the vortex breakdown.
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
The use of numerical methods in the solution of academic problems of classic mechanics
International Nuclear Information System (INIS)
Gonzalez Gonzalez, A.; Rubayo Soneira, J.; Portuondo Campa, E.
2001-01-01
In this work the use of numerical methods in the solution of physics academic problems is discussed, particularly those on classical mechanics. Frequently the solution of academic problems is limited to finding a differential equation which is left unsolved for having no analytical solution. However, by means of numerical methods we can solve these equations and enrich the physical analysis of the problem. This approach also makes the academic process a little closer to modern physical research, where numerical methods have increasingly been used in almost every field. In the present paper we discuss a classical mechanics problem using these methods. We start from both Newton's and Lagrange's formulations and apply different numerical algorithms in the solution of the obtained equations. During last academic semester, recently concluded, we tested the ideas of this work with students of Nuclear Physics career of the Higher Institute of Nuclear Sciences and technologies, at Havana, cuba. The results were encouraging. (Author) 7 refs
rights reserved Numerical Solution of the Differential Equation for ...
African Journals Online (AJOL)
ADOWIE PERE
2017-12-10
Dec 10, 2017 ... ABSTRACT: Rice blast disease is one of the diseases that causes damage to rice yield in Thailand. This research aims to simulate the severity of rice blast disease using the EPIRICE model for Khao Dawk Mali 105 that caused by. Pyricularia oryzae in Prachin Buri, Thailand, and evaluate the simulation ...
JASEM ISSN 1119- All rights reserved Numerical Solution of the ...
African Journals Online (AJOL)
ADOWIE PERE
2017-12-10
Dec 10, 2017 ... ABSTRACT: Rice blast disease is one of the diseases that causes damage to rice yield in Thailand. This research aims to simulate the severity of rice blast disease using the EPIRICE model for Khao Dawk Mali 105 that caused by. Pyricularia oryzae in Prachin Buri, Thailand, and evaluate the simulation ...
A quasilinear model for solute transport under unsaturated flow
International Nuclear Information System (INIS)
Houseworth, J.E.; Leem, J.
2009-01-01
We developed an analytical solution for solute transport under steady-state, two-dimensional, unsaturated flow and transport conditions for the investigation of high-level radioactive waste disposal. The two-dimensional, unsaturated flow problem is treated using the quasilinear flow method for a system with homogeneous material properties. Dispersion is modeled as isotropic and is proportional to the effective hydraulic conductivity. This leads to a quasilinear form for the transport problem in terms of a scalar potential that is analogous to the Kirchhoff potential for quasilinear flow. The solutions for both flow and transport scalar potentials take the form of Fourier series. The particular solution given here is for two sources of flow, with one source containing a dissolved solute. The solution method may easily be extended, however, for any combination of flow and solute sources under steady-state conditions. The analytical results for multidimensional solute transport problems, which previously could only be solved numerically, also offer an additional way to benchmark numerical solutions. An analytical solution for two-dimensional, steady-state solute transport under unsaturated flow conditions is presented. A specific case with two sources is solved but may be generalized to any combination of sources. The analytical results complement numerical solutions, which were previously required to solve this class of problems.
Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil
Directory of Open Access Journals (Sweden)
Kryštůfek P.
2015-01-01
Full Text Available 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.
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.
Numerical solution of incompressible flow through branched channels
Czech Academy of Sciences Publication Activity Database
Louda, Petr; Kozel, K.; Příhoda, Jaromír; Beneš, L.; Kopáček, T.
2011-01-01
Roč. 46, č. 1 (2011), s. 318-324 ISSN 0045-7930 R&D Projects: GA ČR GA103/09/0977; GA ČR GAP101/10/1230 Institutional research plan: CEZ:AV0Z20760514 Keywords : channel flow * branched channel * EARSM turbulence model Subject RIV: BK - Fluid Dynamics Impact factor: 1.810, year: 2011 http://www.sciencedirect.com/science/article/pii/S0045793010003506
Towards a direct numerical solution of Schroedinger's equation for (e, 2e) reactions
International Nuclear Information System (INIS)
Jones, S.; Stelbovics, A.T.
1999-01-01
The finite-difference method for electron-hydrogen scattering is presented in a simple, easily understood form for a model collision problem in which all angular momentum is neglected. The model Schroedinger equation is integrated outwards from the atomic centre on a grid of fixed spacing h. The number of difference equations is reduced each step outwards using an algorithm due to Poet, resulting in a propagating solution of the partial-differential equation. By imposing correct asymptotic boundary conditions on this general, propagating solution, the particular solution that physically corresponds to scattering is obtained along with the scattering amplitudes. Previous works using finite differences (and finite elements) have extracted scattering amplitudes only for low-level transitions (elastic scattering and n = 2 excitation). If we are to eventually extract ionisation amplitudes, however, the numerical method must remain stable for higher-level transitions. Here we report converged cross sections for transitions up to n = 8, as a first step towards obtaining ionisation (e, 2e) results. Copyright (1999) CSIRO Australia
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
Kryštůfek, P.; Kozel, K.
2013-04-01
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.
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.
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.
Directory of Open Access Journals (Sweden)
Grégory Antoni
2017-01-01
Full Text Available The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.
A numerical solution for a class of time fractional diffusion equations with delay
Directory of Open Access Journals (Sweden)
Pimenov Vladimir G.
2017-09-01
Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
Numerical solutions of ordinary and partial differential equations in the frequency domain
International Nuclear Information System (INIS)
Hazi, G.; Por, G.
1997-01-01
Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)
Aerosol numerical modelling at local scale
International Nuclear Information System (INIS)
Albriet, Bastien
2007-01-01
At local scale and in urban areas, an important part of particulate pollution is due to traffic. It contributes largely to the high number concentrations observed. Two aerosol sources are mainly linked to traffic. Primary emission of soot particles and secondary nanoparticle formation by nucleation. The emissions and mechanisms leading to the formation of such bimodal distribution are still badly understood nowadays. In this thesis, we try to provide an answer to this problematic by numerical modelling. The Modal Aerosol Model MAM is used, coupled with two 3D-codes: a CFD (Mercure Saturne) and a CTM (Polair3D). A sensitivity analysis is performed, at the border of a road but also in the first meters of an exhaust plume, to identify the role of each process involved and the sensitivity of different parameters used in the modelling. (author) [fr
Posttraumatic Orbital Emphysema: A Numerical Model
Directory of Open Access Journals (Sweden)
Andrzej Skorek
2014-01-01
Full Text Available Orbital emphysema is a common symptom accompanying orbital fracture. The pathomechanism is still not recognized and the usually assumed cause, elevated pressure in the upper airways connected with sneezing or coughing, does not always contribute to the occurrence of this type of fracture. Observations based on the finite model (simulating blowout type fracture of the deformations of the inferior orbital wall after a strike in its lower rim. Authors created a computer numeric model of the orbit with specified features—thickness and resilience modulus. During simulation an evenly spread 14400 N force was applied to the nodular points in the inferior rim (the maximal value not causing cracking of the outer rim, but only ruptures in the inferior wall. The observation was made from 1·10-3 to 1·10-2 second after a strike. Right after a strike dislocations of the inferior orbital wall toward the maxillary sinus were observed. Afterwards a retrograde wave of the dislocation of the inferior wall toward the orbit was noticed. Overall dislocation amplitude reached about 6 mm. Based on a numeric model of the orbit submitted to a strike in the inferior wall an existence of a retrograde shock wave causing orbital emphysema has been found.
A numerical model of peritectoid transformation
International Nuclear Information System (INIS)
Das, A.; Manna, I.; Pabi, S.K.
1999-01-01
A rigorous numerical model of the diffusion-controlled peritectoid transformation based on the isoconcentration contour migration method is presented here. The model is capable of considering the concentration dependence of diffusivity in the participating phases. The predictions from the model show an encouraging kinetics in the Ni-Mo diffusion couple. An extensive parametric study through the present formulation indicates that the peritectoid kinetics may be considerably affected by the diffusivities and phase field widths (in the equilibrium diagram) of the concerned solids. In this regard, the field width and diffusivity in the peritectoid phase appear to exert the most significant influence on the reaction rate. The numerically calculated transformation kinetics have been effectively rationalized by means of two dimensionless parameters, φ 1 and φ 2 , which are functions of the concerned phase field widths and diffusivity in the product phase. In addition, these parameters enable prediction of the minimum time required for the completion of peritectoid transformation without going through any rigorous computation
Numerical modeling of atmospheric washout processes
International Nuclear Information System (INIS)
Bayer, D.; Beheng, K.D.; Herbert, F.
1987-01-01
For the washout of particles from the atmosphere by clouds and rain one has to distinguish between processes which work in the first phase of cloud development, when condensation nuclei build up in saturated air (Nucleation Aerosol Scavenging, NAS) and those processes which work at the following cloud development. In the second case particles are taken off by cloud droplets or by falling rain drops via collision (Collision Aerosol Scavenging, CAS). The physics of both processes is described. For the CAS process a numerical model is presented. The report contains a documentation of the mathematical equations and the computer programs (FORTRAN). (KW) [de
Numerical solution of Q evolution equations for fragmentation functions
Hirai, M.; Kumano, S.
2012-04-01
bytes Classification: 11.5 Nature of problem: This program solves time-like DGLAP Q evolution equations with or without next-to-leading order αs effects for fragmentation functions. The evolved functions can be calculated for Dgh, Duh, Dubarh, Ddh, Ddbarh, Dsh, Dsbarh, Dch, Dcbarh, Dbh and Dbbarh of a hadron h. Solution method: The DGLAP integro-differential equations are solved by the Euler method for the differentiation of ln Q and the Gauss-Legendre method for the x integral as explained in Section 4 of the manuscript. Restrictions: This program is used for calculating Q evolution of fragmentation functions in the leading order or in the next-to-leading order of αs. Q evolution equations are the time-like DGLAP equations. The double precision arithmetic is used. The renormalization scheme is the modified minimal subtraction scheme (MSbar). A user provides initial fragmentation functions as the subroutines FF_INI and HQFF in the end of the distributed code FF_DGLAP.f. In FF_DGLAP.f, the subroutines are given by taking the HKNS07 (2) functions as an example of the initial functions. Then, the user inputs kinematical parameters in the file setup.ini as explained in Section 5.2 of the manuscript. Running time: A few seconds on HP DL360G5-DC-X5160.
Botello-Smith, Wesley M; Luo, Ray
2015-10-26
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membranes into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multigrid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations.
International Nuclear Information System (INIS)
Owen, D.R.J.; Gomez, C.M.B.
1981-01-01
The aim of the paper is to critically compare the relative efficiency of numerical algorithms available for the solution of nonlinear finite element problems. The methods considered include the Conjugate Newton, Quasi Newton and Secant Newton methods. The performance of these algorithms is compared against the standard Newton Raphson and Modified Newton Raphson solution processes. (orig./HP)
Numerical study of traveling-wave solutions for the Camassa-Holm equation
International Nuclear Information System (INIS)
Kalisch, Henrik; Lenells, Jonatan
2005-01-01
We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied
Numerical solutions of a three-point boundary value problem with an ...
African Journals Online (AJOL)
Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.
Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method
Directory of Open Access Journals (Sweden)
Limei Yan
2013-01-01
Full Text Available A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.
Numerical Model of the DARHT Accelerating Cell
Hughes, Thomas P; Genoni, Thomas C; Kang, Mike; Prichard, Benjamin A
2005-01-01
The DARHT-2 facility at Los Alamos National Laboratory accelerates a 2 microsecond electron beam using a series of inductive accelerating cells. The cell inductance is provided by large Metglas cores, which are driven by a pulse-forming network. The original cell design was susceptible to electrical breakdown near the outer radius of the cores. We developed a numerical model for the magnetic properties of Metglas over the range of dB/dt (magnetization rate) relevant to DARHT. The model was implemented in a radially-resolved circuit code, and in the LSP* electromagnetic code. LSP simulations showed that the field stress distribution across the outer radius of the cores was highly nonuniform. This was subsequently confirmed in experiments at LBNL. The calculated temporal evolution of the electric field stress inside the cores approximately matches experimental measurements. The cells have been redesigned to greatly reduce the field stresses along the outer radius.
Partial Differential Equations Modeling and Numerical Simulation
Glowinski, Roland
2008-01-01
This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...
Numerical modeling of materials under extreme conditions
Brown, Eric
2014-01-01
The book presents twelve state of the art contributions in the field of numerical modeling of materials subjected to large strain, high strain rates, large pressure and high stress triaxialities, organized into two sections. The first part is focused on high strain rate-high pressures such as those occurring in impact dynamics and shock compression related phenomena, dealing with material response identification, advanced modeling incorporating microstructure and damage, stress waves propagation in solids and structures response under impact. The latter part is focused on large strain-low strain rates applications such as those occurring in technological material processing, dealing with microstructure and texture evolution, material response at elevated temperatures, structural behavior under large strain and multi axial state of stress.
Finite analytic numerical solution axisymmetric Navier-Stokes and energy equations
International Nuclear Information System (INIS)
Chen, C.; Yoon, Y.H.
1983-01-01
Convective heat transfer for steady-state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature, and heat transfer coefficients for flow with Reynolds numbers of 5, 100, 1000, and 2000, and Prandtl numbers of 0.1, 1.0, and 10.0 with uniform grid sizes, are reported for an axisymmetric pipe with a sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic is stable converges rapidly, and simulates the convection of fluid flow accurately, since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values, thereby minimizing the false numerical diffusion
Energy Technology Data Exchange (ETDEWEB)
Loch, Guilherme G.; Bevilacqua, Joyce S., E-mail: guiloch@ime.usp.br, E-mail: joyce@ime.usp.br [Universidade de Sao Paulo (IME/USP), Sao Paulo, SP (Brazil). Departamento de Matematica Aplicada. Instituto de Matematica e Estatistica; Hiromoto, Goro; Rodrigues Junior, Orlando, E-mail: rodrijr@ipen.br, E-mail: hiromoto@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN-CNEN/SP), Sao Paulo, SP (Brazil)
2013-07-01
The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)
A global numerical solution of the radial Schroedinger equation by second-order perturbation theory
International Nuclear Information System (INIS)
Adam, G.
1979-01-01
A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
Numerical Solution of the Electron Transport Equation in the Upper Atmosphere
Energy Technology Data Exchange (ETDEWEB)
Woods, Mark Christopher [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Holmes, Mark [Rensselaer Polytechnic Inst., Troy, NY (United States); Sailor, William C [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-07-01
A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.
Darmana, D.; Henket, R.L.B.; Deen, N.G.; Kuipers, J.A.M.
2007-01-01
This paper describes simulations that were performed with an Euler–Lagrange model that takes into account mass transfer and chemical reaction reported by Darmana et al. (2005. Detailed modelling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
Adaptive numerical algorithms in space weather modeling
Tóth, Gábor; van der Holst, Bart; Sokolov, Igor V.; De Zeeuw, Darren L.; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Najib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav
2012-02-01
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit
Adaptive numerical algorithms in space weather modeling
International Nuclear Information System (INIS)
Tóth, Gábor; Holst, Bart van der; Sokolov, Igor V.; De Zeeuw, Darren L.; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng Xing; Najib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav
2012-01-01
Space weather describes the various processes in the Sun–Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit
Adaptive Numerical Algorithms in Space Weather Modeling
Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.;
2010-01-01
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical
Numerical solution of unsteady generalized Newtonian and Oldroyd-B fluids flow by dual time-stepping method
Keslerová, R.; Kozel, K.
2014-03-01
This work deals with the numerical solution of viscous and viscoelastic fluids flow. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible laminar fluids. Different models for the stress tensor are considered. For viscous fluids flow Newtonian model is used. For the describing of the behaviour of the mixture of viscous and viscoelastic fluids Oldroyd-B model is used. Numerical solution of the described models is based on cell-centered finite volume method in conjunction with artificial compressibility method. For time integration an explicit multistage Runge-Kutta scheme is used. In the case of unsteady computation dual-time stepping method is considered. The principle of dual-time stepping method is following. The artificial time is introduced and the artificial compressibility method in the artificial time is applied.
Numerical solution of linearized resistive MHD equations in a cylindrical geometry
Energy Technology Data Exchange (ETDEWEB)
Li, Jin
1995-06-01
Linearized resistive MHD eigenequations in a cylindrical geometry are derived and numerical methods are presented. The eigenequations are solved in a global manner such that there is no need to distinguish inner resistive layer and outer ideal region analytically. Resistive layer is numerically treated by using non-uniform mesh grid technique and high accuracy discretization scheme. Lundquist number S up to 10{sup 9} can be easily achieved. Numerical results are benchmarked by known analytical solutions and other numerical methods. 6 refs, 5 figs.
Mathematical and Numerical Techniques in Energy and Environmental Modeling
Chen, Z.; Ewing, R. E.
Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms
Advanced modelling and numerical strategies in nuclear thermal-hydraulics
International Nuclear Information System (INIS)
Staedtke, H.
2001-01-01
The first part of the lecture gives a brief review of the current status of nuclear thermal hydraulics as it forms the basis of established system codes like TRAC, RELAP5, CATHARE or ATHLET. Specific emphasis is given to the capabilities and limitations of the underlying physical modelling and numerical solution strategies with regard to the description of complex transient two-phase flow and heat transfer conditions as expected to occur in PWR reactors during off-normal and accident conditions. The second part of the lecture focuses on new challenges and future needs in nuclear thermal-hydraulics which might arise with regard to re-licensing of old plants using bestestimate methodologies or the design and safety analysis of Advanced Light Water Reactors relying largely on passive safety systems. In order to meet these new requirements various advanced modelling and numerical techniques will be discussed including extended wellposed (hyperbolic) two-fluid models, explicit modelling of interfacial area transport or higher order numerical schemes allowing a high resolution of local multi-dimensional flow processes.(author)
Low Mach number analysis of idealized thermoacoustic engines with numerical solution.
Hireche, Omar; Weisman, Catherine; Baltean-Carlès, Diana; Le Quéré, Patrick; Bauwens, Luc
2010-12-01
A model of an idealized thermoacoustic engine is formulated, coupling nonlinear flow and heat exchange in the heat exchangers and stack with a simple linear acoustic model of the resonator and load. Correct coupling results in an asymptotically consistent global model, in the small Mach number approximation. A well-resolved numerical solution is obtained for two-dimensional heat exchangers and stack. The model assumes that the heat exchangers and stack are shorter than the overall length by a factor of the order of a representative Mach number. The model is well-suited for simulation of the entire startup process, whereby as a result of some excitation, an initially specified temperature profile in the stack evolves toward a near-steady profile, eventually reaching stationary operation. A validation analysis is presented, together with results showing the early amplitude growth and approach of a stationary regime. Two types of initial excitation are used: Random noise and a small periodic wave. The set of assumptions made leads to a heat-exchanger section that acts as a source of volume but is transparent to pressure and to a local heat-exchanger model characterized by a dynamically incompressible flow to which a locally spatially uniform acoustic pressure fluctuation is superimposed.
Numerical resolution of a model of tumour growth.
Muñoz, Ana I
2016-03-01
We consider and solve numerically a mathematical model of tumour growth based on cancer stem cells (CSC) hypothesis with the aim of gaining some insight into the relation of different processes leading to exponential growth in solid tumours and into the evolution of different subpopulations of cells. The model consists of four hyperbolic equations of first order to describe the evolution of four subpopulations of cells. A fifth equation is introduced to model the evolution of the moving boundary. The coefficients of the model represent the rates at which reactions occur. In order to integrate numerically the four hyperbolic equations, a formulation in terms of the total derivatives is posed. A finite element discretization is applied to integrate the model equations in space. Our numerical results suggest the existence of a pseudo-equilibrium state reached at the early stage of the tumour, for which the fraction of CSC remains small. We include the study of the behaviour of the solutions for longer times and we obtain that the solutions to the system of partial differential equations stabilize to homogeneous steady states whose values depend only on the values of the parameters. We show that CSC may comprise different proportions of the tumour, becoming, in some cases, the predominant type of cells within the tumour. We also obtain that possible effective measure to detain tumour progression should combine the targeting of CSC with the targeting of progenitor cells. © The Authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Directory of Open Access Journals (Sweden)
V. M. Mikhailov
2017-12-01
Full Text Available Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use
Numerical modelling of ion transport in flames
Han, Jie
2015-10-20
This paper presents a modelling framework to compute the diffusivity and mobility of ions in flames. The (n, 6, 4) interaction potential is adopted to model collisions between neutral and charged species. All required parameters in the potential are related to the polarizability of the species pair via semi-empirical formulas, which are derived using the most recently published data or best estimates. The resulting framework permits computation of the transport coefficients of any ion found in a hydrocarbon flame. The accuracy of the proposed method is evaluated by comparing its predictions with experimental data on the mobility of selected ions in single-component neutral gases. Based on this analysis, the value of a model constant available in the literature is modified in order to improve the model\\'s predictions. The newly determined ion transport coefficients are used as part of a previously developed numerical approach to compute the distribution of charged species in a freely propagating premixed lean CH4/O2 flame. Since a significant scatter of polarizability data exists in the literature, the effects of changes in polarizability on ion transport properties and the spatial distribution of ions in flames are explored. Our analysis shows that changes in polarizability propagate with decreasing effect from binary transport coefficients to species number densities. We conclude that the chosen polarizability value has a limited effect on the ion distribution in freely propagating flames. We expect that the modelling framework proposed here will benefit future efforts in modelling the effect of external voltages on flames. Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/13647830.2015.1090018. © 2015 Taylor & Francis.
Numerical methods for the Lévy LIBOR model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
2010-01-01
but the methods are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure....... This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\\'evy LIBOR model of Eberlein and \\"Ozkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates...
Numerical Methods for the Lévy LIBOR Model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables...... simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods...
Modeling and numerical simulations of the influenced Sznajd model
Karan, Farshad Salimi Naneh; Srinivasan, Aravinda Ramakrishnan; Chakraborty, Subhadeep
2017-08-01
This paper investigates the effects of independent nonconformists or influencers on the behavioral dynamic of a population of agents interacting with each other based on the Sznajd model. The system is modeled on a complete graph using the master equation. The acquired equation has been numerically solved. Accuracy of the mathematical model and its corresponding assumptions have been validated by numerical simulations. Regions of initial magnetization have been found from where the system converges to one of two unique steady-state PDFs, depending on the distribution of influencers. The scaling property and entropy of the stationary system in presence of varying level of influence have been presented and discussed.
New Trends in Model Coupling Theory, Numerics and Applications
International Nuclear Information System (INIS)
Coquel, F.; Godlewski, E.; Herard, J. M.; Segre, J.
2010-01-01
This special issue comprises selected papers from the workshop New Trends in Model Coupling, Theory, Numerics and Applications (NTMC'09) which took place in Paris, September 2 - 4, 2009. The research of optimal technological solutions in a large amount of industrial systems requires to perform numerical simulations of complex phenomena which are often characterized by the coupling of models related to various space and/or time scales. Thus, the so-called multi-scale modelling has been a thriving scientific activity which connects applied mathematics and other disciplines such as physics, chemistry, biology or even social sciences. To illustrate the variety of fields concerned by the natural occurrence of model coupling we may quote: meteorology where it is required to take into account several turbulence scales or the interaction between oceans and atmosphere, but also regional models in a global description, solid mechanics where a thorough understanding of complex phenomena such as propagation of cracks needs to couple various models from the atomistic level to the macroscopic level; plasma physics for fusion energy for instance where dense plasmas and collisionless plasma coexist; multiphase fluid dynamics when several types of flow corresponding to several types of models are present simultaneously in complex circuits; social behaviour analysis with interaction between individual actions and collective behaviour. (authors)
Mathematical models and numerical simulation in electromagnetism
Bermúdez, Alfredo; Salgado, Pilar
2014-01-01
The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.
Directory of Open Access Journals (Sweden)
Mark A Lau
2016-09-01
Full Text Available This paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical solutions. The numerical solutions can be easily obtained once the differential equations are discretized via finite differences and then using cell formulas to implement the resulting recursive algorithms and other iterative methods such as the successive over-relaxation (SOR method. The graphing capabilities of spreadsheets can be exploited to enhance the visualization of the solutions to these equations. Furthermore, using Visual Basic for Applications (VBA can greatly facilitate the implementation of the analytical solutions to these equations, and in the process, one obtains Fourier series approximations to functions governing initial and/or boundary conditions.
Numerical modeling of spray combustion with an advanced VOF method
Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul
1995-01-01
This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.
The steady state of epidermis: mathematical modeling and numerical simulations.
Gandolfi, Alberto; Iannelli, Mimmo; Marinoschi, Gabriela
2016-12-01
We consider a model with age and space structure for the epidermis evolution. The model, previously presented and analyzed with respect to the suprabasal epidermis, includes different types of cells (proliferating cells, differentiated cells, corneous cells, and apoptotic cells) moving with the same velocity, under the constraint that the local volume fraction occupied by the cells is constant in space and time. Here, we complete the model proposing a mechanism regulating the cell production in the basal layer and we focus on the stationary case of the problem, i.e. on the case corresponding to the normal status of the skin. A numerical scheme to compute the solution of the model is proposed and its convergence is studied. Simulations are provided for realistic values of the parameters, showing the possibility of reproducing the structure of both "thin" and "thick" epidermis.
Computational numerical modelling of plasma focus
International Nuclear Information System (INIS)
Brollo, Fabricio
2005-01-01
Several models for calculation of the dynamics of Plasma Focus have been developed. All of them begin from the same physic principle: the current sheet run down the anode length, ionizing and collecting the gas that finds in its way.This is known as snow-plow model.Concerning pinch's compression, a MHD model is proposed.The plasma is treated as a fluid , particularly as a high ionized gas.However, there are not many models that, taking into account thermal equilibrium inside the plasma, make approximated calculations of the maximum temperatures reached in the pinch.Besides, there are no models which use those temperatures to estimate the termofusion neutron yield for the Deuterium or Deuterium-Tritium gas filled cases.In the PLADEMA network (Dense Magnetized Plasmas) a code was developed with the objective of describe the plasma focus dynamics, in a conceptual engineering stage.The codes calculates the principal variables (currents, time to focus, etc) and estimates the neutron yield in Deuterium-filled plasma focus devices.It can be affirmed that the code's experimental validation, in its axial and radial stages, was very successfully. However, it was accepted that the compression stage should be formulated again, to find a solution for a large variation of a parameter related with velocity profiles for the particles trapped inside the pinch.The objectives of this work can be stated in the next way : - Check the compression's model hypothesis. Develop a new model .- Implement the new model in the code. Compare results against experimental data of Plasma Focus devices from all around the world [es
Numerical modelling of ion transport in flames
Han, Jie; Belhi, Memdouh; Bisetti, Fabrizio; Mani Sarathy, S.
2015-11-01
This paper presents a modelling framework to compute the diffusivity and mobility of ions in flames. The (n, 6, 4) interaction potential is adopted to model collisions between neutral and charged species. All required parameters in the potential are related to the polarizability of the species pair via semi-empirical formulas, which are derived using the most recently published data or best estimates. The resulting framework permits computation of the transport coefficients of any ion found in a hydrocarbon flame. The accuracy of the proposed method is evaluated by comparing its predictions with experimental data on the mobility of selected ions in single-component neutral gases. Based on this analysis, the value of a model constant available in the literature is modified in order to improve the model's predictions. The newly determined ion transport coefficients are used as part of a previously developed numerical approach to compute the distribution of charged species in a freely propagating premixed lean CH4/O2 flame. Since a significant scatter of polarizability data exists in the literature, the effects of changes in polarizability on ion transport properties and the spatial distribution of ions in flames are explored. Our analysis shows that changes in polarizability propagate with decreasing effect from binary transport coefficients to species number densities. We conclude that the chosen polarizability value has a limited effect on the ion distribution in freely propagating flames. We expect that the modelling framework proposed here will benefit future efforts in modelling the effect of external voltages on flames. Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/13647830.2015.1090018.
Ocean wave prediction using numerical and neural network models
Digital Repository Service at National Institute of Oceanography (India)
Mandal, S.; Prabaharan, N.
This paper presents an overview of the development of the numerical wave prediction models and recently used neural networks for ocean wave hindcasting and forecasting. The numerical wave models express the physical concepts of the phenomena...
A numerical forecast model for road meteorology
Meng, Chunlei
2017-05-01
A fine-scale numerical model for road surface parameters prediction (BJ-ROME) is developed based on the Common Land Model. The model is validated using in situ observation data measured by the ROSA road weather stations of Vaisala Company, Finland. BJ-ROME not only takes into account road surface factors, such as imperviousness, relatively low albedo, high heat capacity, and high heat conductivity, but also considers the influence of urban anthropogenic heat, impervious surface evaporation, and urban land-use/land-cover changes. The forecast time span and the update interval of BJ-ROME in vocational operation are 24 and 3 h, respectively. The validation results indicate that BJ-ROME can successfully simulate the diurnal variation of road surface temperature both under clear-sky and rainfall conditions. BJ-ROME can simulate road water and snow depth well if the artificial removing was considered. Road surface energy balance in rainy days is quite different from that in clear-sky conditions. Road evaporation could not be neglected in road surface water cycle research. The results of sensitivity analysis show solar radiation correction coefficient, asphalt depth, and asphalt heat conductivity are important parameters in road interface temperatures simulation. The prediction results could be used as a reference of maintenance decision support system to mitigate the traffic jam and urban water logging especially in large cities.
Numerical modeling of bubble dynamics in magmas
Huber, Christian; Su, Yanqing; Parmigiani, Andrea
2014-05-01
Understanding the complex non-linear physics that governs volcanic eruptions is contingent on our ability to characterize the dynamics of bubbles and its effect on the ascending magma. The exsolution and migration of bubbles has also a great impact on the heat and mass transport in and out of magma bodies stored at shallow depths in the crust. Multiphase systems like magmas are by definition heterogeneous at small scales. Although mixture theory or homogenization methods are convenient to represent multiphase systems as a homogeneous equivalent media, these approaches do not inform us on possible feedbacks at the pore-scale and can be significantly misleading. In this presentation, we discuss the development and application of bubble-scale multiphase flow modeling to address the following questions : How do bubbles impact heat and mass transport in magma chambers ? How efficient are chemical exchanges between the melt and bubbles during magma decompression? What is the role of hydrodynamic interactions on the deformation of bubbles while the magma is sheared? Addressing these questions requires powerful numerical methods that accurately model the balance between viscous, capillary and pressure stresses. We discuss how these bubble-scale models can provide important constraints on the dynamics of magmas stored at shallow depth or ascending to the surface during an eruption.
Optimization methods and silicon solar cell numerical models
Girardini, K.; Jacobsen, S. E.
1986-01-01
An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.
Numerical Modelling of Flow and Settling in Secondary Settling Tanks
DEFF Research Database (Denmark)
Dahl, Claus Poulsen
This thesis discusses the development of a numerical model for the simulation of secondary settling tanks. In the first part, the status on the development of numerical models for settling tanks and a discussion of the current design practice are presented. A study of the existing numerical models...... and design practice proved a demand for further development to include numerical models in the design of settling tanks, thus improving the future settling tanks....
Directory of Open Access Journals (Sweden)
Sherif Amirov
2017-08-01
Full Text Available The recent work on the solvability of the boundary value problem for the nonlinear analogue of the Boussinesq equation has been further extended to focus on the characteristics of the solution. Since this type of equation does not have a known analytical solution for arbitrary boundary conditions, the problem has been solved numerically. The stability of the solution and the effect of the input function on the stability have been investigated from the physics point of view. For the special case of a discontinuous function at the right hand side of the equation, the solution has been analyzed around the discontinuity points.
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)
Energy Technology Data Exchange (ETDEWEB)
Teixeira, Vinicius Ligiero; Pires, Adolfo Puime; Bedrikovetsky, Pavel G. [Universidade Estadual do Norte Fluminense (UENF), Macae, RJ (Brazil). Lab. de Engenharia e Exploracao do Petroleo (LENEP)
2004-07-01
Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. The EOR methods may be classified into the following kinds: injection of chemical solutions, injection of solvents and thermal methods. The chemical fluids most commonly injected are polymers, surfactants, micellar solutions, etc. Displacement of oil by any of these fluids involves complex physico-chemical processes of interphase mass transfer, phase transitions and transport properties changes. These processes can be divided into two main categories: thermodynamical and hydrodynamical ones. They occur simultaneously during the displacement, and are coupled in the modern mathematical models of EOR. The model for one-dimensional displacement of oil by polymer solutions is analyzed in this paper. The Courant number is fixed, and we compare the results of different runs of a numerical simulator with the analytical solution of this problem. Each run corresponds to a different spatial discretization. (author)
Handling geophysical flows: Numerical modelling using Graphical Processing Units
Garcia-Navarro, Pilar; Lacasta, Asier; Juez, Carmelo; Morales-Hernandez, Mario
2016-04-01
Computational tools may help engineers in the assessment of sediment transport during the decision-making processes. The main requirements are that the numerical results have to be accurate and simulation models must be fast. The present work is based on the 2D shallow water equations in combination with the 2D Exner equation [1]. The resulting numerical model accuracy was already discussed in previous work. Regarding the speed of the computation, the Exner equation slows down the already costly 2D shallow water model as the number of variables to solve is increased and the numerical stability is more restrictive. On the other hand, the movement of poorly sorted material over steep areas constitutes a hazardous environmental problem. Computational tools help in the predictions of such landslides [2]. In order to overcome this problem, this work proposes the use of Graphical Processing Units (GPUs) for decreasing significantly the simulation time [3, 4]. The numerical scheme implemented in GPU is based on a finite volume scheme. The mathematical model and the numerical implementation are compared against experimental and field data. In addition, the computational times obtained with the Graphical Hardware technology are compared against Single-Core (sequential) and Multi-Core (parallel) CPU implementations. References [Juez et al.(2014)] Juez, C., Murillo, J., & Garca-Navarro, P. (2014) A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed. Advances in Water Resources. 71 93-109. [Juez et al.(2013)] Juez, C., Murillo, J., & Garca-Navarro, P. (2013) . 2D simulation of granular flow over irregular steep slopes using global and local coordinates. Journal of Computational Physics. 225 166-204. [Lacasta et al.(2014)] Lacasta, A., Morales-Hernndez, M., Murillo, J., & Garca-Navarro, P. (2014) An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes Advances in Engineering Software. 78 1-15. [Lacasta
Reinharz, Vladimir; Dahari, Harel; Barash, Danny
2018-03-15
Age-structured PDE models have been developed to study viral infection and treatment. However, they are notoriously difficult to solve. Here, we investigate the numerical solutions of an age-based multiscale model of hepatitis C virus (HCV) dynamics during antiviral therapy and compare them with an analytical approximation, namely its long-term approximation. First, starting from a simple yet flexible numerical solution that also considers an integral approximated over previous iterations, we show that the long-term approximation is an underestimate of the PDE model solution as expected since some infection events are being ignored. We then argue for the importance of having a numerical solution that takes into account previous iterations for the associated integral, making problematic the use of canned solvers. Second, we demonstrate that the governing differential equations are stiff and the stability of the numerical scheme should be considered. Third, we show that considerable gain in efficiency can be achieved by using adaptive stepsize methods over fixed stepsize methods for simulating realistic scenarios when solving multiscale models numerically. Finally, we compare between several numerical schemes for the solution of the equations and demonstrate the use of a numerical optimization scheme for the parameter estimation performed directly from the equations. Copyright © 2018 Elsevier Inc. All rights reserved.
A numerical model of aerosol scavenging
International Nuclear Information System (INIS)
Bradley, M.M.; Molenkamp, C.R.
1991-10-01
Using a three-dimensional numerical cloud/smoke-plume model, we have simulated the burning of a large, mid-latitude city following a nuclear exchange. The model includes 18 dynamic and microphysical equations that predict the fire-driven airflow, cloud processes, and smoke-cloud interactions. In the simulation, the intense heating from the burning city produces a firestorm with updraft velocities exceeding 60 m/s. Within 15 minutes of ignition, the smoke plume penetrates the tropopause. The updraft triggers a cumulonimbus cloud that produces significant quantities of ice, snow, and hail. These solid hydrometeors, as well as cloud droplets and rain, interact with the smoke particles from the fire. At the end of the one-hour simulation, over 20% of the smoke is in slowly falling snowflakes. If the snow reaches the ground before the flakes completely sublimate (or melt and then evaporate), then only approximately 50% of the smoke will survive the scavenging processes and remain in the atmosphere to affect the global climate
Numerical modeling of subaqueous sand dune morphodynamics
Doré, Arnaud; Bonneton, Philippe; Marieu, Vincent; Garlan, Thierry
2016-03-01
The morphodynamic evolution of subaqueous sand dunes is investigated, using a 2-D Reynolds-averaged Navier-Stokes numerical model. A laboratory experiment where dunes are generated under stationary unidirectional flow conditions is used as a reference case. The model reproduces the evolution of the erodible bed until a state of equilibrium is reached. In particular, the simulation exhibits the different stages of the bed evolution, e.g., the incipient ripple generation, the nonlinear bed form growing phase, and the dune field equilibrium phase. The results show good agreement in terms of dune geometrical dimensions and time to equilibrium. After the emergence of the first ripple field, the bed growth is driven by cascading merging sequences between bed forms of different heights. A sequence extracted from the simulation shows how the downstream bed form is first eroded before merging with the upstream bed form. Superimposed bed forms emerge on the dune stoss sides during the simulation. An analysis of the results shows that they emerge downstream of a slight deflection on the dune profile. The deflection arises due to a modification of the sediment flux gradient consecutive to a reduction in the turbulence relaxation length while the upstream bed form height decreases. As they migrate, superimposed bed forms grow on the dune stoss side and eventually provoke the degeneration of the dune crest. Cascading merging sequences and superimposed bed forms dynamics both influence the dune field evolution and size and therefore play a fundamental role in the dune field self-organization process.
Numerical modeling of the autumnal thermal bar
Tsydenov, Bair O.
2018-03-01
The autumnal riverine thermal bar of Kamloops Lake has been simulated using atmospheric data from December 1, 2015, to January 4, 2016. The nonhydrostatic 2.5D mathematical model developed takes into account the diurnal variability of the heat fluxes and wind on the lake surface. The average values for shortwave and longwave radiation and latent and sensible heat fluxes were 19.7 W/m2, - 95.9 W/m2, - 11.8 W/m2, and - 32.0 W/m2 respectively. Analysis of the wind regime data showed prevailing easterly winds and maximum speed of 11 m/s on the 8th and 19th days. Numerical experiments with different boundary conditions at the lake surface were conducted to evaluate effects of variable heat flux and wind stress. The results of modeling demonstrated that the variable heat flux affects the process of thermal bar evolution, especially during the lengthy night cooling. However, the wind had the greatest impact on the behavior of the autumnal thermal bar: The easterly winds contributed to an earlier appearance of the thermal bar, but the strong winds generating the intensive circulations (the velocity of the upper lake flow increased to 6 cm/s) may destroy the thermal bar front.
Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline
Directory of Open Access Journals (Sweden)
Ravi Kanth A.S.V.
2016-01-01
Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.
Numerical treatment of elliptic BVP with several solutions and of MHD equilibrium problems
International Nuclear Information System (INIS)
Meyer-Spasche, R.
1975-12-01
It is found out empirically that Newton iteration and difference methods are very suitable for the numerical treatment of elliptic boundary value problems (Lu)(x) = f(x,u(x)) in D c R 2 , u/deltaD = g having several solutions. Some convergence theorems for these methods are presented. Some notable numerical examples are given, including bifurcation diagrams, which are interesting in themselves and show also the applicability of the methods developed. (orig./WB) [de
Numerical solutions of multi-order fractional differential equations by Boubaker polynomials
Directory of Open Access Journals (Sweden)
Bolandtalat A.
2016-01-01
Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.
Oscillating solutions of the Vlasov-Poisson system-A numerical investigation
Ramming, Tobias; Rein, Gerhard
2018-02-01
Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington-Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies.
Numerical Solution of The Linear Fredholm Integral Equations of the Second Kind
Directory of Open Access Journals (Sweden)
N. Parandin
2010-03-01
Full Text Available The theory of integral equation is one of the major topics of applied mathematics. The main purpose of this paper is to introduce a numerical method based on the interpolation for approximating the solution of the second kind linear Fredholm integral equation. In this case, the divided differences method is applied. At last, two numerical examples are presented to show the accuracy of the proposed method
Numerical solution of compressible steady flows in a 2D GAMM channel and DCA 18% profile
Directory of Open Access Journals (Sweden)
Kozel Karel
2012-04-01
Full Text Available The article presents results of a numerical solution of subsonic and transonic flows described by the system of Euler equations in 2D flows in a channel and around a profile. Authors used Lax-Wendroff scheme to numerically solve the flows in a GAMM channel and around half DCA 18% profile. Authors programmed the mesh generator of the type C for profile with a blunt leading edge.
Numerical solution of compressible steady flows in a 2D GAMM channel and DCA 18% profile
Kryštůfek, Pavel; Kozel, Karel
2012-04-01
The article presents results of a numerical solution of subsonic and transonic flows described by the system of Euler equations in 2D flows in a channel and around a profile. Authors used Lax-Wendroff scheme to numerically solve the flows in a GAMM channel and around half DCA 18% profile. Authors programmed the mesh generator of the type C for profile with a blunt leading edge.
GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD
2016-01-01
This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...
Modelling of cardiovascular system: development of a hybrid (numerical-physical) model.
Ferrari, G; Kozarski, M; De Lazzari, C; Górczyńska, K; Mimmo, R; Guaragno, M; Tosti, G; Darowski, M
2003-12-01
Physical models of the circulation are used for research, training and for testing of implantable active and passive circulatory prosthetic and assistance devices. However, in comparison with numerical models, they are rigid and expensive. To overcome these limitations, we have developed a model of the circulation based on the merging of a lumped parameter physical model into a numerical one (producing therefore a hybrid). The physical model is limited to the barest essentials and, in this application, developed to test the principle, it is a windkessel representing the systemic arterial tree. The lumped parameters numerical model was developed in LabVIEW environment and represents pulmonary and systemic circulation (except the systemic arterial tree). Based on the equivalence between hydraulic and electrical circuits, this prototype was developed connecting the numerical model to an electrical circuit--the physical model. This specific solution is valid mainly educationally but permits the development of software and the verification of preliminary results without using cumbersome hydraulic circuits. The interfaces between numerical and electrical circuits are set up by a voltage controlled current generator and a voltage controlled voltage generator. The behavior of the model is analyzed based on the ventricular pressure-volume loops and on the time course of arterial and ventricular pressures and flow in different circulatory conditions. The model can represent hemodynamic relationships in different ventricular and circulatory conditions.
Nacozy, P. E.
1984-01-01
The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.
Solutions manual to accompany An introduction to numerical methods and analysis
Epperson, James F
2014-01-01
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp
Understanding Etna flank instability through numerical models
Apuani, Tiziana; Corazzato, Claudia; Merri, Andrea; Tibaldi, Alessandro
2013-02-01
As many active volcanoes, Mount Etna shows clear evidence of flank instability, and different mechanisms were suggested to explain this flank dynamics, based on the recorded deformation pattern and character. Shallow and deep deformations, mainly associated with both eruptive and seismic events, are concentrated along recognised fracture and fault systems, mobilising the eastern and south-eastern flank of the volcano. Several interacting causes were postulated to control the phenomenon, including gravity force, magma ascent along the feeding system, and a very complex local and/or regional tectonic activity. Nevertheless, the complexity of such dynamics is still an open subject of research and being the volcano flanks heavily urbanised, the comprehension of the gravitative dynamics is a major issue for public safety and civil protection. The present research explores the effects of the main geological features (in particular the role of the subetnean clays, interposed between the Apennine-Maghrebian flysch and the volcanic products) and the role of weakness zones, identified by fracture and fault systems, on the slope instability process. The effects of magma intrusions are also investigated. The problem is addressed by integrating field data, laboratory tests and numerical modelling. A bi- and tri-dimensional stress-strain analysis was performed by a finite difference numerical code (FLAC and FLAC3D), mainly aimed at evaluating the relationship among geological features, volcano-tectonic structures and magmatic activity in controlling the deformation processes. The analyses are well supported by dedicated structural-mechanical field surveys, which allowed to estimate the rock mass strength and deformability parameters. To take into account the uncertainties which inevitably occur in a so complicated model, many efforts were done in performing a sensitivity analysis along a WNW-ESE section crossing the volcano summit and the Valle del Bove depression. This was
Benchmark problems for numerical implementations of phase field models
International Nuclear Information System (INIS)
Jokisaari, A. M.; Voorhees, P. W.; Guyer, J. E.; Warren, J.; Heinonen, O. G.
2016-01-01
Here, we present the first set of benchmark problems for phase field models that are being developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST). While many scientific research areas use a limited set of well-established software, the growing phase field community continues to develop a wide variety of codes and lacks benchmark problems to consistently evaluate the numerical performance of new implementations. Phase field modeling has become significantly more popular as computational power has increased and is now becoming mainstream, driving the need for benchmark problems to validate and verify new implementations. We follow the example set by the micromagnetics community to develop an evolving set of benchmark problems that test the usability, computational resources, numerical capabilities and physical scope of phase field simulation codes. In this paper, we propose two benchmark problems that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model. We demonstrate the utility of benchmark problems by comparing the results of simulations performed with two different adaptive time stepping techniques, and we discuss the needs of future benchmark problems. The development of benchmark problems will enable the results of quantitative phase field models to be confidently incorporated into integrated computational materials science and engineering (ICME), an important goal of the Materials Genome Initiative.
Directory of Open Access Journals (Sweden)
Nilson C. Roberty
2011-01-01
Full Text Available We introduce algorithms marching over a polygonal mesh with elements consistent with the propagation directions of the particle (radiation flux. The decision for adopting this kind of mesh to solve the one-speed Boltzmann transport equation is due to characteristics of the domain of the transport operator which controls derivatives only in the direction of propagation of the particles (radiation flux in the absorbing and scattering media. This a priori adaptivity has the advantages that it formulates a consistent scheme which makes appropriate the application of the Lax equivalence theorem framework to the problem. In this work, we present the main functional spaces involved in the formalism and a description of the algorithms for the mesh generation and the transport equation solution. Some numerical examples related to the solution of a transmission problem in a high-contrast model with absorption and scattering are presented. Also, a comparison with benchmarks problems for source and reactor criticality simulations shows the compatibility between calculations with the algorithms proposed here and theoretical results.
On the numerical evaluation of algebro-geometric solutions to integrable equations
International Nuclear Information System (INIS)
Kalla, C; Klein, C
2012-01-01
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations
International Nuclear Information System (INIS)
Esmail, S.F.H.
2011-01-01
The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.
Numerical modeling of atoll island hydrogeology.
Bailey, R T; Jenson, J W; Olsen, A E
2009-01-01
We implemented Ayers and Vachers' (1986) inclusive conceptual model for atoll island aquifers in a comprehensive numerical modeling study to evaluate the response of the fresh water lens to selected controlling climatic and geologic variables. Climatic factors include both constant and time-varying recharge rates, with particular attention paid to the effects of El Niño and the associated drought it brings to the western Pacific. Geologic factors include island width; hydraulic conductivity of the uppermost Holocene-age aquifer, which contains the fresh water lens; the depth to the contact with the underlying, and much more conductive, Pleistocene karst aquifer, which transmits tidal signals to the base of the lens; and the presence or absence of a semiconfining reef flat plate on the ocean side. Sensitivity analyses of steady-steady simulations show that lens thickness is most strongly sensitive to the depth to the Holocene-Pleistocene contact and to the hydraulic conductivity of the Holocene aquifer, respectively. Comparisons between modeling results and published observations of atoll island lens thicknesses suggest a hydraulic conductivity of approximately 50 m/d for leeward islands and approximately 400 m/d for windward islands. Results of transient simulations show that lens thickness fluctuations during average seasonal conditions and El Niño events are quite sensitive to island width, recharge rate, and hydraulic conductivity of the Holocene aquifer. In general, the depletion of the lens during drought conditions is most drastic for small, windward islands. Simulation results suggest that recovery from a 6-month drought requires about 1.5 years.
Two different methods for numerical solution of the modified Burgers' equation.
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.
Numerical solution of nonlinear Urisohn-Volterra fuzzy functional integral equations
Georgieva, Atanaska; Naydenova, Iva
2017-12-01
In the present paper, we propose an efficient iterative numerical method of successive approximations to approximate solution of nonlinear Urisohn-Volterra fuzzy functional integral equations by fuzzy trapezoidal quadrature formula for classes of fuzzy-number-valued functions of Lipschitz type. We prove the convergence of the method and investigate the numerical stability of the present method with respect to the choice of the first iteration. The convergence of the method is tested through a numerical experiment, that confirms the obtained theoretical results.
Large scale experiments as a tool for numerical model development
DEFF Research Database (Denmark)
Kirkegaard, Jens; Hansen, Erik Asp; Fuchs, Jesper
2003-01-01
for improvement of the reliability of physical model results. This paper demonstrates by examples that numerical modelling benefits in various ways from experimental studies (in large and small laboratory facilities). The examples range from very general hydrodynamic descriptions of wave phenomena to specific......Experimental modelling is an important tool for study of hydrodynamic phenomena. The applicability of experiments can be expanded by the use of numerical models and experiments are important for documentation of the validity of numerical tools. In other cases numerical tools can be applied...... hydrodynamic interaction with structures. The examples also show that numerical model development benefits from international co-operation and sharing of high quality results....
A note on numerical solution of a parabolic-Schrödinger equation
Ozdemir, Yildirim; Alp, Mustafa
2016-08-01
In the present study, a nonlocal boundary value problem for a parabolic-Schrödinger equation is considered. The stability estimates for the solution of the given problem is established. The first and second order of difference schemes are presented for approximately solving a specific nonlocal boundary problem. The theoretical statements for the solution of these difference schemes are supported by the result of numerical examples.
TLC scheme for numerical solution of the transport equation on equilateral triangular meshes
International Nuclear Information System (INIS)
Walters, W.F.
1983-01-01
A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy
The Numerical Solution of the Equilibrium Problem for a Stretchable Elastic Beam
Mehdiyeva, G. Y.; Aliyev, A. Y.
2017-08-01
The boundary value problem under consideration describes the equilibrium of an elastic beam that is stretched or contracted by specified forces. The left end of the beam is free of load, and the right end is rigidly lapped. To solve the problem numerically, an appropriate difference problem is constructed. Solving the difference problem, we obtain an approximate solution of the problem. We estimate the approximate solution of the stated problem.
International Nuclear Information System (INIS)
Kotler, Z.; Neria, E.; Nitzan, A.
1991-01-01
The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.)
Numerical Model of Detonation for Insensitive HE
Klimenko, Vladimir
2011-06-01
Most of modern munitions are filled by insensitive HE. However, mechanism of initiation of these HE is still unknown. IHE have not any pores and, therefore, hot spot mechanism does not work here. What is a mechanism working in this case? We have used 3D hydrocode to study process of shock wave loading of mixture of HMX grains with different binders (HMX/binder=88/12) and have determined formation of surface layers with increased plastic deformation. According to the dislocation mechanism of detonation (V. Klimenko, I. Kozyreva, J. Energetic Materials, 2010, v. 28, pp. 249-262) plastic deformation generates definite concentration of radicals. Surface layers have also increased temperature due to viscous work. So, these activated layers have increased temperature and number of radicals in comparison with values inside grains. Kinetic calculation has shown fast decomposition of these layers. As a result, the activated layer is ignited and this gives beginning of grain burning process. The developed two-stages mechanism has been incorporated into 2D hydrocode. The developed numerical model demonstrates high accuracy in simulation of detonation processes in IHE (in particular, PBXN-110 and B2241).
Numerical Problems and Agent-Based Models for a Mass Transfer Course
Murthi, Manohar; Shea, Lonnie D.; Snurr, Randall Q.
2009-01-01
Problems requiring numerical solutions of differential equations or the use of agent-based modeling are presented for use in a course on mass transfer. These problems were solved using the popular technical computing language MATLABTM. Students were introduced to MATLAB via a problem with an analytical solution. A more complex problem to which no…
New methods For Modeling Transport Of Water And Solutes In Soils
DEFF Research Database (Denmark)
Møldrup, Per
Recent models for water and solute transport in unsaturated soils have been mechanistically based but numerically very involved. This dissertation concerns the development of mechanistically-based but numerically simple models for calculating and analyzing transport of water and solutes in soil s...
Numerical modelling of new rockfall interception nets
von Boetticher, Albrecht; Volkwein, Axel; Wendeler, Corinna
2010-05-01
The design and certification of effective rockfall protection barriers is mainly achieved through 1:1 prototype testing. In order to reduce development costs of a prototype it is recommended that pre-studies using numerical simulations are performed. A large component to modelling rockfall protection systems is the numerical simulation of the nets. To date there exist several approaches to model the different mesh types such as ring nets or diagonal meshes (Nicot 1999, Cazzani et al. 2002, Volkwein 2004). However, the consideration of chain link meshes has not yet been realised. Chain link meshes are normally found as standard fence structures. However, they also exist in setups using high-strength steel and wire bundles. These variants show an enormous capacity to retain loads e.g. rockfalls, and at the same time are very efficient due to their low demand of steel material. The increasing application of chain link mesh in barrier systems requires an accurate model is available to complete prototype studies. A new approach now aims to perform a Finite Element simulation of such chain link meshes. The main challenge herein is to achieve the net deformation behaviour that is observed in field tests also in the simulation. A simulation using simple truss elements would not work since it neglects the out-of-plane-height of the mesh construction providing important reserves for local and global high deformations. Thus addressing this, a specially developed Discrete Element is able to reconstruct the mechanical behaviour of the single chain wire (bundles). As input parameters it utilises typical properties such as longitudinal and transversal mesh widths, and break loads resulting from in-plane-tension tests and steel strength. The single chain elements then can be combined to a complete mesh (e.g. 130 x 65 mm, 3 - 4 mm wire with a strength of 1770 N-mm2). Combining these elements with a supporting structure consisting of posts, ropes and energy absorbers, enables the
A numerical method for finding sign-changing solutions of superlinear Dirichlet problems
Energy Technology Data Exchange (ETDEWEB)
Neuberger, J.M.
1996-12-31
In a recent result it was shown via a variational argument that a class of superlinear elliptic boundary value problems has at least three nontrivial solutions, a pair of one sign and one which sign changes exactly once. These three and all other nontrivial solutions are saddle points of an action functional, and are characterized as local minima of that functional restricted to a codimension one submanifold of the Hilbert space H-0-1-2, or an appropriate higher codimension subset of that manifold. In this paper, we present a numerical Sobolev steepest descent algorithm for finding these three solutions.
Directory of Open Access Journals (Sweden)
Elmira Ashpazzadeh
2018-04-01
Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Directory of Open Access Journals (Sweden)
Minghui Song
2012-01-01
Full Text Available The main purpose of this paper is to investigate the convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs. The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations (SDEs without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for SEPCAs. Firstly, this paper shows SEPCAs which have nonexplosion global solutions under local Lipschitz condition without the linear growth condition. Then the convergence in probability of numerical solutions to SEPCAs under the same conditions is established. Finally, an example is provided to illustrate our theory.
Advanced Combustion Numerics and Modeling - FY18 First Quarter Report
Energy Technology Data Exchange (ETDEWEB)
Whitesides, R. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Killingsworth, N. J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); McNenly, M. J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Petitpas, G. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2018-01-05
This project is focused on early stage research and development of numerical methods and models to improve advanced engine combustion concepts and systems. The current focus is on development of new mathematics and algorithms to reduce the time to solution for advanced combustion engine design using detailed fuel chemistry. The research is prioritized towards the most time-consuming workflow bottlenecks (computer and human) and accuracy gaps that slow ACS program members. Zero-RK, the fast and accurate chemical kinetics solver software developed in this project, is central to the research efforts and continues to be developed to address the current and emerging needs of the engine designers, engine modelers and fuel mechanism developers.
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Directory of Open Access Journals (Sweden)
SURE KÖME
2014-12-01
Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.
Numerical solutions of stochastic Lotka-Volterra equations via operational matrices
Directory of Open Access Journals (Sweden)
F. Hosseini Shekarabi
2016-03-01
Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.
Numerical solution of modified fokker-planck equation with poissonian input
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Král, Radomil
2010-01-01
Roč. 17, 3/4 (2010), s. 251-268 ISSN 1802-1484 R&D Projects: GA AV ČR(CZ) IAA200710805; GA ČR(CZ) GA103/09/0094 Institutional research plan: CEZ:AV0Z20710524 Keywords : Fokker-Planck equation * poisson ian exciation * numerical solution * transition effects Subject RIV: JN - Civil Engineering
Analytical and numerical solutions of the Schrödinger–KdV equation
Indian Academy of Sciences (India)
solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The G /G method is also used to integrate this equation. Subsequently, the variational iteration method and homotopy perturbation method are also applied to solve this equation. The numerical simulations are ...
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.
Analytical and numerical solutions of the Schrödinger–KdV equation
Indian Academy of Sciences (India)
journal of. January 2012 physics pp. 59–90. Analytical and numerical solutions of the Schrödinger–KdV equation. MANEL LABIDI1, GHODRAT EBADI2, ESSAID ZERRAD3 and. ANJAN BISWAS4,∗. 1Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of Carthage,. BP 743, La Marsa 2070, ...
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Numerical solution of inviscid transonic flow through 3D axial blade row
Energy Technology Data Exchange (ETDEWEB)
Fort, J.; Fuerst, J.; Halama, J.; Kozel, K. [CTU Prague (Czech Republic). Dept. of Technical Mathematics
2000-07-01
Presented paper deals with numerical solution of 3D inviscid transonic flow through axial cascades. Two different finite volume methods are mentioned. Authors show a comparison of both methods using results computed for the stator and the rotor cascades. A role of inlet parameters and body forces in the case of a rotor flow has been also investigated. (orig.)
Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling
Energy Technology Data Exchange (ETDEWEB)
Du, Qiang [Pennsylvania State Univ., State College, PA (United States)
2014-11-12
generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.
Variable thickness transient groundwater flow model theory and numerical implementation
International Nuclear Information System (INIS)
Kipp, K.L.; Reisenauer, A.E.; Cole, C.R.; Bryan, C.A.
1976-01-01
Modeling of radionuclide movement in the groundwater system beneath the Hanford Reservation requires mathematical simulation of the two-dimensional flow in the unconfined aquifer. This was accomplished using the nonlinear, transient Boussinesq equation with appropriate initial and boundary conditions, including measured Columbia River stages and rates of wastewater disposal to the ground. The heterogeneous permeability (hydraulic conductivity) distribution was derived by solution of the Boussinesq equation along instantaneous streamtubes of flow employing a measured water table surface and a limited number of field-measured hydraulic conductivity values. Use of a successive line over-relaxation technique with unequal time steps resulted in a more rapid convergence of the numerical solution than with previous techniques. The model was used to simulate the water table changes for the period 1968 through 1973 using known inputs and boundary conditions. A comparison of calculated and measured water table elevations was made at specific well locations and the quality of the verification simulation was evaluated using a data retrieval and display system. Agreement between the model results and measured data was good over two-thirds of the Hanford Reservation. The capability of the model to simulate flow with time-varying boundary conditions, complex boundary shapes, and a heterogeneous distribution of aquifer properties was demonstrated
Steady and Unsteady Numerical Solution of Generalized Newtonian Fluids Flow by Runge-Kutta method
Keslerová, R.; Kozel, K.; Prokop, V.
2010-09-01
In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non-Newtonian) fluids is considered. The governing system of equations is the system of Navier-Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time-stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non-Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented.
Numerical models for high beta magnetohydrodynamic flow
International Nuclear Information System (INIS)
Brackbill, J.U.
1987-01-01
The fundamentals of numerical magnetohydrodynamics for highly conducting, high-beta plasmas are outlined. The discussions emphasize the physical properties of the flow, and how elementary concepts in numerical analysis can be applied to the construction of finite difference approximations that capture these features. The linear and nonlinear stability of explicit and implicit differencing in time is examined, the origin and effect of numerical diffusion in the calculation of convective transport is described, and a technique for maintaining solenoidality in the magnetic field is developed. Many of the points are illustrated by numerical examples. The techniques described are applicable to the time-dependent, high-beta flows normally encountered in magnetically confined plasmas, plasma switches, and space and astrophysical plasmas. 40 refs
Numerical modelling of nearshore wave transformation
Digital Repository Service at National Institute of Oceanography (India)
Chandramohan, P.; Nayak, B.U.; SanilKumar, V.
A software has been developed for numerical refraction study based on finite amplitude wave theories. Wave attenuation due to shoaling, bottom friction, bottom percolation and viscous dissipation has also been incorporated. The software...
New numerical methods for open-loop and feedback solutions to dynamic optimization problems
Ghosh, Pradipto
The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development
Numerical modeling of oceanic crustal hydrothermal systems
Latychev, Konstantin
The oceanic crust is a complex rock-mineral formation which extends up to several kilometers below the sea floor and covers laterally about two thirds of the planet. Hydrothermal circulation within the crust is driven by magmatic sources and carried by the fluid residing in pores and cracks. Hydrothermal advection transfers about one quarter of the Earth's total heat power from the interior. Marine sediments are believed to be the largest repositories of solid ice-like methane clathrate hydrates. The compliance technique is an important tool for assessment of this resource. It makes use of the oceanic surface gravity waves to induce pressure variations on the sea floor and measure the corresponding vertical deformation. This thesis deals with the convective heat and mass transfer within the oceanic crust, as a fractured porous medium, and the elastic, quasi-static response of hydrated marine sediments to gravity wave loading. Both generic and site-specific applications are considered. Most applications are tackled numerically in three spatial dimensions. The major results are as follows. Fractures can trigger and maintain hydrothermal circulation. The permeability-thickness product in the direction of flow is an adequate parameter to represent the fracture if convection is not vigorous. A new temperature homogenization mechanism for the off-axial convection is proposed which is due to quasi-lateral circulation within a permeable zone between sediment cover and basalt. It explains both the observed correlation between surface heat flux and sediment thickness, as well as regular heat flux variations when no buried topography is present. A hydrothermal model for the CoAxial Segment of the Juan de Fuca Ridge predicts ridge-parallel convection with the low-temperature vents spaced 1 km apart. The compliance approach is feasible for a non-layered medium. The average compliance response depends on the bulk hydrate content, but not on a particular connectivity pattern
Numerical modeling of tunneling-induced seismicity
Rinaldi, Antonio Pio; Urpi, Luca
2017-04-01
Removal of rock mass in mining environment has been associated since long-time with seismic event of magnitude 3 and above, with the potential to cause damage to the infrastructures or even loss of human life. Although with similarities with mining, relatively unknown up to now are seismic events induced by tunneling. However with modern mechanized tunneling techniques, making possible to digging deeper and longer underground infrastructure, the risk is not negligible. As an example, the excavation of the 57km long Gotthard Base Tunnel has been associated more than hundred seismic events, with the largest one having magnitude of ML 2.4, damaging the tunnel infrastructures. For future scenario of deep geological storage of nuclear waste, tunneling will constitute the primary activity during site construction. Hence, it will be crucial to understand the risk associated with the underground construction operation that can reactivate seismogenic features nearby the future location of emplacement tunnels. Here we present numerical simulation aimed at understanding the potential for inducing seismicity during tunnel construction. The stress changes and their evolution during the excavation are evaluated with a finite element solver (FLAC3d). A strain-softening friction model is then used to simulate the occurrence of a sudden slip on a fault zone (if critical conditions for reactivation are reached). We also present a sensitivity analysis of the potential for inducing different seismic events by different tunnel sizes at varying distance from a nearby failure plane, with the final purpose of evaluating safety of a potential nuclear repository site on the short- and long-term.
Local solution method for numerical solving of the wave propagation problem
Moiseenko, V. E.; Pilipenko, V. V.
2001-12-01
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential increase (decrease) is proposed. It is based on the approximation of the solution sought for in the form of a superposition of certain polynomial-exponential basic functions. The method is studied for the Helmholtz equation in comparison with the standard finite difference and finite element methods. The numerical tests have shown the convergence of the method proposed. In comparison with the standard methods the same accuracy is obtained on substantially coarser mesh. This advantage becomes more pronounced, if the solution varies very rapidly.
Numerical solution of stochastic differential equations with Poisson and Lévy white noise
Grigoriu, M.
2009-08-01
A fixed time step method is developed for integrating stochastic differential equations (SDE’s) with Poisson white noise (PWN) and Lévy white noise (LWN). The method for integrating SDE’s with PWN has the same structure as that proposed by Kim [Phys. Rev. E 76, 011109 (2007)], but is established by using different arguments. The integration of SDE’s with LWN is based on a representation of Lévy processes by sums of scaled Brownian motions and compound Poisson processes. It is shown that the numerical solutions of SDE’s with PWN and LWN converge weakly to the exact solutions of these equations, so that they can be used to estimate not only marginal properties but also distributions of functionals of the exact solutions. Numerical examples are used to demonstrate the applications and the accuracy of the proposed integration algorithms.
Numerical solution of stochastic differential equations with Poisson and Lévy white noise.
Grigoriu, M
2009-08-01
A fixed time step method is developed for integrating stochastic differential equations (SDE's) with Poisson white noise (PWN) and Lévy white noise (LWN). The method for integrating SDE's with PWN has the same structure as that proposed by Kim [Phys. Rev. E 76, 011109 (2007)], but is established by using different arguments. The integration of SDE's with LWN is based on a representation of Lévy processes by sums of scaled Brownian motions and compound Poisson processes. It is shown that the numerical solutions of SDE's with PWN and LWN converge weakly to the exact solutions of these equations, so that they can be used to estimate not only marginal properties but also distributions of functionals of the exact solutions. Numerical examples are used to demonstrate the applications and the accuracy of the proposed integration algorithms.
A numerical 4D Collision Risk Model
Schmitt, Pal; Culloch, Ross; Lieber, Lilian; Kregting, Louise
2017-04-01
With the growing number of marine renewable energy (MRE) devices being installed across the world, some concern has been raised about the possibility of harming mobile, marine fauna by collision. Although physical contact between a MRE device and an organism has not been reported to date, these novel sub-sea structures pose a challenge for accurately estimating collision risks as part of environmental impact assessments. Even if the animal motion is simplified to linear translation, ignoring likely evasive behaviour, the mathematical problem of establishing an impact probability is not trivial. We present a numerical algorithm to obtain such probability distributions using transient, four-dimensional simulations of a novel marine renewable device concept, Deep Green, Minesto's power plant and hereafter referred to as the 'kite' that flies in a figure-of-eight configuration. Simulations were carried out altering several configurations including kite depth, kite speed and kite trajectory while keeping the speed of the moving object constant. Since the kite assembly is defined as two parts in the model, a tether (attached to the seabed) and the kite, collision risk of each part is reported independently. By comparing the number of collisions with the number of collision-free simulations, a probability of impact for each simulated position in the cross- section of the area is considered. Results suggest that close to the bottom, where the tether amplitude is small, the path is always blocked and the impact probability is 100% as expected. However, higher up in the water column, the collision probability is twice as high in the mid line, where the tether passes twice per period than at the extremes of its trajectory. The collision probability distribution is much more complex in the upper end of the water column, where the kite and tether can simultaneously collide with the object. Results demonstrate the viability of such models, which can also incorporate empirical
Numerical modelling of electrochemical polarization around charged metallic particles
Bücker, Matthias; Undorf, Sabine; Flores Orozco, Adrián; Kemna, Andreas
2017-04-01
We extend an existing analytical model and carry out numerical simulations to study the polarization process around charged metallic particles immersed in an electrolyte solution. Electro-migration and diffusion processes in the electrolyte are described by the Poisson-Nernst-Planck system of partial differential equations. To model the surface charge density, we consider a time- and frequency-invariant electric potential at the particle surface, which leads to the build-up of a static electrical double layer (EDL). Upon excitation by an external electric field at low frequencies, we observe the superposition of two polarization processes. On the one hand, the induced dipole moment on the metallic particle leads to the accumulation of opposite charges in the electrolyte. This charge polarization corresponds to the long-known response of uncharged metallic particles. On the other hand, the unequal cation and anion concentrations in the EDL give rise to a salinity gradient between the two opposite sides of the metallic particle. The resulting concentration polarization enhances the magnitude of the overall polarization response. Furthermore, we use our numerical model to study the effect of relevant model parameters such as surface charge density and ionic strength of the electrolyte on the resulting spectra of the effective conductivity of the composite model system. Our results do not only give interesting new insight into the time-harmonic variation of electric potential and ion concentrations around charged metallic particle. They are also able to reduce incongruities between earlier model predictions and geophysical field and laboratory measurements. Our model thereby improves the general understanding of IP signatures of metallic particles and represents the next step towards a quantitative interpretation of IP imaging results. Part of this research is funded by the Austrian Federal Ministry of Science, Research and Economy under the Raw Materials Initiative.
Stratified flows with variable density: mathematical modelling and numerical challenges.
Murillo, Javier; Navas-Montilla, Adrian
2017-04-01
Stratified flows appear in a wide variety of fundamental problems in hydrological and geophysical sciences. They may involve from hyperconcentrated floods carrying sediment causing collapse, landslides and debris flows, to suspended material in turbidity currents where turbulence is a key process. Also, in stratified flows variable horizontal density is present. Depending on the case, density varies according to the volumetric concentration of different components or species that can represent transported or suspended materials or soluble substances. Multilayer approaches based on the shallow water equations provide suitable models but are not free from difficulties when moving to the numerical resolution of the governing equations. Considering the variety of temporal and spatial scales, transfer of mass and energy among layers may strongly differ from one case to another. As a consequence, in order to provide accurate solutions, very high order methods of proved quality are demanded. Under these complex scenarios it is necessary to observe that the numerical solution provides the expected order of accuracy but also converges to the physically based solution, which is not an easy task. To this purpose, this work will focus in the use of Energy balanced augmented solvers, in particular, the Augmented Roe Flux ADER scheme. References: J. Murillo , P. García-Navarro, Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods. J. Comput. Phys. 231 (2012) 1963-2001. J. Murillo B. Latorre, P. García-Navarro. A Riemann solver for unsteady computation of 2D shallow flows with variable density. J. Comput. Phys.231 (2012) 4775-4807. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux
An asymptotic solution to a passive biped walker model
Yudaev, Sergey A.; Rachinskii, Dmitrii; Sobolev, Vladimir A.
2017-02-01
We consider a simple model of a passive dynamic biped robot walker with point feet and legs without knee. The model is a switched system, which includes an inverted double pendulum. Robot’s gait and its stability depend on parameters such as the slope of the ramp, the length of robot’s legs, and the mass distribution along the legs. We present an asymptotic solution of the model. The first correction to the zero order approximation is shown to agree with the numerical solution for a limited parameter range.
Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J
2017-01-01
A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Masonry constructions mechanical models and numerical applications
Lucchesi, Massimiliano; Padovani, Cristina
2008-01-01
Numerical methods for the structural analysis of masonry constructions can be of great value in assessing the safety of artistically important masonry buildings and optimizing potential operations of maintenance and strengthening in terms of their cost-effectiveness, architectural impact and static effectiveness. This monograph firstly provides a detailed description of the constitutive equation of masonry-like materials, clearly setting out its most important features. It then goes on to provide a numerical procedure to solve the equilibrium problem of masonry solids. A large portion of the w
Numerical modelling of collapsing volcanic edifices
Costa, Ana; Marques, Fernando; Kaus, Boris
2017-04-01
The flanks of Oceanic Volcanic Edifice's (OVEs) can occasionally become unstable. If that occurs, they can deform in two different modes: either slowly along localization failure zones (slumps) or catastrophically as debris avalanches. Yet the physics of this process is incompletely understood, and the role of factors such as the OVE's strength (viscosity, cohesion, friction angle), dimensions, geometry, and existence of weak layers remain to be addressed. Here we perform numerical simulations to study the interplay between viscous and plastic deformation on the gravitational collapse of an OVE (diffuse deformation vs. localization of failure along discrete structures). We focus on the contribution of the edifice's strength parameters for the mode of deformation, as well as on the type of basement. Tests were performed for a large OVE (7.5 km high, 200 km long) and either purely viscous (overall volcano edifice viscosities between 1019-1023 Pa.s), or viscoplastic rheology (within a range of cohesion and friction angle values). Results show that (a) for a strong basement (no slip basal boundary condition), the deformation pattern suggests wide/diffuse "listric" deformation within the volcanic edifice, without the development of discrete plastic failure zones; (b) for a weak basement (free slip basal boundary condition), rapid collapse of the edifice through the propagation of plastic failure structures within the edifice occurs. Tests for a smaller OVE (4.5 km by 30 km) show that failure localization along large-scale listric structures occurs more readily for different combinations of cohesion and friction angles. In these tests, high cohesion values combined with small friction angles lead to focusing of deformation along a narrower band. Tests with a weak layer underlying part of the volcanic edifice base show deformation focused along discrete structures mainly dipping towards the distal sector of the volcano. These tests for a small OVE constitute a promising
Numerical Modelling of Double-Steel Plate Composite Shear Walls
Directory of Open Access Journals (Sweden)
Michaela Elmatzoglou
2017-02-01
Full Text Available Double-steel plate concrete composite shear walls are being used for nuclear plants and high-rise buildings. They consist of thick concrete walls, exterior steel faceplates serving as reinforcement and shear connectors, which guarantee the composite action between the two different materials. Several researchers have used the Finite Element Method to investigate the behaviour of double-steel plate concrete walls. The majority of them model every element explicitly leading to a rather time-consuming solution, which cannot be easily used for design purposes. In the present paper, the main objective is the introduction of a three-dimensional finite element model, which can efficiently predict the overall performance of a double-steel plate concrete wall in terms of accuracy and time saving. At first, empirical formulations and design relations established in current design codes for shear connectors are evaluated. Then, a simplified finite element model is used to investigate the nonlinear response of composite walls. The developed model is validated using results from tests reported in the literature in terms of axial compression and monotonic, cyclic in-plane shear loading. Several finite element modelling issues related to potential convergence problems, loading strategies and computer efficiency are also discussed. The accuracy and simplicity of the proposed model make it suitable for further numerical studies on the shear connection behaviour at the steel-concrete interface.
Numerical time integration for air pollution models
J.G. Verwer (Jan); W. Hundsdorfer (Willem); J.G. Blom (Joke)
1998-01-01
textabstractDue to the large number of chemical species and the three space dimensions, off-the-shelf stiff ODE integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations [ fracpar{c{t + nabla cdot left( vu{u c right) = nabla cdot left(
Some Experiences with Numerical Modelling of Overflows
DEFF Research Database (Denmark)
Larsen, Torben; Nielsen, L.; Jensen, B.
2007-01-01
across the edge of the overflow. To ensure critical flow across the edge, the upstream flow must be subcritical whereas the downstream flow is either supercritical or a free jet. Experimentally overflows are well studied. Based on laboratory experiments and Froude number scaling, numerous accurate...
International Nuclear Information System (INIS)
Houfek, Karel
2008-01-01
Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.
Directory of Open Access Journals (Sweden)
Thoudam Roshan
2016-10-01
Full Text Available Numerical solutions of the coupled Klein-Gordon-Schrödinger equations is obtained by using differential quadrature methods based on polynomials and quintic B-spline functions for space discretization and Runge-Kutta fourth order for time discretization. Stability of the schemes are studied using matrix stability analysis. The accuracy and efficiency of the methods are shown by conducting some numerical experiments on test problems. The motion of single soliton and interaction of two solitons are simulated by the proposed methods.
A New Method to Solve Numeric Solution of Nonlinear Dynamic System
Directory of Open Access Journals (Sweden)
Min Hu
2016-01-01
Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.
International Nuclear Information System (INIS)
Novkovic, D.; Tomasevic, M.; Subotic, K.
1998-01-01
A system of reduced differential equations generally valid for plane-parallel, cylindrical and spherical ionization chambers, which is appropriate for numerical solution, has been derived. The system has been solved numerically for plane-parallel and spherical ionization chambers filled with air. The comparison of the calculated results of Armstrong and Tate, for plane-parallel ionization chambers, and Sprinkle and Tate, for spherical ionization chambers, with the present calculations has shown a good agreement. The calculated values for ionization chambers filled with CO 2 were also in good agreement with the experimental data of Moriuchi et al. (author)
Numerical solution of several 2D and 3D internal flow problems
Fialová, M.; Fořt, J.; Fürst, J.; Huněk, M.; Kozel, K.
The work deals with numerical solution of 3D Euler and 2D or 3D Navier-Stokes equations. Incompressible, subsonic and transonic flow through a cascade or in a channel of constant cross-section is numerically solved. Two versions of Lax-Wendroff type finite volume schemes and Runge-Kutta scheme were developed for 3D computations. The work presents some 2D and 3D results of laminar viscous flows through a cascade or in a channel as well as 2D results achieved by ENO scheme. The results of cascade computation are compared with experimental measurement.
A new numerical scheme for bounding acceleration in the LWR model
LECLERCQ, L; ELSEVIER
2005-01-01
This paper deals with the numerical resolution of bounded acceleration extensions of the LWR model. Two different manners for bounding accelerations in the LWR model will be presented: introducing a moving boundary condition in front of an accelerating flow or defining a field of constraints on the maximum allowed speed in the (x,t) plane. Both extensions lead to the same solutions if the declining branch of the fundamental diagram is linear. The existing numerical scheme for the latter exte...
A numerical solution to the radial equation of the tidal wave propagation
International Nuclear Information System (INIS)
Makarious, S.H.
1981-08-01
The tidal wave function y(x) is a solution to an inhomogeneous, linear, second-order differential equation with variable coefficient. Numerical values for the height-dependence terms, in the observed tides, have been utilized in finding y(x) as a solution to an initial-value problem. Complex Fast Fourier Transform technique is also used to obtain the solution in a complex form. Based on a realistic temperature structure, the atmosphere - below 110 km - has been divided into layers with distinct characteristics, and thus the technique of propagation in stratified media has been applied. The reduced homogeneous equation assumes the form of Helmholtz equation and with initial conditions the general solution is obtained. (author)
Numerical modeling and the physical basis of seismic discriminants
International Nuclear Information System (INIS)
Denny, M.D.
1993-01-01
Accurate seismic event discrimination is critical to detection of nuclear explosions. Numerical modeling applied to seismic event discrimination can lead to increased reliability of proliferation detection. It is particularly applicable to error budgeting and to understanding explosion and earthquake phenomenologies. There also is a need for minimum requirements to validate the models used in numerical modeling
2-dimensional numerical modeling of active magnetic regeneration
DEFF Research Database (Denmark)
Nielsen, Kaspar Kirstein; Pryds, Nini; Smith, Anders
2009-01-01
Various aspects of numerical modeling of Active Magnetic Regeneration (AMR) are presented. Using a 2-dimensional numerical model for solving the unsteady heat transfer equations for the AMR system, a range of physical effects on both idealized and non-idealized AMR are investigated. The modeled...
BGS GISGroundwater: the first numerical seamless GIS groundwater flow model
Wang, Lei; Jackson, Christopher; Kingdon, Andrew; Pachocka, Magdalena
2013-01-01
Geographic Information Systems (GISs) are the major data sources for numerical groundwater modelling, and it is common practice to couple groundwater models with GISs. There are three methods for coupling the numerical groundwater models with GISs, namely, “loose”, “tight”, and “seamless”. A seamless GIS groundwater model allows constructing, running model and visualisation of modelled results to be carried out all in a GIS environment, thus having the advantages of being easy to use and high...
Bessel collocation approach for approximate solutions of Hantavirus infection model
Directory of Open Access Journals (Sweden)
Suayip Yuzbasi
2017-11-01
Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.
Small-scale engagement model with arrivals: analytical solutions
International Nuclear Information System (INIS)
Engi, D.
1977-04-01
This report presents an analytical model of small-scale battles. The specific impetus for this effort was provided by a need to characterize hypothetical battles between guards at a nuclear facility and their potential adversaries. The solution procedure can be used to find measures of a number of critical parameters; for example, the win probabilities and the expected duration of the battle. Numerical solutions are obtainable if the total number of individual combatants on the opposing sides is less than 10. For smaller force size battles, with one or two combatants on each side, symbolic solutions can be found. The symbolic solutions express the output parameters abstractly in terms of symbolic representations of the input parameters while the numerical solutions are expressed as numerical values. The input parameters are derived from the probability distributions of the attrition and arrival processes. The solution procedure reduces to solving sets of linear equations that have been constructed from the input parameters. The approach presented in this report does not address the problems associated with measuring the inputs. Rather, this report attempts to establish a relatively simple structure within which small-scale battles can be studied
Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations
Directory of Open Access Journals (Sweden)
Shaobo Zhou
2014-01-01
Full Text Available Our effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis of the exact solution. We will prove that the Euler-Maruyama (EM method can preserve almost surely exponential stability of stochastic pantograph differential equations under the linear growth conditions. And the backward EM method can reproduce almost surely exponential stability for highly nonlinear stochastic pantograph differential equations. A highly nonlinear example is provided to illustrate the main theory.
Numerical Solutions for Supersonic Flow of an Ideal Gas Around Blunt Two-Dimensional Bodies
Fuller, Franklyn B.
1961-01-01
The method described is an inverse one; the shock shape is chosen and the solution proceeds downstream to a body. Bodies blunter than circular cylinders are readily accessible, and any adiabatic index can be chosen. The lower limit to the free-stream Mach number available in any case is determined by the extent of the subsonic field, which in turn depends upon the body shape. Some discussion of the stability of the numerical processes is given. A set of solutions for flows about circular cylinders at several Mach numbers and several values of the adiabatic index is included.
Irandoust-Pakchin, Safar; Abdi-Mazraeh, Somayeh; Khani, Ali
2017-12-01
In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of class of fractional partial differential equation with variable coefficient of fractional differential equation in various continues functions of spatial and time orders. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. Finally, illustrative examples are included to demonstrate the validity and applicability of the presented technique.
Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification
Energy Technology Data Exchange (ETDEWEB)
Blottner, F.G.; Lopez, A.R.
1998-10-01
This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.
Lötstedt, Erik; Jentschura, Ulrich D
2009-02-01
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
The Navier-Stokes-Fourier system: From weak solutions to numerical analysis
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2015-01-01
Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml
Numerical solution to the problem of criticality by Monte Carlo method
International Nuclear Information System (INIS)
Kyncl, J.
1989-04-01
A new method of numerical solution of the criticality problem is proposed. The method is based on the results of the Krein and Rutman theory. Monte Carlo method is used and the random process is chosen in such a way that the differences between results obtained and exact ones would be arbitrarily small. The method can be applied for both analogous and nonanalogous random processes. (author). 8 refs
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Energy Technology Data Exchange (ETDEWEB)
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
An efficient approach to the numerical solution of rate-independent problems with nonconvex energies
Czech Academy of Sciences Publication Activity Database
Bartels, S.; Kružík, Martin
2011-01-01
Roč. 9, č. 3 (2011), s. 1275-1300 ISSN 1540-3459 R&D Projects: GA AV ČR IAA100750802 Grant - others:GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : numerical solution * nonconvexity Subject RIV: BA - General Mathematics Impact factor: 2.009, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/kruzik-0364707.pdf
The Navier-Stokes-Fourier system: From weak solutions to numerical analysis
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2015-01-01
Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes- Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300.xml
Numerical solutions of the nonlinear fractional-order brusselator system by Bernstein polynomials.
Khan, Hasib; Jafari, Hossein; Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane
2014-01-01
In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
Directory of Open Access Journals (Sweden)
Hakon A. Hoel
2007-07-01
Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.
Numerical Analysis of Ginzburg-Landau Models for Superconductivity.
Coskun, Erhan
Thin film conventional, as well as High T _{c} superconductors of various geometric shapes placed under both uniform and variable strength magnetic field are studied using the universially accepted macroscopic Ginzburg-Landau model. A series of new theoretical results concerning the properties of solution is presented using the semi -discrete time-dependent Ginzburg-Landau equations, staggered grid setup and natural boundary conditions. Efficient serial algorithms including a novel adaptive algorithm is developed and successfully implemented for solving the governing highly nonlinear parabolic system of equations. Refinement technique used in the adaptive algorithm is based on modified forward Euler method which was also developed by us to ease the restriction on time step size for stability considerations. Stability and convergence properties of forward and modified forward Euler schemes are studied. Numerical simulations of various recent physical experiments of technological importance such as vortes motion and pinning are performed. The numerical code for solving time-dependent Ginzburg-Landau equations is parallelized using BlockComm -Chameleon and PCN. The parallel code was run on the distributed memory multiprocessors intel iPSC/860, IBM-SP1 and cluster of Sun Sparc workstations, all located at Mathematics and Computer Science Division, Argonne National Laboratory.
Energy Technology Data Exchange (ETDEWEB)
Ojeda Gonzalez, A.; Domingues, M.O.; Mendes, O., E-mail: ojeda.gonzalez.a@gmail.com [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil); Kaibara, M.K. [Universidade Federal Fluminense (GMA/IME/UFF), Niteroi, RJ (Brazil); Prestes, A. [Universidade do Vale do Paraiba (IP and D/UNIVAP), Sao Jose dos Campos, SP (Brazil). Lab. de Fisica e Astronomia
2015-10-15
The Grad-Shafranov equation is a Poisson's equation, i.e., a partial differential equation of elliptic type. The problem is depending on the initial condition and can be treated as a Cauchy problem. Although it is ill-posed or ill-conditioned, it can be integrated numerically. In the integration of the GS equation, singularities with large values of the potential arise after a certain number of integration steps away from the original data line, and a filter should be used. The Grad-Shafranov reconstruction (GSR) technique was developed from 1996 to 2000 for recovering two-dimensional structures in the magnetopause in an ideal MHD formulation. Other works have used the GSR techniques to study magnetic flux ropes in the solar wind and in the magnetotail from a single spacecraft dataset; posteriorly, it was extended to treat measurements from multiple satellites. From Vlasov equation, it is possible to arrive at the GS-equation in function of the normalized vector potential. A general solution is obtained using complex variable theory. A specific solution was chosen as benchmark case to solve numerically the GS equation.We propose some changes in the resolution scheme of the GS equation to improve the solution. The result of each method is compared with the solution proposed by Hau and Sonnerup (J. Geophys. Res. 104(A4), 6899-6917 (1999)). The main improvement found in the GS resolution was the need to filter Bx values at each y value. (author)
Warsta, L.; Karvonen, T.
2017-12-01
There are currently 25 shooting and training areas in Finland managed by The Finnish Defence Forces (FDF), where military activities can cause contamination of open waters and groundwater reservoirs. In the YMPYRÄ project, a computer software framework is being developed that combines existing open environmental data and proprietary information collected by FDF with computational models to investigate current and prevent future environmental problems. A data centric philosophy is followed in the development of the system, i.e. the models are updated and extended to handle available data from different areas. The results generated by the models are summarized as easily understandable flow and risk maps that can be opened in GIS programs and used in environmental assessments by experts. Substances investigated with the system include explosives and metals such as lead, and both surface and groundwater dominated areas can be simulated. The YMPYRÄ framework is composed of a three dimensional soil and groundwater flow model, several solute transport models and an uncertainty assessment system. Solute transport models in the framework include particle based, stream tube and finite volume based approaches. The models can be used to simulate solute dissolution from source area, transport in the unsaturated layers to groundwater and finally migration in groundwater to water extraction wells and springs. The models can be used to simulate advection, dispersion, equilibrium adsorption on soil particles, solubility and dissolution from solute phase and dendritic solute decay chains. Correct numerical solutions were confirmed by comparing results to analytical 1D and 2D solutions and by comparing the numerical solutions to each other. The particle based and stream tube type solute transport models were useful as they could complement the traditional finite volume based approach which in certain circumstances produced numerical dispersion due to piecewise solution of the
Forecast Jointed Rock Mass Compressive Strength Using a Numerical Model
Directory of Open Access Journals (Sweden)
Protosenya Anatoliy
2016-01-01
Full Text Available The method of forecasting the strength of the jointed rock mass by numerical modeling of finite element method in ABAQUS was described. The paper presents advantages of this method to solve the problem of determining the mechanical characteristics of jointed rock mass and the basic steps of creating a numerical geomechanical model of jointed rock mass and numerical experiment. Numerical simulation was carried out with jointed rock mass in order to obtain the ratio of strain and stress while loading the numerical model, determining parameters of quantitative assessment of the impact of the discontinuities orientation on the value of the compressive strength, compressive strength anisotropy. The results of the numerical experiment are compared with the data of experimental studies investigations. Innovative materials and structures are analyzed in this paper. The results that were obtained by calculation show qualitative agreement with the results of laboratory experiments of jointed rock mass.
Neilson, D. G.; Incropera, F. D.; Bennon, W. D.
1990-01-01
A computational study of solidification of a binary Na2CO3 solution in a horizontal cylindrical annulus is performed using a continuum formulation with a control-volume based, finite-difference scheme. The initial conditions were selected to facilitate the study of counter thermal and solutal convection, accompanied by extensive mushy region growth. Numerical results are compared with experimental data with mixed success. Qualitative agreement is obtained for the overall solidification process and associated physical phenomena. However, the plume thickness calculated for the solutally-driven convective upflow is substantially smaller than the observed value. Evolution of double-diffusive layers is predicted, but over a time scale much smaller than that observed experimentally. Good agreement is obtained between predicted and measured results for solid growth, but the mushy region thickness is significantly overpredicted.
ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.
Hromadka, T.V.
1987-01-01
Besides providing an exact solution for steady-state heat conduction processes (Laplace-Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil-water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximate boundary generation.
Schuler, James J.; Felippa, Carlos A.
1994-01-01
This paper discusses an incremental-iterative nonlinear solution technique for solving the nonlinear finite element equations of the superconducting state of a superconductor. The untreated equations are highly ill-conditioned and are impossible to solve within the typical 16-place double precision supplied by most computers. A combination of matrix scaling and mesh grading techniques is used to reduce the condition number of the tangent stiffness matrix and increase the accuracy of the current carrying boundary layer representation. Numerical results for a one-dimensional model of a time-independent superconductor treated by the Ginzburg-Landau model are presented and discussed. The computed solutions clearly display the Meissner effect of magnetic field expulsion from the central region of the superconductor. These results are compared to the physics of a low-viscosity fluid problem. From this analogy, a physical argument is advanced about the macroscopic behavior of superconductors.
A model and numerical method for compressible flows with capillary effects
Energy Technology Data Exchange (ETDEWEB)
Schmidmayer, Kevin, E-mail: kevin.schmidmayer@univ-amu.fr; Petitpas, Fabien, E-mail: fabien.petitpas@univ-amu.fr; Daniel, Eric, E-mail: eric.daniel@univ-amu.fr; Favrie, Nicolas, E-mail: nicolas.favrie@univ-amu.fr; Gavrilyuk, Sergey, E-mail: sergey.gavrilyuk@univ-amu.fr
2017-04-01
A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.
Numerical Model of High Strength Concrete
Wang, R. Z.; Wang, C. Y.; Lin, Y. L.
2018-03-01
The purpose of this paper is to present a three-dimensional constitutive model based on the concept of equivalent uniaxial strain. closed Menetrey-Willam (CMW) failure surfaces which combined with Menetrey-Willam meridian and the cap model are introduced in this paper. Saenz stress-strain model is applied and adjusted by the ultimate strength parameters from CMW failure surface to reflect the latest stress or strain condition. The high strength concrete (HSC) under tri-axial non-proportional loading is considered and the model in this paper performed a good prediction.
Atlas : A library for numerical weather prediction and climate modelling
Deconinck, Willem; Bauer, Peter; Diamantakis, Michail; Hamrud, Mats; Kühnlein, Christian; Maciel, Pedro; Mengaldo, Gianmarco; Quintino, Tiago; Raoult, Baudouin; Smolarkiewicz, Piotr K.; Wedi, Nils P.
2017-11-01
The algorithms underlying numerical weather prediction (NWP) and climate models that have been developed in the past few decades face an increasing challenge caused by the paradigm shift imposed by hardware vendors towards more energy-efficient devices. In order to provide a sustainable path to exascale High Performance Computing (HPC), applications become increasingly restricted by energy consumption. As a result, the emerging diverse and complex hardware solutions have a large impact on the programming models traditionally used in NWP software, triggering a rethink of design choices for future massively parallel software frameworks. In this paper, we present Atlas, a new software library that is currently being developed at the European Centre for Medium-Range Weather Forecasts (ECMWF), with the scope of handling data structures required for NWP applications in a flexible and massively parallel way. Atlas provides a versatile framework for the future development of efficient NWP and climate applications on emerging HPC architectures. The applications range from full Earth system models, to specific tools required for post-processing weather forecast products. The Atlas library thus constitutes a step towards affordable exascale high-performance simulations by providing the necessary abstractions that facilitate the application in heterogeneous HPC environments by promoting the co-design of NWP algorithms with the underlying hardware.
Numerical Modeling of Electrical Contact Conductance of Rough Bodies
Directory of Open Access Journals (Sweden)
M. V. Murashov
2015-01-01
Full Text Available Since the beginning of the 20th century to the present time, efforts have been made to develop a model of the electrical contact conductance. The development of micro- and nanotechnologies make contact conductance problem more essential. To conduct borrowing from a welldeveloped thermal contact conductance models on the basis of thermal and electrical conductivity analogy is often not possible due to a number of fundamental differences. While some 3Dmodels of rough bodies deformation have been developed in one way or another, a 3D-model of the electrical conductance through rough bodies contact is still not. A spatial model of electrical contact of rough bodies is proposed, allows one to calculate the electrical contact conductance as a function of the contact pressure. Representative elements of the bodies are parallelepipeds with deterministic roughness on the contacting surfaces. First the non-linear elastic-plastic deformation of rough surface under external pressure is solved using the finite element software ANSYS. Then the solution of electrostatic problem goes on the same finite element mesh. Aluminum AD1 is used as the material of the contacting bodies with properties that account for cold work hardening of the surface. The numerical model is built within the continuum mechanics and nanoscale effects are not taken into account. The electrical contact conductance was calculated on the basis of the concept of electrical resistance of the model as the sum of the electrical resistances of the contacting bodies and the contact itself. It was assumed that there is no air in the gap between the bodies. The dependence of the electrical contact conductance on the contact pressure is calculated as well as voltage and current density distributions in the contact bodies. It is determined that the multi-asperity contact mode, adequate to real roughness, is achieved at pressures higher than 3MPa, while results within the single contact spot are
NUMERICAL SIMULATION AND MODELING OF UNSTEADY FLOW ...
African Journals Online (AJOL)
2014-06-30
Jun 30, 2014 ... It was resolved the Navier-Stokes Reynolds averaged using a single closed equation, which models the Reynolds stress (-ρ (u_i U_j) ̅) by solving the transport equation for the turbulent kinematic viscosity this model proposed by Spalart-. Allmaras. The equations of continuity and Navier-Stokes Reynolds ...
Numerical Modelling of Wave Run-Up
DEFF Research Database (Denmark)
Ramirez, Jorge Robert Rodriguez; Frigaard, Peter; Andersen, Thomas Lykke
2011-01-01
Wave loads are important in problems related to offshore structure, such as wave run-up, slamming. The computation of such wave problems are carried out by CFD models. This paper presents one model, NS3, which solve 3D Navier-Stokes equations and use Volume of Fluid (VOF) method to treat the free...
Simple Numerical Model of Laminated Glass Beams
Directory of Open Access Journals (Sweden)
A. Zemanová
2008-01-01
Full Text Available This paper presents a simple Finite Element model aimed at efficient simulation of layered glass units. The approach is based on considering the independent kinematics of each layer, tied together via Lagrange multipliers. Validation and verification of the resulting model against independent data demonstrate its accuracy, showing its potential for generalization towards more complex problems.
Paleoclimate validation of a numerical climate model
International Nuclear Information System (INIS)
Schelling, F.J.; Church, H.W.; Zak, B.D.; Thompson, S.L.
1994-01-01
An analysis planned to validate regional climate model results for a past climate state at Yucca Mountain, Nevada, against paleoclimate evidence for the period is described. This analysis, which will use the GENESIS model of global climate nested with the RegCM2 regional climate model, is part of a larger study for DOE's Yucca Mountain Site Characterization Project that is evaluating the impacts of long term future climate change on performance of the potential high level nuclear waste repository at Yucca Mountain. The planned analysis and anticipated results are presented
Numerical Modeling and Experimental Testing of a Wave Energy Converter
DEFF Research Database (Denmark)
Zurkinden, Andrew Stephen; Kramer, Morten; Ferri, Francesco
numerical values for comparison with the experimental test results which were carried out in the same time. It is for this reason why Chapter 4 does consist exclusively of numerical values. Experimental values and measured time series of wave elevations have been used throughout the report in order to a......) validate the numerical model and b) preform stochastic analysis. The latter technique is introduced in order to optimize the control parameters of the power take off system....
Pseudoclassical fermionic model and classical solutions
International Nuclear Information System (INIS)
Smailagic, A.
1981-08-01
We study classical limit of fermionic fields seen as Grassmann variables and deduce the proper quantization prescription using Dirac's method for constrained systems and investigate quantum meaning of classical solutions for the Thirring model. (author)
Modelling asteroid brightness variations. I - Numerical methods
Karttunen, H.
1989-01-01
A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.
Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems
Frohne, Jörg
2015-08-06
© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.
Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem
Directory of Open Access Journals (Sweden)
Won-Tak Hong
2016-01-01
Full Text Available We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1 as well as oscillating singularities (of type rαsin(ϵlogr. It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.
The influence of numerical models on determining the drag coefficient
Directory of Open Access Journals (Sweden)
Dobeš Josef
2014-03-01
Full Text Available The paper deals with numerical modelling of body aerodynamic drag coefficient in the transition from laminar to turbulent flow regimes, where the selection of a suitable numerical model is problematic. On the basic problem of flow around a simple body – sphere selected computational models are tested. The values obtained by numerical simulations of drag coefficients of each model are compared with the graph of dependency of the drag coefficient vs. Reynolds number for a sphere. Next the dependency of Strouhal number vs. Reynolds number is evaluated, where the vortex shedding frequency values for given speed are obtained numerically and experimentally and then the values are compared for each numerical model and experiment. The aim is to specify trends for the selection of appropriate numerical model for flow around bodies problem in which the precise description of the flow field around the obstacle is used to define the acoustic noise source. Numerical modelling is performed by finite volume method using CFD code.
Flute-like musical instruments: A toy model investigated through numerical continuation
Terrien, Soizic; Vergez, Christophe; Fabre, Benoît
2013-07-01
Self-sustained musical instruments (bowed string, woodwind and brass instruments) can be modelled by nonlinear lumped dynamical systems. Among these instruments, flutes and flue organ pipes present the particularity to be modelled as a delay dynamical system. In this paper, such a system, a toy model of flute-like instruments, is studied using numerical continuation. Equilibrium and periodic solutions are explored with respect to the blowing pressure, with focus on amplitude and frequency evolutions along the different solution branches, as well as "jumps" between periodic solution branches. The influence of a second model parameter (namely the inharmonicity) on the behaviour of the system is addressed. It is shown that harmonicity plays a key role in the presence of hysteresis or quasiperiodic regime. Throughout the paper, experimental results on a real instrument are presented to illustrate various phenomena, and allow some qualitative comparisons with numerical results.
International Nuclear Information System (INIS)
Imhof, Armando Luis; Calvo, Carlos Adolfo; Moyano, Amalia; Sanchez, Manuel
2015-01-01
A determined curve path is followed by the propagation of seismic waves generated in emitters and detected in receivers by the principle of minimum time of Fermat. An ordinary differential equation is derived from the application of the calculation of variations. Due to the compaction of the terrain, the speed usually increases with depth. The experimental laws for each soil have led to this variation leading to a numerical resolution. The adjustment of experimental speed data by an exponential function; the analytical integration of the differential equation and the numerical determination of the integration constants are studied. A geophysical method such as up-hole or down-hole has determined the experimental data. Its main application is centered in the validation of numerical models of curved trajectories. Then time of first arrivals through tomographic algorithms for detection and modeling of anomalies in the first 12 m depth. (author) [es
An accurate solution of elastodynamic problems by numerical local Green's functions
Loureiro, F. S.; Silva, J. E. A.; Mansur, W. J.
2015-09-01
Green's function based methodologies for elastodynamics in both time and frequency domains, which can be either numerical or analytical, appear in many branches of physics and engineering. Thus, the development of exact expressions for Green's functions is of great importance. Unfortunately, such expressions are known only for relatively few kinds of geometry, medium and boundary conditions. In this way, due to the difficulty in finding exact Green's functions, specially in the time domain, the present paper presents a solution of the transient elastodynamic equations by a time-stepping technique based on the Explicit Green's Approach method written in terms of the Green's and Step response functions, both being computed numerically by the finite element method. The major feature is the computation of these functions separately by the central difference time integration scheme and locally owing to the principle of causality. More precisely, Green's functions are computed only at t = Δt adopting two time substeps while Step response functions are computed directly without substeps. The proposed time-stepping method shows to be quite accurate with distinct numerical properties not presented in the standard central difference scheme as addressed in the numerical example.
Evaluation of wave runup predictions from numerical and parametric models
Stockdon, Hilary F.; Thompson, David M.; Plant, Nathaniel G.; Long, Joseph W.
2014-01-01
Wave runup during storms is a primary driver of coastal evolution, including shoreline and dune erosion and barrier island overwash. Runup and its components, setup and swash, can be predicted from a parameterized model that was developed by comparing runup observations to offshore wave height, wave period, and local beach slope. Because observations during extreme storms are often unavailable, a numerical model is used to simulate the storm-driven runup to compare to the parameterized model and then develop an approach to improve the accuracy of the parameterization. Numerically simulated and parameterized runup were compared to observations to evaluate model accuracies. The analysis demonstrated that setup was accurately predicted by both the parameterized model and numerical simulations. Infragravity swash heights were most accurately predicted by the parameterized model. The numerical model suffered from bias and gain errors that depended on whether a one-dimensional or two-dimensional spatial domain was used. Nonetheless, all of the predictions were significantly correlated to the observations, implying that the systematic errors can be corrected. The numerical simulations did not resolve the incident-band swash motions, as expected, and the parameterized model performed best at predicting incident-band swash heights. An assimilated prediction using a weighted average of the parameterized model and the numerical simulations resulted in a reduction in prediction error variance. Finally, the numerical simulations were extended to include storm conditions that have not been previously observed. These results indicated that the parameterized predictions of setup may need modification for extreme conditions; numerical simulations can be used to extend the validity of the parameterized predictions of infragravity swash; and numerical simulations systematically underpredict incident swash, which is relatively unimportant under extreme conditions.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions. Copyright © 2017 Elsevier B.V. All rights reserved.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J.; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions.
Circulating fluidized bed boiler numerical modeling
Energy Technology Data Exchange (ETDEWEB)
Di Maggio, T. [Electricite de France, 75 - Paris (France). Direction des Etudes et Recherches; Bursi, J.M.; Lafanechere, L.; Jestin, L. [Electricite de France (EDF), 69 - Villeurbanne (France); Roulet, V. [E.D.F./DE/CNET, 92 - La Defense (France)
1996-12-31
Electricite de France (EdF) is actively involved in the development of CFB power plants. Thanks to a wide Research and Development program around the 125 MWe Emile Huchet and the 250 MWe Provence units (two boilers designed by Stein-Lurgi), EdF has been able to get a good knowledge of hydrodynamics and heat transfer in the circulating loop as well as the back pass. One of the main objectives of the R and D program was to gather this information and results in a steady state operating model of a CFB boiler and to simulate the operation of the 250 MWe Provence power plant. This model has been developed before the first ignition of the Provence power plant in order to check the design and to help on-field engineers during the start-up phase. Furthermore, this model allows R and D engineers to make parametric studies and to evaluate new designs. (authors) 5 refs.
International Nuclear Information System (INIS)
Aouled-Dlala, N.; Sghaier, T.; Seddiki, E.
2007-01-01
A new technique is presented to improve the performance of the discrete ordinates method when solving the coupled conduction-radiation problems in spherical and cylindrical media. In this approach the angular derivative term of the discretized one-dimensional radiative transfer equation is derived from an expansion of the radiative intensity on the basis of Chebyshev polynomials. The set of resulting differential equations, obtained by the application of the S N method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the Chebyshev transform method compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order S N calculations
Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method
Korkmaz, Bahar; Dereli, Yilmaz
2016-04-01
In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.
Henclik, Sławomir
2018-03-01
The influence of dynamic fluid-structure interaction (FSI) onto the course of water hammer (WH) can be significant in non-rigid pipeline systems. The essence of this effect is the dynamic transfer of liquid energy to the pipeline structure and back, which is important for elastic structures and can be negligible for rigid ones. In the paper a special model of such behavior is analyzed. A straight pipeline with a steady flow, fixed to the floor with several rigid supports is assumed. The transient is generated by a quickly closed valve installed at the end of the pipeline. FSI effects are assumed to be present mainly at the valve which is fixed with a spring dash-pot attachment. Analysis of WH runs, especially transient pressure changes, for various stiffness and damping parameters of the spring dash-pot valve attachment is presented in the paper. The solutions are found analytically and numerically. Numerical results have been computed with the use of an own computer program developed on the basis of the four equation model of WH-FSI and the specific boundary conditions formulated at the valve. Analytical solutions have been found with the separation of variables method for slightly simplified assumptions. Damping at the dash-pot is taken into account within the numerical study. The influence of valve attachment parameters onto the WH courses was discovered and it was found the transient amplitudes can be reduced. Such a system, elastically attached shut-off valve in a pipeline or other, equivalent design can be a real solution applicable in practice.
Numerical model updating technique for structures using firefly algorithm
Sai Kubair, K.; Mohan, S. C.
2018-03-01
Numerical model updating is a technique used for updating the existing experimental models for any structures related to civil, mechanical, automobiles, marine, aerospace engineering, etc. The basic concept behind this technique is updating the numerical models to closely match with experimental data obtained from real or prototype test structures. The present work involves the development of numerical model using MATLAB as a computational tool and with mathematical equations that define the experimental model. Firefly algorithm is used as an optimization tool in this study. In this updating process a response parameter of the structure has to be chosen, which helps to correlate the numerical model developed with the experimental results obtained. The variables for the updating can be either material or geometrical properties of the model or both. In this study, to verify the proposed technique, a cantilever beam is analyzed for its tip deflection and a space frame has been analyzed for its natural frequencies. Both the models are updated with their respective response values obtained from experimental results. The numerical results after updating show that there is a close relationship that can be brought between the experimental and the numerical models.
Numeričko modeliranje detonacije / Numerical modelling of detonation
Directory of Open Access Journals (Sweden)
Radun Jeremić
2002-03-01
Full Text Available Radi izračunavanja teorijskih vrednosti detonacionih parametara različitih eksplozivnih sastava izvršeno je numeričko modeliranje detonacije i sačinjen računarski program u programskom paketu PASCAL. Za opisivanje ponašanja produkata detonacije primenjena je BK.W jednačina stanja, a sistem jednačina hemijske ravnoteže rešavan je metodom minimizacije slobodne energije. Testiranje programskog rešenja izvršeno je za nekoliko eksplozivnih sastava različitih gustina, pri čemu je ostvarena dobra konvergencija rešenja i velika brzina rada. Dobijeno je dobro slaganje eksperimentalnih i teorijskih vrednosti pritisaka i brzina detonacije, čime je potvrđena ispravnost modela. / Numerical modeling of detonation of different explosive compositions has been carried out in order to calculate theoretical values of detonation parameters. A computer program in the PASCAL program package has been created. The BKW state equation has been applied to describe the behavior of detonation products and the equation system of chemical equilibrium has been solved by the method of free energy minimization. The program has been tested for several explosive compositions of various densities, operation speed being high and solution convergence good. The experimental and theoretical values of pressures and detonation velocities show good accordance, which confirms the model validity.
Modeling and numerical simulation of multi-component flow in porous media
International Nuclear Information System (INIS)
Saad, B.
2011-01-01
This work deals with the modelization and numerical simulation of two phase multi-component flow in porous media. The study is divided into two parts. First we study and prove the mathematical existence in a weak sense of two degenerate parabolic systems modeling two phase (liquid and gas) two component (water and hydrogen) flow in porous media. In the first model, we assume that there is a local thermodynamic equilibrium between both phases of hydrogen by using the Henry's law. The second model consists of a relaxation of the previous model: the kinetic of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is no longer instantaneous. The second part is devoted to the numerical analysis of those models. Firstly, we propose a numerical scheme to compare numerical solutions obtained with the first model and numerical solutions obtained with the second model where the characteristic time to recover the thermodynamic equilibrium goes to zero. Secondly, we present a finite volume scheme with a phase-by-phase upstream weighting scheme without simplified assumptions on the state law of gas densities. We also validate this scheme on a 2D test cases. (author)
Numerical Modeling of Rotary Kiln Productivity Increase
Romero-Valle, M.A.; Pisaroni, M.; Van Puyvelde, D.; Lahaye, D.J.P.; Sadi, R.
2013-01-01
Rotary kilns are used in many industrial processes ranging from cement manufacturing to waste incineration. The operating conditions vary widely depending on the process. While there are many models available within the literature and industry, the wide range of operating conditions justifies
Numerical modeling and simulation in various processes
Directory of Open Access Journals (Sweden)
Eliza Consuela ISBĂŞOIU
2011-12-01
The economic modeling offers the manager the rigorous side of his actions, multiple chances in order to connect existing resources with the objectives pursued for a certain period of time, offering the possibility of a better and faster thinking and deciding process, without deforming the reality.
Numerical Modeling of Foam Drilling Hydraulics
Directory of Open Access Journals (Sweden)
Ozcan Baris
2007-12-01
Full Text Available The use of foam as a drilling fluid was developed to meet a special set of conditions under which other common drilling fluids had failed. Foam drilling is defined as the process of making boreholes by utilizing foam as the circulating fluid. When compared with conventional drilling, underbalanced or foam drilling has several advantages. These advantages include: avoidance of lost circulation problems, minimizing damage to pay zones, higher penetration rates and bit life. Foams are usually characterized by the quality, the ratio of the volume of gas, and the total foam volume. Obtaining dependable pressure profiles for aerated (gasified fluids and foam is more difficult than for single phase fluids, since in the former ones the drilling mud contains a gas phase that is entrained within the fluid system. The primary goal of this study is to expand the knowledge-base of the hydrodynamic phenomena that occur in a foam drilling operation. In order to gain a better understanding of foam drilling operations, a hydrodynamic model is developed and run at different operating conditions. For this purpose, the flow of foam through the drilling system is modeled by invoking the basic principles of continuum mechanics and thermodynamics. The model was designed to allow gas and liquid flow at desired volumetric flow rates through the drillstring and annulus. Parametric studies are conducted in order to identify the most influential variables in the hydrodynamic modeling of foam flow.
Directory of Open Access Journals (Sweden)
Jana Sajgalikova
2015-01-01
Full Text Available Mathematical models for description of physical phenomena often use the statistical description of the individual phenomena and solve those using suitable methods. If we want to develop numerical model of optical communication system based on transmission through single mode optical fibres, we need to consider whole series of phenomena that affect various parts of the system. In the single-mode optical fibre we often encounter influence of chromatic dispersion and nonlinear Kerr effects. By observing various different degradation mechanisms, every numerical model should have its own limits, which fulfil more detailed specification. It is inevitable to consider them in evaluation. In this paper, we focus on numerical modelling of degradation mechanisms in single-mode optical fibre. Numerical solution of non-linear Schroedinger equation is performed by finite difference method applied in MATLAB environment and split-step Fourier method, which is implemented by VPIphotonics software.
Czech Academy of Sciences Publication Activity Database
Papež, Jan; Liesen, J.; Strakoš, Z.
2014-01-01
Roč. 449, 15 May (2014), s. 89-114 ISSN 0024-3795 R&D Projects: GA AV ČR IAA100300802; GA ČR GA201/09/0917 Grant - others:GA MŠk(CZ) LL1202; GA UK(CZ) 695612 Institutional support: RVO:67985807 Keywords : numerical solution of partial differential equations * finite element method * adaptivity * a posteriori error analysis * discretization error * algebra ic error * spatial distribution of the error Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014
Rosenbaum, J. S.
1971-01-01
Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.
Directory of Open Access Journals (Sweden)
Mohamed Ali
2017-10-01
Full Text Available This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. Bernoulli wavelets have been Created by dilation and translation of Bernoulli polynomials. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, and then we used it to transform the integral equations to the system of algebraic equations. We compared the result of the proposed method with the exact solution to show the convergence and advantages of the new method. The results got by present wavelet method are compared with that of by collocation method based on radial basis functions method. Finally, the numerical examples explain the accuracy of this method.
Numerical solution of the Schrodinger equation for stationary bound states using nodel theorem
International Nuclear Information System (INIS)
Chen Zhijiang; Kong Fanmei; Din Yibin
1987-01-01
An iterative procedure for getting the numerical solution of Schrodinger equation on stationary bound states is introduced. The theoretical foundtion, the practical steps and the method are presented. An example is added at the end. Comparing with other methods, the present one requires less storage, less running time but posesses higher accuracy. It can be run on the personal computer or microcomputer with 256 K memory and 16 bit word length such as IBM/PC, MC68000/83/20, PDP11/23 etc
The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory
International Nuclear Information System (INIS)
Woznicki, Z.I.
1994-01-01
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs
Human-computer interfaces applied to numerical solution of the Plateau problem
Elias Fabris, Antonio; Soares Bandeira, Ivana; Ramos Batista, Valério
2015-09-01
In this work we present a code in Matlab to solve the Problem of Plateau numerically, and the code will include human-computer interface. The Problem of Plateau has applications in areas of knowledge like, for instance, Computer Graphics. The solution method will be the same one of the Surface Evolver, but the difference will be a complete graphical interface with the user. This will enable us to implement other kinds of interface like ocular mouse, voice, touch, etc. To date, Evolver does not include any graphical interface, which restricts its use by the scientific community. Specially, its use is practically impossible for most of the Physically Challenged People.
The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory
International Nuclear Information System (INIS)
Woznicki, Z.I.
1995-01-01
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs
International Nuclear Information System (INIS)
Carver, M.B.
1995-08-01
The discussion briefly establishes some requisite concepts of differential equation theory, and applies these to describe methods for numerical solution of the thermalhydraulic conservation equations in their various forms. The intent is to cover the general methodology without obscuring the principles with details. As a short overview of computational thermalhydraulics, the material provides an introductory foundation, so that those working on the application of thermalhydraulic codes can begin to understand the many intricacies involved without having to locate and read the references given. Those intending to work in code development will need to read and understand all the references. (author). 49 refs
The quantum Rabi model: solution and dynamics
International Nuclear Information System (INIS)
Xie, Qiongtao; Zhong, Honghua; Lee, Chaohong; Batchelor, Murray T
2017-01-01
This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given. (topical review)
Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling
Energy Technology Data Exchange (ETDEWEB)
Gunzburger, Max [Florida State Univ., Tallahassee, FL (United States)
2015-02-17
We have treated the modeling, analysis, numerical analysis, and algorithmic development for nonlocal models of diffusion and mechanics. Variational formulations were developed and finite element methods were developed based on those formulations for both steady state and time dependent problems. Obstacle problems and optimization problems for the nonlocal models were also treated and connections made with fractional derivative models.
Analytical and numerical modeling for flexible pipes
Wang, Wei; Chen, Geng
2011-12-01
The unbonded flexible pipe of eight layers, in which all the layers except the carcass layer are assumed to have isotropic properties, has been analyzed. Specifically, the carcass layer shows the orthotropic characteristics. The effective elastic moduli of the carcass layer have been developed in terms of the influence of deformation to stiffness. With consideration of the effective elastic moduli, the structure can be properly analyzed. Also the relative movements of tendons and relative displacements of wires in helical armour layer have been investigated. A three-dimensional nonlinear finite element model has been presented to predict the response of flexible pipes under axial force and torque. Further, the friction and contact of interlayer have been considered. Comparison between the finite element model and experimental results obtained in literature has been given and discussed, which might provide practical and technical support for the application of unbonded flexible pipes.
Numerical modeling of a vaporizing multicomponent droplet
Megaridis, C. M.; Sirignano, W. A.
The fundamental processes governing the energy, mass, and momentum exchange between the liquid and gas phases of vaporizing, multicomponent liquid droplets have been investigated. The axisymmetric configuration under consideration consists of an isolated multicomponent droplet vaporizing in a convective environment. The model considers different volatilities of the liquid components, variable liquid properties due to variation of the species concentrations, and non-Fickian multicomponent gaseous diffusion. The bicomponent droplet model was employed to examine the commonly used assumptions of unity Lewis number in the liquid phase and Fickian gaseous diffusion. It is found that the droplet drag coefficients, the vaporization rates, and the related transfer numbers are not influenced by the above assumptions in a significant way.
A Numerical Solution for Hirota-Satsuma Coupled KdV Equation
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M. S. Ismail
2014-01-01
Full Text Available A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic B-splines as test functions and a linear B-spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.
Voytishek, Anton V.; Shipilov, Nikolay M.
2017-11-01
In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.
Mustafa, Meraj; Farooq, Muhammad A; Hayat, Tasawar; Alsaedi, Ahmed
2013-01-01
This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies.
Numerical solution of quadratic matrix equations for free vibration analysis of structures
Gupta, K. K.
1975-01-01
This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.
International Nuclear Information System (INIS)
Graf, U.
1986-01-01
A combination of several numerical methods is used to construct a procedure for effective calculation of complex three-dimensional fluid flow problems. The split coefficient matrix (SCM) method is used so that the differenced equations of the hyperbolic system do not disturb correct signal propagation. The semi-discretisation of the equations of the SCM method is done with the asymmetric, separated region, weighted residual (ASWR) method to give accurate solutions on a relatively coarse mesh. For the resulting system of ordinary differential equations, a general-purpose ordinary differential equation solver is used in conjunction with a method of fractional steps for an economic solution of the large system of linear equations. (orig.) [de
Fluid pumping: Some exploratory numerical models
Ord, A.; Henley, S.
The concept of fluid pumping evolved from considerations of fluid behaviour within and surrounding faults and shear zones, particularly associated with earthquake initiation and propagation. Further, the interpretation of specific vein textures as originating from a crack-seal mechanism requires precipitation of material during pumping cycles. We explore here a new simple model for fluid pumping initiating within a dilatant, pressure dependant material, and the mechanical consequences of such a model, including the predicted behaviour of a fluid within the SiO2-H2O system. Changes in various properties such as permeability and mechanical properties are allowed according to rules based on defined geological processes. For example, porosity may increase with increasing shear and dilatancy of the rock, and both porosity and permeability decrease when and where the rock ‘seals’ as a result of pressure decrease and the resultant precipitation of SiO2. Histories of any variable may be explored for any part of the model. We may therefore test in a quantitative manner hypotheses for fluid pumping, and the deposition of quartz, and ultimately gold, in a deforming rock mass. Through exploring the feedback links between deformation, fluid flow, chemical transport, thermal transfer, we have the opportunity to test conceptually and quantitatively the various hypotheses for the formation of world class ore deposits.
Sweilam, N. H.; Abou Hasan, M. M.
2017-05-01
In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.
Numerical simulation of a thermodynamically consistent four-species tumor growth model.
Hawkins-Daarud, Andrea; van der Zee, Kristoffer G; Oden, J Tinsley
2012-01-01
In this paper, we develop a thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this 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. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce. A time-stepping algorithm is then presented for this system, which is shown to be first order accurate and energy gradient stable. The results of an array of numerical experiments are presented, which demonstrate a wide range of solutions produced by various choices of model parameters.
International Nuclear Information System (INIS)
Boudjemadi, R.
1996-03-01
The main objectives of this thesis are the direct numerical simulation of natural convection in a vertical differentially heated slot and the improvements of second-order turbulence modelling. A three-dimensional direct numerical simulation code has been developed in order to gain a better understanding of turbulence properties in natural convection flows. This code has been validated in several physical configurations: non-stratified natural convection flows (conduction solution), stratified natural convection flows (double boundary layer solution), transitional and turbulent Poiseuille flows. For the conduction solution, the turbulent regime was reached at a Rayleigh number of 1*10 5 and 5.4*10 5 . A detailed analysis of these results has revealed the principal qualities of the available models but has also pointed our their shortcomings. This data base has been used in order to improve the triple correlations transport models and to select the turbulent time scales suitable for such flows. (author). 122 refs., figs., tabs., 4 appends
Mathematical and numerical foundations of turbulence models and applications
Chacón Rebollo, Tomás
2014-01-01
With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...
Numerical Models of Sewage Dispersion and Statistica Bathing Water Standards
DEFF Research Database (Denmark)
Petersen, Ole; Larsen, Torben
1991-01-01
As bathing water standards usually are founded in statistical methods, the numerical models used in outfall design should reflect this. A statistical approach, where stochastic variations in source strength and bacterial disappearance is incorporated into a numerical dilution model is presented. ....... It is demonstrated for a specific outfall how the method can be used to estimate the bathing water quality. The ambition with the paper has been to demonstrate how stochastic variations in a simple manner can be included in the analysis of water quality.......As bathing water standards usually are founded in statistical methods, the numerical models used in outfall design should reflect this. A statistical approach, where stochastic variations in source strength and bacterial disappearance is incorporated into a numerical dilution model is presented...
Numerical and physical model study of a vertical slot fishway
Directory of Open Access Journals (Sweden)
Bombač Martin
2014-06-01
Full Text Available This paper presents the results of an experimental and numerical study of a vertical slot fishway (VSF. A 2-D depth-averaged shallow water numerical model PCFLOW2D coupled with three different turbulent models (constant eddy viscosity, Smagorinsky and k - ε was used. A detailed analysis of numerical parameters needed for a correct simulation of the phenomenon was carried out. Besides the velocity field, attention was paid to important hydraulic parameters such as maximum velocity in the slot region and energy dissipation rate ε in order to evaluate the performance of VSF. A scaled physical hydraulic model was built to ensure reliable experimental data for the validation of the numerical model. Simulations of variant configurations of VSF showed that even small changes in geometry can produce more fishfriendly flow characteristics in pools. The present study indicates that the PCFLOW2D program is an appropriate tool to meet the main demands of the VSF design.
Summary of Numerical Modeling for Underground Nuclear Test Monitoring Symposium
International Nuclear Information System (INIS)
Taylor, S.R.; Kamm, J.R.
1993-01-01
This document contains the Proceedings of the Numerical Modeling for Underground Nuclear Test Monitoring Symposium held in Durango, Colorado on March 23-25, 1993. The symposium was sponsored by the Office of Arms Control and Nonproliferation of the United States Department of Energy and hosted by the Source Region Program of Los Alamos National Laboratory. The purpose of the meeting was to discuss state-of-the-art advances in numerical simulations of nuclear explosion phenomenology for the purpose of test ban monitoring. Another goal of the symposium was to promote discussion between seismologists and explosion source-code calculators. Presentation topics include the following: numerical model fits to data, measurement and characterization of material response models, applications of modeling to monitoring problems, explosion source phenomenology, numerical simulations and seismic sources
Numerical modeling of underground storage system for natural gas
Ding, J.; Wang, S.
2017-12-01
Natural gas is an important type of base-load energy, and its supply needs to be adjusted according to different demands in different seasons. For example, since natural gas is increasingly used to replace coal for winter heating, the demand for natural gas in winter is much higher than that in other seasons. As storage systems are the essential tools for balancing seasonal supply and demand, the design and simulation of natural gas storage systems form an important research direction. In this study, a large-scale underground storage system for natural gas is simulated based on theoretical analysis and finite element modeling.It is proven that the problem of axi-symmetric Darcy porous flow of ideal gas is governed by the Boussinesq equation. In terms of the exact solution to the Boussinesq equation, the basic operating characteristics of the underground storage system is analyzed, and it is demonstrated that the propagation distance of the pore pressure is proportional to the 1/4 power of the mass flow rate and to the 1/2 power of the propagation time. This quantitative relationship can be used to guide the overall design of natural gas underground storage systems.In order to fully capture the two-way coupling between pore pressure and elastic matrix deformation, a poro-elastic finite element model for natural gas storage is developed. Based on the numerical model, the dynamic processes of gas injection, storage and extraction are simulated, and the corresponding time-dependent surface deformations are obtained. The modeling results not only provide a theoretical basis for real-time monitoring for the operating status of the underground storage system through surface deformation measurements, but also demonstrate that a year-round balance can be achieved through periodic gas injection and extraction.This work is supported by the CAS "100 talents" Program and the National Natural Science Foundation of China (41371090).
Preliminary 2D numerical modeling of common granular problems
Wyser, Emmanuel; Jaboyedoff, Michel
2017-04-01
Granular studies received an increasing interest during the last decade. Many scientific investigations were successfully addressed to acknowledge the ubiquitous behavior of granular matter. We investigate liquid impacts onto granular beds, i.e. the influence of the packing and compaction-dilation transition. However, a physically-based model is still lacking to address complex microscopic features of granular bed response during liquid impacts such as compaction-dilation transition or granular bed uplifts (Wyser et al. in review). We present our preliminary 2D numerical modeling based on the Discrete Element Method (DEM) using nonlinear contact force law (the Hertz-Mindlin model) for disk shape particles. The algorithm is written in C programming language. Our 2D model provides an analytical tool to address granular problems such as i) granular collapses and ii) static granular assembliy problems. This provides a validation framework of our numerical approach by comparing our numerical results with previous laboratory experiments or numerical works. Inspired by the work of Warnett et al. (2014) and Staron & Hinch (2005), we studied i) the axisymetric collapse of granular columns. We addressed the scaling between the initial aspect ratio and the final runout distance. Our numerical results are in good aggreement with the previous studies of Warnett et al. (2014) and Staron & Hinch (2005). ii) Reproducing static problems for regular and randomly stacked particles provides a valid comparison to results of Egholm (2007). Vertical and horizontal stresses within the assembly are quite identical to stresses obtained by Egholm (2007), thus demonstating the consistency of our 2D numerical model. Our 2D numerical model is able to reproduce common granular case studies such as granular collapses or static problems. However, a sufficient small timestep should be used to ensure a good numerical consistency, resulting in higher computational time. The latter becomes critical
Numerical Solution of Mixed Problems of the Theory of Elasticity with One-Sided Constraints
Directory of Open Access Journals (Sweden)
I. V. Stankevich
2017-01-01
Full Text Available The paper deals with the application features of the finite element technologies to solve the problems of elasticity with one-sided constraints. On the one hand, the area of this study is determined by the fact that many critical parts and assemblies of mechanical and power engineering constructions have a significant contact within some given surface. To assess the strength and the life of these parts and assemblies, reliable stress-strain state data are demandable. Data on the stress-strain state can be obtained using the contemporary mathematical modeling means, e.g., finite element technology.To solve the problems of the theory of elasticity with one-sided constraints, a method of finite elements in a traditional classical form can be used, but it is necessary to consider some of its shortcomings. The most significant one is an approximation of the tensile stress and strain, as well as a considerably lower order of convergence of the approximation for stresses and strains as compared to displacements. Improving the accuracy through increasing a density of the finite element models and/or the transition to more complex approximations is not always optimal, because increasing a dimension of the discrete problem leads to a significant computational cost and demand for expensive computing resources.One of the alternatives in numerical analysis of contact problems of the elasticity theory is to use the mixed variational formulations of the finite element method in which stresses and/or strains appear in the resolving equations along with displacements as equal unknown. A major positive factor when using the mixed formulations of the finite element method is reduction of the approximation error of stress and strain, which leads to a more accurate assessment of the stress-strain state in comparison with the classical approach of the finite element method in the form of the method of displacements.Besides, mixed schemes of the finite element method
The Turbulent Interstellar Medium: Insights and Questions from Numerical Models
Mac Low, Mordecai-Mark; de Avillez, Miguel A.; Korpi, Maarit J.
2003-01-01
"The purpose of numerical models is not numbers but insight." (Hamming) In the spirit of this adage, and of Don Cox's approach to scientific speaking, we discuss the questions that the latest generation of numerical models of the interstellar medium raise, at least for us. The energy source for the interstellar turbulence is still under discussion. We review the argument for supernovae dominating in star forming regions. Magnetorotational instability has been suggested as a way of coupling di...
Numerical modeling in photonic crystals integrated technology: the COPERNICUS Project
DEFF Research Database (Denmark)
Malaguti, Stefania; Armaroli, Andrea; Bellanca, Gaetano
2011-01-01
Photonic crystals will play a fundamental role in the future of optical communications. The relevance of the numerical modeling for the success of this technology is assessed by using some examples concerning the experience of the COPERNICUS Project.......Photonic crystals will play a fundamental role in the future of optical communications. The relevance of the numerical modeling for the success of this technology is assessed by using some examples concerning the experience of the COPERNICUS Project....
Carmona, A.; Pérez-Segarra, C. D.; Lehmkuhl, O.; Oliva, A.
2012-11-01
The aim of this work is to provide numerical solutions for the fluid flow and the heat transfer generated in closed systems containing viscoplastic-type non-Newtonian fluids. A lid driven cavity (LDC) and a differentially heated cavity (DHC) are used as test cases. These numerical solutions can be an appropriate tool for verifying CFD codes which have been developed or adapted to deal with this kind of non-Newtonian fluids. In order to achieve this objective, an in-house CFD code has been implemented and correctly verified by the method of manufactured solutions and by some numerical solutions too. Furthermore, a high-performance CFD code (Termo Fluids S.L.) has been adapted and properly verified, by the corresponding numerical solutions, to deal with this kind of non-Newtonian fluids. The viscoplastic behaviour of certain non-Newtonian fluids will be generated from a viscous stress which has been defined by a potential-type rheological law. The pseudoplastic and dilatant behaviours will be studied. On this matter, the influence of different physical aspects on the numerical simulations will be analysed, e.g. different exponent values in the potential-type rheological law and different values of the non-dimensional numbers. Moreover, the influence of different numerical aspects on the numerical simulations will also be analysed, e.g. unstructured meshes, conservative numerical schemes and more efficient and parallel algorithms and solvers.
Applied Integer Programming Modeling and Solution
Chen, Der-San; Dang, Yu
2011-01-01
An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and
A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation
Directory of Open Access Journals (Sweden)
Rongwu Lu
2017-01-01
Full Text Available Considering the popular use of a certain kind of supervision management problem in many fields, we firstly build an ordinary supervision game model of multiple stakeholders. Secondly, a fractional supervision game model is set up and solved based on the theory of fractional calculus and a predictor-corrector numerical approach. Thirdly, the methods of phase diagram and time series graph were applied to simulate and analyse the dynamic process of the fractional order game model. Results of numerical solutions are given to illustrate our conclusions and referred to the practice.
Numerical approaches to expansion process modeling
Directory of Open Access Journals (Sweden)
G. V. Alekseev
2017-01-01
Full Text Available Forage production is currently undergoing a period of intensive renovation and introduction of the most advanced technologies and equipment. More and more often such methods as barley toasting, grain extrusion, steaming and grain flattening, boiling bed explosion, infrared ray treatment of cereals and legumes, followed by flattening, and one-time or two-time granulation of the purified whole grain without humidification in matrix presses By grinding the granules. These methods require special apparatuses, machines, auxiliary equipment, created on the basis of different methods of compiled mathematical models. When roasting, simulating the heat fields arising in the working chamber, provide such conditions, the decomposition of a portion of the starch to monosaccharides, which makes the grain sweetish, but due to protein denaturation the digestibility of the protein and the availability of amino acids decrease somewhat. Grain is roasted mainly for young animals in order to teach them to eat food at an early age, stimulate the secretory activity of digestion, better development of the masticatory muscles. In addition, the high temperature is detrimental to bacterial contamination and various types of fungi, which largely avoids possible diseases of the gastrointestinal tract. This method has found wide application directly on the farms. Apply when used in feeding animals and legumes: peas, soy, lupine and lentils. These feeds are preliminarily ground, and then cooked or steamed for 1 hour for 30–40 minutes. In the feed mill. Such processing of feeds allows inactivating the anti-nutrients in them, which reduce the effectiveness of their use. After processing, legumes are used as protein supplements in an amount of 25–30% of the total nutritional value of the diet. But it is recommended to cook and steal a grain of good quality. A poor-quality grain that has been stored for a long time and damaged by pathogenic micro flora is subject to
Medl'a, Matej; Mikula, Karol; Čunderlík, Róbert; Macák, Marek
2018-01-01
The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth's topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth's surface. It is based on an evolution of a surface, which approximates the Earth's topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth's surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth's topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.
Numerical bifurcation analysis of delay differential equations arising from physiological modeling.
Engelborghs, K; Lemaire, V; Bélair, J; Roose, D
2001-04-01
This paper has a dual purpose. First, we describe numerical methods for continuation and bifurcation analysis of steady state solutions and periodic solutions of systems of delay differential equations with an arbitrary number of fixed, discrete delays. Second, we demonstrate how these methods can be used to obtain insight into complex biological regulatory systems in which interactions occur with time delays: for this, we consider a system of two equations for the plasma glucose and insulin concentrations in a diabetic patient subject to a system of external assistance. The model has two delays: the technological delay of the external system, and the physiological delay of the patient's liver. We compute stability of the steady state solution as a function of two parameters, compare with analytical results and compute several branches of periodic solutions and their stability. These numerical results allow to infer two categories of diabetic patients for which the external system has different efficiency.
Numerical model for learning concepts of streamflow simulation
DeLong, L.L.; ,
1993-01-01
Numerical models are useful for demonstrating principles of open-channel flow. Such models can allow experimentation with cause-and-effect relations, testing concepts of physics and numerical techniques. Four PT is a numerical model written primarily as a teaching supplement for a course in one-dimensional stream-flow modeling. Four PT options particularly useful in training include selection of governing equations, boundary-value perturbation, and user-programmable constraint equations. The model can simulate non-trivial concepts such as flow in complex interconnected channel networks, meandering channels with variable effective flow lengths, hydraulic structures defined by unique three-parameter relations, and density-driven flow.The model is coded in FORTRAN 77, and data encapsulation is used extensively to simplify maintenance and modification and to enhance the use of Four PT modules by other programs and programmers.
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and