Transient productivity index for numerical well test simulations

Energy Technology Data Exchange (ETDEWEB)

Blanc, G.; Ding, D.Y.; Ene, A. [Institut Francais du Petrole, Pau (France)] [and others

1997-08-01

The most difficult aspect of numerical simulation of well tests is the treatment of the Bottom Hole Flowing (BHF) Pressure. In full field simulations, this pressure is derived from the Well-block Pressure (WBP) using a numerical productivity index which accounts for the grid size and permeability, and for the well completion. This productivity index is calculated assuming a pseudo-steady state flow regime in the vicinity of the well and is therefore constant during the well production period. Such a pseudo-steady state assumption is no longer valid for the early time of a well test simulation as long as the pressure perturbation has not reached several grid-blocks around the well. This paper offers two different solutions to this problem: (1) The first one is based on the derivation of a Numerical Transient Productivity Index (NTPI) to be applied to Cartesian grids; (2) The second one is based on the use of a Corrected Transmissibility and Accumulation Term (CTAT) in the flow equation. The representation of the pressure behavior given by both solutions is far more accurate than the conventional one as shown by several validation examples which are presented in the following pages.

Practical considerations in developing numerical simulators for thermal recovery

Energy Technology Data Exchange (ETDEWEB)

Abou-Kassem, J.H. [Chemical and Petroleum Engineering Department, UAE University, Al-Ain (United Arab Emirates)

1996-08-15

Numerical simulation of steam injection and in-situ combustion-based oil recovery processes is of great importance in project design. Development of such numerical simulators is an on-going process, with improvements made as the process description becomes more complete, and also as better methods are devised to resolve certain numerical difficulties. This paper addresses some of the latter, and based on the author`s experience gives useful guidelines for developing more efficient numerical simulators of steam injection and in-situ combustion. The paper takes up a series of questions related to simulating thermal processes. Included are: the elimination of constraint equations at the matrix level, phase change, steam injection rate, alternative treatments of heat loss, relative permeabilities and importance of hysteresis effects, improved solutions to the grid orientation problem and other simulation problems such as potential inversion, grid block size, time-step size control and induced fractures. The points discussed in the paper should be of use to both simulator developers and users alike, and will lead to a better understanding of simulation results

Applications of Operator-Splitting Methods to the Direct Numerical Simulation of Particulate and Free-Surface Flows and to the Numerical Solution of the Two-Dimensional Elliptic Monge--Ampère Equation

OpenAIRE

Glowinski, R.; Dean, E.J.; Guidoboni, G.; Juárez, L.H.; Pan, T.-W.

2008-01-01

The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various areas in Mechanics, Physics and Differential Geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and the elliptic real Monge--Ampère equation. The results of numerical ...

Numerical simulation of fire vortex

Science.gov (United States)

Barannikova, D. D.; Borzykh, V. E.; Obukhov, A. G.

2018-05-01

The article considers the numerical simulation of the swirling flow of air around the smoothly heated vertical cylindrical domain in the conditions of gravity and Coriolis forces action. The solutions of the complete system of Navie-Stocks equations are numerically solved at constant viscosity and heat conductivity factors. Along with the proposed initial and boundary conditions, these solutions describe the complex non-stationary 3D flows of viscous compressible heat conducting gas. For various instants of time of the initial flow formation stage using the explicit finite-difference scheme the calculations of all gas dynamics parameters, that is density, temperature, pressure and three velocity components of gas particles, have been run. The current instant lines corresponding to the trajectories of the particles movement in the emerging flow have been constructed. A negative direction of the air flow swirling occurred in the vertical cylindrical domain heating has been defined.

Numerical Asymptotic Solutions Of Differential Equations

Science.gov (United States)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Fluid dynamics theory, computation, and numerical simulation

CERN Document Server

Pozrikidis, C

2001-01-01

Fluid Dynamics Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes Two distinguishing features of the discourse are solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty Matlab codes are presented and discussed for a broad...

On the numerical simulation of tracer flows in porous media

International Nuclear Information System (INIS)

Aquino, J.; Pereira, F.; Amaral Souto, H.P.; Francisco, A.S.

2007-01-01

We discuss in detail a new Lagrangian, locally conservative procedure which has been proposed for the numerical solution of linear transport problems in porous media. The new scheme is computationally efficient, virtually free of numerical diffusion, and can be applied to investigate numerically the time evolution of radionuclide contaminant plumes. Results of two-dimensional simulations of tracer flows will be presented to show the influence on the computed solutions of distinct interpolation functions for evaluating the velocity field at any position of the physical domain, as required by the Lagrangian scheme. (author)

Numerical Simulation of a Seaway with Breaking

Science.gov (United States)

Dommermuth, Douglas; O'Shea, Thomas; Brucker, Kyle; Wyatt, Donald

2012-11-01

The focus of this presentation is to describe the recent efforts to simulate a fully non-linear seaway with breaking by using a high-order spectral (HOS) solution of the free-surface boundary value problem to drive a three-dimensional Volume of Fluid (VOF) solution. Historically, the two main types of simulations to simulate free-surface flows are the boundary integral equations method (BIEM) and high-order spectral (HOS) methods. BIEM calculations fail at the point at which the surface impacts upon itself, if not sooner, and HOS methods can only simulate a single valued free-surface. Both also employ a single-phase approximation in which the effects of the air on the water are neglected. Due to these limitations they are unable to simulate breaking waves and air entrainment. The Volume of Fluid (VOF) method on the other hand is suitable for modeling breaking waves and air entrainment. However it is computationally intractable to generate a realistic non-linear sea-state. Here, we use the HOS solution to quickly drive, or nudge, the VOF solution into a non-linear state. The computational strategies, mathematical formulation, and numerical implementation will be discussed. The results of the VOF simulation of a seaway with breaking will also be presented, and compared to the single phase, single valued HOS results.

Numerical simulation of the drying of inkjet-printed droplets

NARCIS (Netherlands)

Siregar, D.P.; Kuerten, J.G.M.; Geld, van der C.W.M.

2013-01-01

In this paper we study the behavior of an inkjet-printed droplet of a solute dissolved in a solvent on a solid horizontal surface by numerical simulation. An extended model for drying of a droplet and the final distribution of the solute on an impermeable substrate is proposed. The model extends the

Direct Numerical Simulations of turbulent flow in a driven cavity

NARCIS (Netherlands)

Verstappen, R.; Wissink, J.G.; Cazemier, W.; Veldman, A.E.P.

Direct numerical simulations (DNS) of 2 and 3D turbulent flows in a lid-driven cavity have been performed. DNS are numerical solutions of the unsteady (here: incompressible) Navier-Stokes equations that compute the evolution of all dynamically significant scales of motion. In view of the large

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)

Solution of AntiSeepage for Mengxi River Based on Numerical Simulation of Unsaturated Seepage

Science.gov (United States)

Ji, Youjun; Zhang, Linzhi; Yue, Jiannan

2014-01-01

Lessening the leakage of surface water can reduce the waste of water resources and ground water pollution. To solve the problem that Mengxi River could not store water enduringly, geology investigation, theoretical analysis, experiment research, and numerical simulation analysis were carried out. Firstly, the seepage mathematical model was established based on unsaturated seepage theory; secondly, the experimental equipment for testing hydraulic conductivity of unsaturated soil was developed to obtain the curve of two-phase flow. The numerical simulation of leakage in natural conditions proves the previous inference and leakage mechanism of river. At last, the seepage control capacities of different impervious materials were compared by numerical simulations. According to the engineering actuality, the impervious material was selected. The impervious measure in this paper has been proved to be effectible by hydrogeological research today. PMID:24707199

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Directory of Open Access Journals (Sweden)

Aydin Secer

2013-01-01

Full Text Available An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

Combining Narrative and Numerical Simulation

DEFF Research Database (Denmark)

Hansen, Mette Sanne; Ladeby, Klaes Rohde; Rasmussen, Lauge Baungaard

2011-01-01

for decision makers to systematically test several different outputs of possible solutions in order to prepare for future consequences. The CSA can be a way to evaluate risks and address possible unforeseen problems in a more methodical way than either guessing or forecasting. This paper contributes...... to the decision making in operations and production management by providing new insights into modelling and simulation based on the combined narrative and numerical simulation approach as a tool for strategy making. The research question asks, “How can the CSA be applied in a practical context to support strategy...... making?” The paper uses a case study where interviews and observations were carried out in a Danish corporation. The CSA is a new way to address decision making and has both practical value and further expands the use of strategic simulation as a management tool....

Solution of AntiSeepage for Mengxi River Based on Numerical Simulation of Unsaturated Seepage

Directory of Open Access Journals (Sweden)

Youjun Ji

2014-01-01

Full Text Available Lessening the leakage of surface water can reduce the waste of water resources and ground water pollution. To solve the problem that Mengxi River could not store water enduringly, geology investigation, theoretical analysis, experiment research, and numerical simulation analysis were carried out. Firstly, the seepage mathematical model was established based on unsaturated seepage theory; secondly, the experimental equipment for testing hydraulic conductivity of unsaturated soil was developed to obtain the curve of two-phase flow. The numerical simulation of leakage in natural conditions proves the previous inference and leakage mechanism of river. At last, the seepage control capacities of different impervious materials were compared by numerical simulations. According to the engineering actuality, the impervious material was selected. The impervious measure in this paper has been proved to be effectible by hydrogeological research today.

Comparison of different soil water extraction systems for the prognoses of solute transport at the field scale using numerical simulations, field and lysimeter experiments

Energy Technology Data Exchange (ETDEWEB)

Weihermueller, L

2005-07-01

To date, the understanding of processes, factors, and interactions that influence the amount of extracted water and the solute composition sampled with suction cups is limited. But this information is required for process description of solute transport in natural soils. Improved system understanding can lead to a low cost and easy to install water sampling system which can help to predict solute transport in natural soils for the benefit of environmental protection. The main objectives of this work were to perform numerical simulations with different boundary conditions and to implement the findings in the interpretation of the lysimeter and field experiments. In a first part of this thesis, theoretical considerations on the processes affecting the spatial influence of a suction cup in soil and changes in solute transport initiated by the suction cups are presented, including testing and validation of available model and experimental approaches. In the second part, a detailed experimental study was conducted to obtain data for the comparison of the different soil water sampling systems. Finally, the numerical experiments of the suction cup influence were used for the interpretation of the experimental data. The main goals are summarized as follows: - Characterization of the suction cup activity domain (SCAD), suction cup extraction domain (SCED) and suction cup sampling area (SCSA) of active suction cups (definitions are given in Chapter 6). - Determination of the boundary conditions and soil properties [e.g. infiltration, applied suction, duration of water extraction, soil hydraulic properties and soil heterogeneity] affecting the activity domain, extraction domain and sampling area of a suction cup. - Identification of processes that change the travel time and travel time variance of solutes extracted by suction cups. - Validation of the numerically derived data with analytical and experimental data from literature. - Comparison of the experimental data obtained

Recent developments in numerical simulation techniques of thermal recovery processes

Energy Technology Data Exchange (ETDEWEB)

Tamim, M. [Bangladesh University of Engineering and Technology, Bangladesh (Bangladesh); Abou-Kassem, J.H. [Chemical and Petroleum Engineering Department, UAE University, Al-Ain 17555 (United Arab Emirates); Farouq Ali, S.M. [University of Alberta, Alberta (Canada)

2000-05-01

Numerical simulation of thermal processes (steam flooding, steam stimulation, SAGD, in-situ combustion, electrical heating, etc.) is an integral part of a thermal project design. The general tendency in the last 10 years has been to use commercial simulators. During the last decade, only a few new models have been reported in the literature. More work has been done to modify and refine solutions to existing problems to improve the efficiency of simulators. The paper discusses some of the recent developments in simulation techniques of thermal processes such as grid refinement, grid orientation, effect of temperature on relative permeability, mathematical models, and solution methods. The various aspects of simulation discussed here promote better understanding of the problems encountered in the simulation of thermal processes and will be of value to both simulator users and developers.

Numerical Modeling for the Solute Uptake from Groundwater by Plants-Plant Uptake Package

OpenAIRE

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...

Numerical simulation of heterogeneous phase transformations

International Nuclear Information System (INIS)

Combeau, H.; Lacaze, J.

1993-01-01

A numerical model is presented for the simulation of diffusion controlled phase transformations in multicomponent alloys. A closed system is considered, with simple geometric shape, either planar, cylindrical or spherical. The temperature inside this microscopic volume is homogeneous, but can vary according to any specified monoteneous law. Particular care has been given to the description of the solute profiles where the concentration gradients are the steepest, i.e. near the interface between the parent and the resultant phases. Solute redistribution at the interface is described by means of an original method which ensures that the overall solute balance is satisfied. A non linear system is obtained which includes the diffusion equations in both phases and the boundary conditions. The solution of this system makes use of a special algorithm which has been devised for a quick convergence. An example is presented which deals with microsegregation build-up during solidification of a multi-component nickel base alloy. (orig.)

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 simulation of water quality in Yangtze Estuary

Directory of Open Access Journals (Sweden)

Xi Li

2009-12-01

Full Text Available In order to monitor water quality in the Yangtze Estuary, water samples were collected and field observation of current and velocity stratification was carried out using a shipboard acoustic Doppler current profiler (ADCP. Results of two representative variables, the temporal and spatial variation of new point source sewage discharge as manifested by chemical oxygen demand (COD and the initial water quality distribution as manifested by dissolved oxygen (DO, were obtained by application of the Environmental Fluid Dynamics Code (EFDC with solutions for hydrodynamics during tides. The numerical results were compared with field data, and the field data provided verification of numerical application: this numerical model is an effective tool for water quality simulation. For point source discharge, COD concentration was simulated with an initial value in the river of zero. The simulated increments and distribution of COD in the water show acceptable agreement with field data. The concentration of DO is much higher in the North Branch than in the South Branch due to consumption of oxygen in the South Branch resulting from discharge of sewage from Shanghai. The DO concentration is greater in the surface layer than in the bottom layer. The DO concentration is low in areas with a depth of less than 20 m, and high in areas between the 20-m and 30-m isobaths. It is concluded that the numerical model is valuable in simulation of water quality in the case of specific point source pollutant discharge. The EFDC model is also of satisfactory accuracy in water quality simulation of the Yangtze Estuary.

A third-order KdV solution for internal solitary waves and its application in the numerical wave tank

Directory of Open Access Journals (Sweden)

Qicheng Meng

2016-04-01

Full Text Available A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system. The solution corrects an error by Mirie and Su (1984. A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam. Various analytical solutions, including the first-order to third-order KdV solutions, the eKdV solution and the MCC solution, have been used to initialise the flow fields in the CFD simulations of internal solitary waves. Two groups including 11 numerical cases have been carried out. In the same group, the initial wave amplitudes are the same but the implemented analytical solutions are different. The simulated wave profiles at different moments have been presented. The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively. It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases. The finding is significant for the further simulations involving internal solitary waves.

Efficient Numerical Simulation of Aerothermoelastic Hypersonic Vehicles

Science.gov (United States)

Klock, Ryan J.

Hypersonic vehicles operate in a high-energy flight environment characterized by high dynamic pressures, high thermal loads, and non-equilibrium flow dynamics. This environment induces strong fluid, thermal, and structural dynamics interactions that are unique to this flight regime. If these vehicles are to be effectively designed and controlled, then a robust and intuitive understanding of each of these disciplines must be developed not only in isolation, but also when coupled. Limitations on scaling and the availability of adequate test facilities mean that physical investigation is infeasible. Ever growing computational power offers the ability to perform elaborate numerical simulations, but also has its own limitations. The state of the art in numerical simulation is either to create ever more high-fidelity physics models that do not couple well and require too much processing power to consider more than a few seconds of flight, or to use low-fidelity analytical models that can be tightly coupled and processed quickly, but do not represent realistic systems due to their simplifying assumptions. Reduced-order models offer a middle ground by distilling the dominant trends of high-fidelity training solutions into a form that can be quickly processed and more tightly coupled. This thesis presents a variably coupled, variable-fidelity, aerothermoelastic framework for the simulation and analysis of high-speed vehicle systems using analytical, reduced-order, and surrogate modeling techniques. Full launch-to-landing flights of complete vehicles are considered and used to define flight envelopes with aeroelastic, aerothermal, and thermoelastic limits, tune in-the-loop flight controllers, and inform future design considerations. A partitioned approach to vehicle simulation is considered in which regions dominated by particular combinations of processes are made separate from the overall solution and simulated by a specialized set of models to improve overall processing

Numerical simulation on coolant flow and heat transfer in core

International Nuclear Information System (INIS)

Yao Zhaohui; Wang Xuefang; Shen Mengyu

1997-01-01

To simulate the coolant flow and the heat transfer characteristics of a core, a computer code, THAPMA (Thermal Hydraulic Analysis Porous Medium Analysis) has been developed. In THAPMA code, conservation equations are based on a porous-medium formulation, which uses four parameters, i.e, volume porosity, directional surface porosity, distributed resistance, and distributed heat source (sink), to model the effects of fuel rods and other internal solid structures on flow and heat transfer. Because the scheme and the solution are very important in accuracy and speed of calculation, a new difference scheme (WSUC) has been used in the energy equation, and a modified PISO solution method have been employed to simulate the steady/transient states. The code has been proved reliable and can effectively solve the transient state problem by several numerical tests. According to the design of Qinshan NPP-II, the flow and heat transfer phenomena in reactor core have been numerically simulated. The distributions of the velocity and the temperature can provide a theoretical basis for core design and safety analysis

Numerical simulation of inertial two-phase flow in heterogenous media

International Nuclear Information System (INIS)

Ali Akbar ABBASIAN ARANI; Didier LASSEUX; Azita AHMADI

2005-01-01

In this work, we present the development of a 3 D numerical tool for simulation of non-Darcy two-phase flow in heterogeneous porous media. The physical model selected is the generalized Darcy-Forchheimer model. A validation is performed first by comparing numerical results with a semi-analytical solution of the Buckley-Leverett type. Secondly, numerical results obtained on 1 D and 2 D heterogeneous configurations are presented and we highlight the importance of the inertial terms according to a Reynolds number of the flow. (authors)

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)

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

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)

Numerical simulations of comets - predictions for Comet Giacobini-Zinner

International Nuclear Information System (INIS)

Fedder, J.A.; Lyon, J.G.; Giuliani, J.L. Jr.

1986-01-01

Simulations of Comet Giacobini-Zinner's interaction with solar wind are described and results are presented. The simulations are carried out via the numerical solution of the ideal MHD equations as an initial value problem in a uniform solar wind. The calculations are performed on a Cartesian mesh centered at the comet. Results reveal that the first significant modifications of the solar wind along the ISEE/ICE trajectory will occur 100,000 km from the solar wind comet axis. 6 references

Numerical simulation of steady cavitating flow of viscous fluid in a Francis hydroturbine

Science.gov (United States)

Panov, L. V.; Chirkov, D. V.; Cherny, S. G.; Pylev, I. M.; Sotnikov, A. A.

2012-09-01

Numerical technique was developed for simulation of cavitating flows through the flow passage of a hydraulic turbine. The technique is based on solution of steady 3D Navier—Stokes equations with a liquid phase transfer equation. The approch for setting boundary conditions meeting the requirements of cavitation testing standard was suggested. Four different models of evaporation and condensation were compared. Numerical simulations for turbines of different specific speed were compared with experiment.

Direct Numerical Simulation and Visualization of Subcooled Pool Boiling

Directory of Open Access Journals (Sweden)

Tomoaki Kunugi

2014-01-01

Full Text Available A direct numerical simulation of the boiling phenomena is one of the promising approaches in order to clarify their heat transfer characteristics and discuss the mechanism. During these decades, many DNS procedures have been developed according to the recent high performance computers and computational technologies. In this paper, the state of the art of direct numerical simulation of the pool boiling phenomena during mostly two decades is briefly summarized at first, and then the nonempirical boiling and condensation model proposed by the authors is introduced into the MARS (MultiInterface Advection and Reconstruction Solver developed by the authors. On the other hand, in order to clarify the boiling bubble behaviors under the subcooled conditions, the subcooled pool boiling experiments are also performed by using a high speed and high spatial resolution camera with a highly magnified telescope. Resulting from the numerical simulations of the subcooled pool boiling phenomena, the numerical results obtained by the MARS are validated by being compared to the experimental ones and the existing analytical solutions. The numerical results regarding the time evolution of the boiling bubble departure process under the subcooled conditions show a very good agreement with the experimental results. In conclusion, it can be said that the proposed nonempirical boiling and condensation model combined with the MARS has been validated.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

Science.gov (United States)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

3D numerical simulation of transient processes in hydraulic turbines

International Nuclear Information System (INIS)

Cherny, S; Chirkov, D; Lapin, V; Eshkunova, I; Bannikov, D; Avdushenko, A; Skorospelov, V

2010-01-01

An approach for numerical simulation of 3D hydraulic turbine flows in transient operating regimes is presented. The method is based on a coupled solution of incompressible RANS equations, runner rotation equation, and water hammer equations. The issue of setting appropriate boundary conditions is considered in detail. As an illustration, the simulation results for runaway process are presented. The evolution of vortex structure and its effect on computed runaway traces are analyzed.

3D numerical simulation of transient processes in hydraulic turbines

Science.gov (United States)

Cherny, S.; Chirkov, D.; Bannikov, D.; Lapin, V.; Skorospelov, V.; Eshkunova, I.; Avdushenko, A.

2010-08-01

An approach for numerical simulation of 3D hydraulic turbine flows in transient operating regimes is presented. The method is based on a coupled solution of incompressible RANS equations, runner rotation equation, and water hammer equations. The issue of setting appropriate boundary conditions is considered in detail. As an illustration, the simulation results for runaway process are presented. The evolution of vortex structure and its effect on computed runaway traces are analyzed.

Numerical solution of the full potential equation using a chimera grid approach

Science.gov (United States)

Holst, Terry L.

1995-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

The Application of Visual Basic Computer Programming Language to Simulate Numerical Iterations

Directory of Open Access Journals (Sweden)

Abdulkadir Baba HASSAN

2006-06-01

Full Text Available This paper examines the application of Visual Basic Computer Programming Language to Simulate Numerical Iterations, the merit of Visual Basic as a Programming Language and the difficulties faced when solving numerical iterations analytically, this research paper encourage the uses of Computer Programming methods for the execution of numerical iterations and finally fashion out and develop a reliable solution using Visual Basic package to write a program for some selected iteration problems.

Development of solute transport models in YMPYRÄ framework to simulate solute migration in military shooting and training areas

Science.gov (United States)

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

The numerical solution of ICRF fields in axisymmetric mirrors

International Nuclear Information System (INIS)

Phillips, M.W.; Todd, A.M.M.

1986-01-01

The numerics of a numerical code called GARFIELD (Grumman Aerospace RF fIELD code) designed to calculate the three-dimensional structure of ICRF fields in axisymmetric mirrors is presented. The code solves the electromagnetic wave equation for the electric field using a cold plasma dispersion relation with a small collision term to simulate absorption. The full wave solution including E.B is computed. The fields are Fourier analyzed in the poloidal direction and solved on a grid in the axial and radial directions. A two-dimensional equilibrium can be used as the source of equilibrium data. This allows us to extend previous studies of ICRF wave propagation and absorption in mirrors to include the effect of axial variation of the magnetic field and density. (orig.)

Numerical simulation of supersonic over/under expanded jets using adaptive grid

International Nuclear Information System (INIS)

Talebi, S.; Shirani, E.

2001-05-01

Numerical simulation of supersonic under and over expanded jet was simulated. In order to achieve the solution efficiently and with high resolution, adaptive grid is used. The axisymmetric compressible, time dependent Navier-Stokes equations in body fitted curvilinear coordinate were solved numerically. The equations were discretized by using control volume, and the Van Leer flux splitting approach. The equations were solved implicitly. The obtained computer code was used to simulate four different cases of moderate and strong under and over expanded jet flows. The results show that with the adaptation of the grid, the various features of this complicated flow can be observed. It was shown that the adaptation method is very efficient and has the ability to make fine grids near the high gradient regions. (author)

GIS-based two-dimensional numerical simulation of rainfall-induced debris flow

Directory of Open Access Journals (Sweden)

C. Wang

2008-02-01

Full Text Available This paper aims to present a useful numerical method to simulate the propagation and deposition of debris flow across the three dimensional complex terrain. A depth-averaged two-dimensional numerical model is developed, in which the debris and water mixture is assumed to be continuous, incompressible, unsteady flow. The model is based on the continuity equations and Navier-Stokes equations. Raster grid networks of digital elevation model in GIS provide a uniform grid system to describe complex topography. As the raster grid can be used as the finite difference mesh, the continuity and momentum equations are solved numerically using the finite difference method. The numerical model is applied to simulate the rainfall-induced debris flow occurred in 20 July 2003, in Minamata City of southern Kyushu, Japan. The simulation reproduces the propagation and deposition and the results are in good agreement with the field investigation. The synthesis of numerical method and GIS makes possible the solution of debris flow over a realistic terrain, and can be used to estimate the flow range, and to define potentially hazardous areas for homes and road section.

On mathematical modelling and numerical simulation of transient compressible flow across open boundaries

Energy Technology Data Exchange (ETDEWEB)

Rian, Kjell Erik

2003-07-01

In numerical simulations of turbulent reacting compressible flows, artificial boundaries are needed to obtain a finite computational domain when an unbounded physical domain is given. Artificial boundaries which fluids are free to cross are called open boundaries. When calculating such flows, non-physical reflections at the open boundaries may occur. These reflections can pollute the solution severely, leading to inaccurate results, and the generation of spurious fluctuations may even cause the numerical simulation to diverge. Thus, a proper treatment of the open boundaries in numerical simulations of turbulent reacting compressible flows is required to obtain a reliable solution for realistic conditions. A local quasi-one-dimensional characteristic-based open-boundary treatment for the Favre-averaged governing equations for time-dependent three-dimensional multi-component turbulent reacting compressible flow is presented. A k-{epsilon} model for turbulent compressible flow and Magnussen's EDC model for turbulent combustion is included in the analysis. The notion of physical boundary conditions is incorporated in the method, and the conservation equations themselves are applied on the boundaries to complement the set of physical boundary conditions. A two-dimensional finite-difference-based computational fluid dynamics code featuring high-order accurate numerical schemes was developed for the numerical simulations. Transient numerical simulations of the well-known, one-dimensional shock-tube problem, a two-dimensional pressure-tower problem in a decaying turbulence field, and a two-dimensional turbulent reacting compressible flow problem have been performed. Flow- and combustion-generated pressure waves seem to be well treated by the non-reflecting subsonic open-boundary conditions. Limitations of the present open-boundary treatment are demonstrated and discussed. The simple and solid physical basis of the method makes it both favourable and relatively easy to

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

KAUST Repository

Frohne, Jö rg; Heister, Timo; Bangerth, Wolfgang

2015-01-01

© 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.

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

KAUST Repository

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.

Influence of mesh non-orthogonality on numerical simulation of buoyant jet flows

International Nuclear Information System (INIS)

Ishigaki, Masahiro; Abe, Satoshi; Sibamoto, Yasuteru; Yonomoto, Taisuke

2017-01-01

Highlights: • Influence of mesh non-orthogonality on numerical solution of buoyant jet flows. • Buoyant jet flows are simulated with hexahedral and prismatic meshes. • Jet instability with prismatic meshes may be overestimated compared to that with hexahedral meshes. • Modified solvers that can reduce the influence of mesh non-orthogonality and reduce computation time are proposed. - Abstract: In the present research, we discuss the influence of mesh non-orthogonality on numerical solution of a type of buoyant flow. Buoyant jet flows are simulated numerically with hexahedral and prismatic mesh elements in an open source Computational Fluid Dynamics (CFD) code called “OpenFOAM”. Buoyant jet instability obtained with the prismatic meshes may be overestimated compared to that obtained with the hexahedral meshes when non-orthogonal correction is not applied in the code. Although the non-orthogonal correction method can improve the instability generated by mesh non-orthogonality, it may increase computation time required to reach a convergent solution. Thus, we propose modified solvers that can reduce the influence of mesh non-orthogonality and reduce the computation time compared to the existing solvers in OpenFOAM. It is demonstrated that calculations for a buoyant jet with a large temperature difference are performed faster by the modified solver.

Influence of mesh non-orthogonality on numerical simulation of buoyant jet flows

Energy Technology Data Exchange (ETDEWEB)

Ishigaki, Masahiro, E-mail: ishigaki.masahiro@jaea.go.jp; Abe, Satoshi; Sibamoto, Yasuteru; Yonomoto, Taisuke

2017-04-01

Highlights: • Influence of mesh non-orthogonality on numerical solution of buoyant jet flows. • Buoyant jet flows are simulated with hexahedral and prismatic meshes. • Jet instability with prismatic meshes may be overestimated compared to that with hexahedral meshes. • Modified solvers that can reduce the influence of mesh non-orthogonality and reduce computation time are proposed. - Abstract: In the present research, we discuss the influence of mesh non-orthogonality on numerical solution of a type of buoyant flow. Buoyant jet flows are simulated numerically with hexahedral and prismatic mesh elements in an open source Computational Fluid Dynamics (CFD) code called “OpenFOAM”. Buoyant jet instability obtained with the prismatic meshes may be overestimated compared to that obtained with the hexahedral meshes when non-orthogonal correction is not applied in the code. Although the non-orthogonal correction method can improve the instability generated by mesh non-orthogonality, it may increase computation time required to reach a convergent solution. Thus, we propose modified solvers that can reduce the influence of mesh non-orthogonality and reduce the computation time compared to the existing solvers in OpenFOAM. It is demonstrated that calculations for a buoyant jet with a large temperature difference are performed faster by the modified solver.

Numerical integration of asymptotic solutions of ordinary differential equations

Science.gov (United States)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Numerical and experimental approaches to simulate soil clogging in porous media

Science.gov (United States)

Kanarska, Yuliya; LLNL Team

2012-11-01

Failure of a dam by erosion ranks among the most serious accidents in civil engineering. The best way to prevent internal erosion is using adequate granular filters in the transition areas where important hydraulic gradients can appear. In case of cracking and erosion, if the filter is capable of retaining the eroded particles, the crack will seal and the dam safety will be ensured. A finite element numerical solution of the Navier-Stokes equations for fluid flow together with Lagrange multiplier technique for solid particles was applied to the simulation of soil filtration. The numerical approach was validated through comparison of numerical simulations with the experimental results of base soil particle clogging in the filter layers performed at ERDC. The numerical simulation correctly predicted flow and pressure decay due to particle clogging. The base soil particle distribution was almost identical to those measured in the laboratory experiment. To get more precise understanding of the soil transport in granular filters we investigated sensitivity of particle clogging mechanisms to various aspects such as particle size ration, the amplitude of hydraulic gradient, particle concentration and contact properties. By averaging the results derived from the grain-scale simulations, we investigated how those factors affect the semi-empirical multiphase model parameters in the large-scale simulation tool. The Department of Homeland Security Science and Technology Directorate provided funding for this research.

Numerical simulations of coupled problems in engineering

CERN Document Server

2014-01-01

This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting together several single-aspect solvers into a network. In this book, research in various fields was selected for consideration: adaptive methodology for multi-physics solvers, multi-physics phenomena and coupled-field solutions, leading to computationally intensive structural analysis. The strategies which are used to keep these problems computationally affordable are of special interest, and make this an essential book.

Liquid phase electro epitaxy growth kinetics of GaAs-A three-dimensional numerical simulation study

International Nuclear Information System (INIS)

Mouleeswaran, D.; Dhanasekaran, R.

2006-01-01

A three-dimensional numerical simulation study for the liquid phase electro epitaxial growth kinetic of GaAs is presented. The kinetic model is constructed considering (i) the diffusive and convective mass transport, (ii) the heat transfer due to thermoelectric effects such as Peltier effect, Joule effect and Thomson effect, (iii) the electric current distribution with electromigration and (iv) the fluid flow coupled with concentration and temperature fields. The simulations are performed for two configurations namely (i) epitaxial growth from the arsenic saturated gallium rich growth solution, i.e., limited solution model and (ii) epitaxial growth from the arsenic saturated gallium rich growth solution with polycrystalline GaAs feed. The governing equations of liquid phase electro epitaxy are solved numerically with appropriate initial and boundary conditions using the central difference method. Simulations are performed to determine the following, a concentration profiles of solute atoms (As) in the Ga-rich growth solution, shape of the substrate evolution, the growth rate of the GaAs epitaxial film, the contributions of Peltier effect and electromigration of solute atoms to the growth with various experimental growth conditions. The growth rate is found to increase with increasing growth temperature and applied current density. The results are discussed in detail

Numerical simulation of subwoofer array congurations using the Finite Element Method

Directory of Open Access Journals (Sweden)

Xavier Banyuls-Juan

2017-08-01

Full Text Available Teaching in the Master of Acoustic Engineering includes contents that require the modeling of acoustic systems of two types: simple systems through analytical theory and complex models using simulation techniques. In the present work, we describe an example of complex acoustic sources modeling using the finite element method: subwoofer sound radiation in different configurations. Numerical simulations in the frequency domain can calculate the radiation pattern of systems that do not have a simple analytical solution.

An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications

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.

Practical integrated simulation systems for coupled numerical simulations in parallel

Energy Technology Data Exchange (ETDEWEB)

Osamu, Hazama; Zhihong, Guo [Japan Atomic Energy Research Inst., Centre for Promotion of Computational Science and Engineering, Tokyo (Japan)

2003-07-01

In order for the numerical simulations to reflect 'real-world' phenomena and occurrences, incorporation of multidisciplinary and multi-physics simulations considering various physical models and factors are becoming essential. However, there still exist many obstacles which inhibit such numerical simulations. For example, it is still difficult in many instances to develop satisfactory software packages which allow for such coupled simulations and such simulations will require more computational resources. A precise multi-physics simulation today will require parallel processing which again makes it a complicated process. Under the international cooperative efforts between CCSE/JAERI and Fraunhofer SCAI, a German institute, a library called the MpCCI, or Mesh-based Parallel Code Coupling Interface, has been implemented together with a library called STAMPI to couple two existing codes to develop an 'integrated numerical simulation system' intended for meta-computing environments. (authors)

A simplified model for TIG-dressing numerical simulation

Science.gov (United States)

Ferro, P.; Berto, F.; James, M. N.

2017-04-01

Irrespective of the mechanical properties of the alloy to be welded, the fatigue strength of welded joints is primarily controlled by the stress concentration associated with the weld toe or weld root. In order to reduce the effects of such notch defects in welds, which are influenced by tensile properties of the alloy, post-weld improvement techniques have been developed. The two most commonly used techniques are weld toe grinding and TIG dressing, which are intended to both remove toe defects such as non-metallic intrusions and to re-profile the weld toe region to give a lower stress concentration. In the case of TIG dressing the weld toe is re-melted to provide a smoother transition between the plate and the weld crown and to beneficially modify the residual stress redistribution. Assessing the changes to weld stress state arising from TIG-dressing is most easily accomplished through a complex numerical simulation that requires coupled thermo-fluid dynamics and solid mechanics. However, this can be expensive in terms of computational cost and time needed to reach a solution. The present paper therefore proposes a simplified numerical model that overcomes such drawbacks and which simulates the remelted toe region by means of the activation and deactivation of elements in the numerical model.

Numerical simulation methods for wave propagation through optical waveguides

International Nuclear Information System (INIS)

Sharma, A.

1993-01-01

The simulation of the field propagation through waveguides requires numerical solutions of the Helmholtz equation. For this purpose a method based on the principle of orthogonal collocation was recently developed. The method is also applicable to nonlinear pulse propagation through optical fibers. Some of the salient features of this method and its application to both linear and nonlinear wave propagation through optical waveguides are discussed in this report. 51 refs, 8 figs, 2 tabs

Numerical simulation of human biped locomotion

International Nuclear Information System (INIS)

Ishiguro, Misako; Fujisaki, Masahide

1988-04-01

This report describes the numerical simulation of the motion of human-like robot which is one of the research theme of human acts simulation program (HASP) begun at the Computing Center of JAERI in 1987. The purpose of the theme is to model the human motion using robotics kinematic/kinetic equations and to get the joint angles as the solution. As the first trial, we treat the biped locomotion (walking) which is the most fundamental human motion. We implemented a computer program on FACOM M-780 computer, where the program is originated from the book of M. Vukobratovic in Yugoslavia, and made a graphic program to draw a walking shot sequence. Mainly described here are the mathematical model of the biped locomotion, implementation method of the computer program, input data for basic walking pattern, computed results and its validation, and graphic representation of human walking image. Literature survey on robotics equation and biped locomotion is also included. (author)

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

The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

Energy Technology Data Exchange (ETDEWEB)

Nielsen, Bjoern Fredrik

1997-12-31

The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

Energy Technology Data Exchange (ETDEWEB)

Nielsen, Bjoern Fredrik

1998-12-31

The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

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 Simulation of Duplex Steel Multipass Welding

Directory of Open Access Journals (Sweden)

Giętka T.

2016-12-01

Full Text Available Analyses based on FEM calculations have significantly changed the possibilities of determining welding strains and stresses at early stages of product design and welding technology development. Such an approach to design enables obtaining significant savings in production preparation and post-weld deformation corrections and is also important for utility properties of welded joints obtained. As a result, it is possible to make changes to a simulated process before introducing them into real production as well as to test various variants of a given solution. Numerical simulations require the combination of problems of thermal, mechanical and metallurgical analysis. The study presented involved the SYSWELD software-based analysis of GMA welded multipass butt joints made of duplex steel sheets. The analysis of the distribution of stresses and displacements were carried out for typical welding procedure as during real welding tests.

Numerical modelling of solute transport at Forsmark with MIKE SHE. Site descriptive modelling SDM-Site Forsmark

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 simulation of two-phase filtration in the near well bore zone

Science.gov (United States)

Maksat, Kalimoldayev; Kalipa, Kuspanova; Kulyash, Baisalbayeva; Orken, Mamyrbayev; Assel, Abdildayeva

2018-04-01

On the basis of the fundamental laws of energy conservation, nonstationary processes of filtration of two-phase liquids in multilayered reservoirs in the near well bore zone are considered. Number of reservoirs, fluid pressure in the given reservoirs, reservoir permeability, oil viscosity, etc. are taken into account upon that. Plane-parallel flow and axisymmetric cases have been studied. In the numerical solution, non-structured meshes are used. Closer to the well, the meshes thicken. The integration step over time is defined by the generalized Courant inequality. As a result, there are no large oscillations in the numerical solutions obtained. Oil production rates, Poisson's ratios, D-diameters of the well, filter height, filter permeability, and cumulative thickness of the filter cake and the area have been taken as the main inputs in numerical simulation of non-stationary processes of two-phase filtration.

Stress Analysis of Non-Ferrous Metals Welds by Numerical Simulation

Directory of Open Access Journals (Sweden)

Kravarikova Helena

2017-01-01

Full Text Available Thermal energy welded material unevenly heated and thus supports the creation of tension. During the fusing process welding transient tensions generated in the welded material. Generation of the transient tensions depends on the thermal expansion and fixed permanently welded parts. Tensions are the result of the interaction of material particles. For welded parts and constructions it is necessary to know the size and direction of application of tensions. The emerging tensions can cause local change or a total deformation of welded materials. Deformations and residual stresses impair the performance of a welded construction, reduces the stability of the parts. To reduce or eliminate of action or a screening direction stresses and strains it is necessary to know the mechanism of their emergence. It is now possible to examine the emergence of tensions numerical experiments on any model using numerical simulation using FEM. Results of numerical experiment is the analysis of stress and deformation course. In the plane the tension it divided into normal σ and τ tangential folders. Decomposition stress on components simplifies the stress analysis. The results obtained from numerical analysis are correct to predict the stress distribution and size. The paper presents the results of numerical experiments stress analysis solutions fillet welds using FEM numerical simulation of welding of non-ferrous metals.

A multiscale numerical algorithm for heat transfer simulation between multidimensional CFD and monodimensional system codes

Science.gov (United States)

Chierici, A.; Chirco, L.; Da Vià, R.; Manservisi, S.; Scardovelli, R.

2017-11-01

Nowadays the rapidly-increasing computational power allows scientists and engineers to perform numerical simulations of complex systems that can involve many scales and several different physical phenomena. In order to perform such simulations, two main strategies can be adopted: one may develop a new numerical code where all the physical phenomena of interest are modelled or one may couple existing validated codes. With the latter option, the creation of a huge and complex numerical code is avoided but efficient methods for data exchange are required since the performance of the simulation is highly influenced by its coupling techniques. In this work we propose a new algorithm that can be used for volume and/or boundary coupling purposes for both multiscale and multiphysics numerical simulations. The proposed algorithm is used for a multiscale simulation involving several CFD domains and monodimensional loops. We adopt the overlapping domain strategy, so the entire flow domain is simulated with the system code. We correct the system code solution by matching averaged inlet and outlet fields located at the boundaries of the CFD domains that overlap parts of the monodimensional loop. In particular we correct pressure losses and enthalpy values with source-sink terms that are imposed in the system code equations. The 1D-CFD coupling is a defective one since the CFD code requires point-wise values on the coupling interfaces and the system code provides only averaged quantities. In particular we impose, as inlet boundary conditions for the CFD domains, the mass flux and the mean enthalpy that are calculated by the system code. With this method the mass balance is preserved at every time step of the simulation. The coupling between consecutive CFD domains is not a defective one since with the proposed algorithm we can interpolate the field solutions on the boundary interfaces. We use the MED data structure as the base structure where all the field operations are

GITTAM program for numerical simulation of one-dimensional targets TIS. Part 2

International Nuclear Information System (INIS)

Arpishkin, Yu.P.; Basko, M.M.; Sokolovskij, M.V.

1989-01-01

A finite-difference algorithm for numeric solution of a system of one-dimensional hydrodynamics equation with heat conductivity, radiation diffusion and thermonuclear combustion is considered. The algorithm presented allows one to simulate one-dimensional thermonuclear targets for heavy-ion synthesis (HIS), irradiated with heavy ion beams. A brief description of a complex of GITTAM programs in which finite-difference algorithm for one-dimensional thermonuclear HIS target simulation is used, is given. 5 refs.; 3 figs

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.

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 simulation of strongly swirling turbulent flows through an abrupt expansion

International Nuclear Information System (INIS)

Paik, Joongcheol; Sotiropoulos, Fotis

2010-01-01

Turbulent swirling flow through an abrupt axisymmetric expansion is investigated numerically using detached-eddy simulation at Reynolds numbers = 3.0 x 10 4 and 1.0 x 10 5 . The effects of swirl intensity on the coherent dynamics of the flow are systematically studied by carrying out numerical simulations over a range of swirl numbers from 0.17 to 1.23. Comparison of the computed solutions with the experimental measurements of shows that the numerical simulations resolve both the axial and swirl mean velocity and turbulence intensity profiles with very good accuracy. Our simulations show that, along with moderate mesh refinement, critical prerequisite for accurate predictions of the flow downstream of the expansion is the specification of inlet conditions at a plane sufficiently far upstream of the expansion in order to avoid the spurious suppression of the low-frequency, large-scale precessing of the vortex core. Coherent structure visualizations with the q-criterion, friction lines and Lagrangian particle tracking are used to elucidate the rich dynamics of the flow as a function of the swirl number with emphasis on the onset of the spiral vortex breakdown, the onset and extent of the on-axis recirculation region and the large-scale instabilities along the shear layers and the pipe wall.

Numerical modelling of solute transport at Forsmark with MIKE SHE. Site descriptive modelling SDM-Site Forsmark

International Nuclear Information System (INIS)

Gustafsson, Lars-Goeran; Sassner, Mona; Bosson, Emma

2008-12-01

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

Dynamic Beam Solutions for Real-Time Simulation and Control Development of Flexible Rockets

Science.gov (United States)

Su, Weihua; King, Cecilia K.; Clark, Scott R.; Griffin, Edwin D.; Suhey, Jeffrey D.; Wolf, Michael G.

2016-01-01

In this study, flexible rockets are structurally represented by linear beams. Both direct and indirect solutions of beam dynamic equations are sought to facilitate real-time simulation and control development for flexible rockets. The direct solution is completed by numerically integrate the beam structural dynamic equation using an explicit Newmark-based scheme, which allows for stable and fast transient solutions to the dynamics of flexile rockets. Furthermore, in the real-time operation, the bending strain of the beam is measured by fiber optical sensors (FOS) at intermittent locations along the span, while both angular velocity and translational acceleration are measured at a single point by the inertial measurement unit (IMU). Another study in this paper is to find the analytical and numerical solutions of the beam dynamics based on the limited measurement data to facilitate the real-time control development. Numerical studies demonstrate the accuracy of these real-time solutions to the beam dynamics. Such analytical and numerical solutions, when integrated with data processing and control algorithms and mechanisms, have the potential to increase launch availability by processing flight data into the flexible launch vehicle's control system.

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

Science.gov (United States)

Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

2018-04-01

This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual

Numerical simulation of flood barriers

Science.gov (United States)

Srb, Pavel; Petrů, Michal; Kulhavý, Petr

This paper deals with testing and numerical simulating of flood barriers. The Czech Republic has been hit by several very devastating floods in past years. These floods caused several dozens of causalities and property damage reached billions of Euros. The development of flood measures is very important, especially for the reduction the number of casualties and the amount of property damage. The aim of flood control measures is the detention of water outside populated areas and drainage of water from populated areas as soon as possible. For new flood barrier design it is very important to know its behaviour in case of a real flood. During the development of the barrier several standardized tests have to be carried out. Based on the results from these tests numerical simulation was compiled using Abaqus software and some analyses were carried out. Based on these numerical simulations it will be possible to predict the behaviour of barriers and thus improve their design.

Numerical simulation of the motion of charged suspended particle in multi-phase flow

Energy Technology Data Exchange (ETDEWEB)

Abd Elkhalek, M M [Nuclear Research Center-Atomic Energy Authority, Cairo (Egypt)

1997-12-31

A method for computing numerical simulation of the motion of charged suspended particle in multi-phase flow between two-long parallel plates is described in detail. The equation of motion of a suspended particle was suggested by closkin. The equations of motion are reduced to ordinary differential equations by similarity transformations and solved numerically by using Runge-Kutta method. The trajectories of particles are calculated by integrating the equation of motion of a single particle. Numerical solutions of the resulting ordinary differential equations provide velocity distributions for both fluid and solid phases and density distributions for the solid. The present simulation requires some empirical parameters concerning the collision of the particles with the wall. Some typical results for both fluid and particle phases and density distributions of the particles are presented graphically. 4 figs.

Numerical Simulation of the Motion of Charged Suspended Particle in Multi-Phase Flow

International Nuclear Information System (INIS)

Abd-El Khalek, M.M.

1998-01-01

A method for computing Numerical simulation of the motion of charged suspended particle in multi-phase flow between two-long parallel plates is described in detail. The equation of motion of a suspended particle was suggested by Closkin. The equations of motion are reduced to ordinary differential equations by similarity transformations and solved numerically by using the Runge-Kutta method. The trajectories of particles are calculated by integrating the equation of motion of a single particle. Numerical solutions of the resulting ordinary differential equations provide velocity distributions for both fluid and solid phases and density distributions for the solid. The present simulation requires some empirical parameters concerning the collision of the particles with the wall. Some typical results for both fluid and particle phases and density distributions of the particles are presented graphically

Visualization of numerically simulated aerodynamic flow fields

International Nuclear Information System (INIS)

Hian, Q.L.; Damodaran, M.

1991-01-01

The focus of this paper is to describe the development and the application of an interactive integrated software to visualize numerically simulated aerodynamic flow fields so as to enable the practitioner of computational fluid dynamics to diagnose the numerical simulation and to elucidate essential flow physics from the simulation. The input to the software is the numerical database crunched by a supercomputer and typically consists of flow variables and computational grid geometry. This flow visualization system (FVS), written in C language is targetted at the Personal IRIS Workstations. In order to demonstrate the various visualization modules, the paper also describes the application of this software to visualize two- and three-dimensional flow fields past aerodynamic configurations which have been numerically simulated on the NEC-SXIA Supercomputer. 6 refs

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

Direct numerical simulation and modeling of turbulent natural convection in a vertical differentially heated slot

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

Comments on numerical simulations

International Nuclear Information System (INIS)

Sato, T.

1984-01-01

The author comments on a couple of things about numerical simulation. One is just about the philosophical discussion that is, spontaneous or driven. The other thing is the numerical or technical one. Frankly, the author didn't want to touch on the technical matter because this should be a common sense one for those who are working at numerical simulation. But since many people take numerical simulation results at their face value, he would like to remind you of the reality hidden behind them. First, he would point out that the meaning of ''driven'' in driven reconnection is different from that defined by Schindler or Akasofu. The author's definition is closer to Axford's definition. In the spontaneous case, for some unpredicted reason an excess energy of the system is suddenly released at a certain point. However, one does not answer how such an unstable state far beyond a stable limit is realized in the magnetotail. In the driven case, there is a definite energy buildup phase starting from a stable state; namely, energy in the black box increases from a stable level subject to an external source. When the state has reached a certain position, the energy is released suddenly. The difference between driven and spontaneous is whether the cause (plasma flow) to trigger reconnection is specified or reconnection is triggered unpredictably. Another difference is that in driven reconnection the reconnection rate is dependent on the speed of the external plasma flow, but in spontaneous reconnection the rate is dependent on the internal condition such as the resistivity

Numerical simulation of a semi-indirect evaporative cooler

Energy Technology Data Exchange (ETDEWEB)

Martin, R. Herrero [Departamento de Ingenieria Termica y de Fluidos, Universidad Politecnica de Cartagena, C/Dr. Fleming, s/n (Campus Muralla), 30202 Cartagena, Murcia (Spain)

2009-11-15

This paper presents the experimental study and numerical simulation of a semi-indirect evaporative cooler (SIEC), which acts as an energy recovery device in air conditioning systems. The numerical simulation was conducted by applying the CFD software FLUENT implementing a UDF to model evaporation/condensation. The numerical model was validated by comparing the simulation results with experimental data. Experimental data and numerical results agree for the lower relative humidity series but not for higher relative humidity values. (author)

Numerical Simulations of Particle Deposition in Metal Foam Heat Exchangers

Science.gov (United States)

Sauret, Emilie; Saha, Suvash C.; Gu, Yuantong

2013-01-01

Australia is a high-potential country for geothermal power with reserves currently estimated in the tens of millions of petajoules, enough to power the nation for at least 1000 years at current usage. However, these resources are mainly located in isolated arid regions where water is scarce. Therefore, wet cooling systems for geothermal plants in Australia are the least attractive solution and thus air-cooled heat exchangers are preferred. In order to increase the efficiency of such heat exchangers, metal foams have been used. One issue raised by this solution is the fouling caused by dust deposition. In this case, the heat transfer characteristics of the metal foam heat exchanger can dramatically deteriorate. Exploring the particle deposition property in the metal foam exchanger becomes crucial. This paper is a numerical investigation aimed to address this issue. Two-dimensional (2D) numerical simulations of a standard one-row tube bundle wrapped with metal foam in cross-flow are performed and highlight preferential particle deposition areas.

Numerical Simulations of Hypersonic Boundary Layer Transition

Science.gov (United States)

Bartkowicz, Matthew David

Numerical schemes for supersonic flows tend to use large amounts of artificial viscosity for stability. This tends to damp out the small scale structures in the flow. Recently some low-dissipation methods have been proposed which selectively eliminate the artificial viscosity in regions which do not require it. This work builds upon the low-dissipation method of Subbareddy and Candler which uses the flux vector splitting method of Steger and Warming but identifies the dissipation portion to eliminate it. Computing accurate fluxes typically relies on large grid stencils or coupled linear systems that become computationally expensive to solve. Unstructured grids allow for CFD solutions to be obtained on complex geometries, unfortunately, it then becomes difficult to create a large stencil or the coupled linear system. Accurate solutions require grids that quickly become too large to be feasible. In this thesis a method is proposed to obtain more accurate solutions using relatively local data, making it suitable for unstructured grids composed of hexahedral elements. Fluxes are reconstructed using local gradients to extend the range of data used. The method is then validated on several test problems. Simulations of boundary layer transition are then performed. An elliptic cone at Mach 8 is simulated based on an experiment at the Princeton Gasdynamics Laboratory. A simulated acoustic noise boundary condition is imposed to model the noisy conditions of the wind tunnel and the transitioning boundary layer observed. A computation of an isolated roughness element is done based on an experiment in Purdue's Mach 6 quiet wind tunnel. The mechanism for transition is identified as an instability in the upstream separation region and a comparison is made to experimental data. In the CFD a fully turbulent boundary layer is observed downstream.

Numerically satisfactory solutions of Kummer recurrence relations

NARCIS (Netherlands)

J. Segura (Javier); N.M. Temme (Nico)

2008-01-01

textabstractPairs of numerically satisfactory solutions as $n\\rightarrow \\infty$ for the three-term recurrence relations satisfied by the families of functions $_1\\mbox{F}_1(a+\\epsilon_1 n; b +\\epsilon_2 n;z)$, $\\epsilon_i \\in {\\mathbb Z}$, are given. It is proved that minimal solutions always

Constructing exact symmetric informationally complete measurements from numerical solutions

Science.gov (United States)

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.

Solved problems in classical mechanics analytical and numerical solutions with comments

CERN Document Server

de Lange, O L

2010-01-01

Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...

Modelling and numerical simulation of liquid-vapor phase transitions

International Nuclear Information System (INIS)

Caro, F.

2004-11-01

This work deals with the modelling and numerical simulation of liquid-vapor phase transition phenomena. The study is divided into two part: first we investigate phase transition phenomena with a Van Der Waals equation of state (non monotonic equation of state), then we adopt an alternative approach with two equations of state. In the first part, we study the classical viscous criteria for selecting weak solutions of the system used when the equation of state is non monotonic. Those criteria do not select physical solutions and therefore we focus a more recent criterion: the visco-capillary criterion. We use this criterion to exactly solve the Riemann problem (which imposes solving an algebraic scalar non linear equation). Unfortunately, this step is quite costly in term of CPU which prevent from using this method as a ground for building Godunov solvers. That is why we propose an alternative approach two equations of state. Using the least action principle, we propose a phase changing two-phase flow model which is based on the second thermodynamic principle. We shall then describe two equilibrium submodels issued from the relaxations processes when instantaneous equilibrium is assumed. Despite the weak hyperbolicity of the last sub-model, we propose stable numerical schemes based on a two-step strategy involving a convective step followed by a relaxation step. We show the ability of the system to simulate vapor bubbles nucleation. (author)

Multiphase flow experiments, mathematical modeling and numerical simulation of the water - gas - solute movement

Science.gov (United States)

Li, Y.; Ma, X.; Su, N.

2013-12-01

The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.

Numerical simulation of sand jet in water

Energy Technology Data Exchange (ETDEWEB)

Azimi, A.H.; Zhu, D.; Rajaratnam, N. [Alberta Univ., Edmonton, AB (Canada). Dept. of Civil and Environmental Engineering

2008-07-01

A numerical simulation of sand jet in water was presented. The study involved a two-phase flow using two-phase turbulent jets. A literature review was also presented, including an experiment on particle laden air jet using laser doppler velocimetry (LDV); experiments on the effect of particle size and concentration on solid-gas jets; an experimental study of solid-liquid jets using particle image velocimetry (PIV) technique where mean velocity and fluctuations were measured; and an experimental study on solid-liquid jets using the laser doppler anemometry (LDA) technique measuring both water axial and radial velocities. Other literature review results included a photographic study of sand jets in water; a comparison of many two-phase turbulent flow; and direct numerical simulation and large-eddy simulation to study the effect of particle in gas jet flow. The mathematical model and experimental setup were also included in the presentation along with simulation results for sand jets, concentration, and kinetic energy. The presentation concluded with some proposed future studies including numerical simulation of slurry jets in water and numerical simulation of slurry jets in MFT. tabs., figs.

Numerical methodologies for investigation of moderate-velocity flow using a hybrid computational fluid dynamics - molecular dynamics simulation approach

International Nuclear Information System (INIS)

Ko, Soon Heum; Kim, Na Yong; Nikitopoulos, Dimitris E.; Moldovan, Dorel; Jha, Shantenu

2014-01-01

Numerical approaches are presented to minimize the statistical errors inherently present due to finite sampling and the presence of thermal fluctuations in the molecular region of a hybrid computational fluid dynamics (CFD) - molecular dynamics (MD) flow solution. Near the fluid-solid interface the hybrid CFD-MD simulation approach provides a more accurate solution, especially in the presence of significant molecular-level phenomena, than the traditional continuum-based simulation techniques. It also involves less computational cost than the pure particle-based MD. Despite these advantages the hybrid CFD-MD methodology has been applied mostly in flow studies at high velocities, mainly because of the higher statistical errors associated with low velocities. As an alternative to the costly increase of the size of the MD region to decrease statistical errors, we investigate a few numerical approaches that reduce sampling noise of the solution at moderate-velocities. These methods are based on sampling of multiple simulation replicas and linear regression of multiple spatial/temporal samples. We discuss the advantages and disadvantages of each technique in the perspective of solution accuracy and computational cost.

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

Numerical simulation of interface movement in gas-liquid two-phase flows with Level Set method

International Nuclear Information System (INIS)

Li Huixiong; Chinese Academy of Sciences, Beijing; Deng Sheng; Chen Tingkuan; Zhao Jianfu; Wang Fei

2005-01-01

Numerical simulation of gas-liquid two-phase flow and heat transfer has been an attractive work for a quite long time, but still remains as a knotty difficulty due to the inherent complexities of the gas-liquid two-phase flow resulted from the existence of moving interfaces with topology changes. This paper reports the effort and the latest advances that have been made by the authors, with special emphasis on the methods for computing solutions to the advection equation of the Level set function, which is utilized to capture the moving interfaces in gas-liquid two-phase flows. Three different schemes, i.e. the simple finite difference scheme, the Superbee-TVD scheme and the 5-order WENO scheme in combination with the Runge-Kutta method are respectively applied to solve the advection equation of the Level Set. A numerical procedure based on the well-verified SIMPLER method is employed to numerically calculate the momentum equations of the two-phase flow. The above-mentioned three schemes are employed to simulate the movement of four typical interfaces under 5 typical flowing conditions. Analysis of the numerical results shows that the 5-order WENO scheme and the Superbee-TVD scheme are much better than the simple finite difference scheme, and the 5-order WENO scheme is the best to compute solutions to the advection equation of the Level Set. The 5-order WENO scheme will be employed as the main scheme to get solutions to the advection equations of the Level Set when gas-liquid two-phase flows are numerically studied in the future. (authors)

Numerical Simulation of Flood Levels for Tropical Rivers

International Nuclear Information System (INIS)

Mohammed, Thamer Ahmed; Said, Salim; Bardaie, Mohd Zohadie; Basri, Shah Nor

2011-01-01

Flood forecasting is important for flood damage reduction. As a result of advances in the numerical methods and computer technologies, many mathematical models have been developed and used for hydraulic simulation of the flood. These simulations usually include the prediction of the flood width and depth along a watercourse. Results obtained from the application of hydraulic models will help engineers to take precautionary measures to minimize flood damage. Hydraulic models were used to simulate the flood can be classified into dynamic hydraulic models and static hydraulic models. The HEC-2 static hydraulic model was used to predict water surface profiles for Linggi river and Langat river in Malaysia. The model is based on the numerical solution of the one dimensional energy equation of the steady gradually varied flow using the iteration technique. Calibration and verification of the HEC-2 model were conducted using the recorded data for both rivers. After calibration, the model was applied to predict the water surface profiles for Q10, Q30, and Q100 along the watercourse of the Linggi river. The water surface profile for Q200 for Langat river was predicted. The predicted water surface profiles were found in agreement with the recorded water surface profiles. The value of the maximum computed absolute error in the predicted water surface profile was found to be 500 mm while the minimum absolute error was 20 mm only.

Numerical methods for the simulation of particle generated electromagnetic fields in acclerator physics

International Nuclear Information System (INIS)

Lau, T.

2006-01-01

In this work modifications of the classical Particle-In-Cell method for the solution of the Maxwell-Vlasov equations are investigated with respect to their application in particle accelerator physics. The aim of the work is to find modifications of the method which minimize and under certain conditions even eliminate the numerical dispersion effect along the beam axis in the numerical solution of Maxwell's equations. This is achieved by the development of dedicated time-integration methods for the Finite Integration Technique and two Finite Volume Methods. The methods are theoretically investigated regarding the conservation of a discrete energy and the existence of a discrete continuity equation. Finally, some of the methods are applied to the simulation of a high frequency rf-gun. (orig.)

Numerical methods in simulation of resistance welding

DEFF Research Database (Denmark)

Nielsen, Chris Valentin; Martins, Paulo A.F.; Zhang, Wenqi

2015-01-01

Finite element simulation of resistance welding requires coupling betweenmechanical, thermal and electrical models. This paper presents the numerical models and theircouplings that are utilized in the computer program SORPAS. A mechanical model based onthe irreducible flow formulation is utilized...... a resistance welding point of view, the most essential coupling between the above mentioned models is the heat generation by electrical current due to Joule heating. The interaction between multiple objects is anothercritical feature of the numerical simulation of resistance welding because it influences...... thecontact area and the distribution of contact pressure. The numerical simulation of resistancewelding is illustrated by a spot welding example that includes subsequent tensile shear testing...

Coincidental match of numerical simulation and physics

Science.gov (United States)

Pierre, B.; Gudmundsson, J. S.

2010-08-01

Consequences of rapid pressure transients in pipelines range from increased fatigue to leakages and to complete ruptures of pipeline. Therefore, accurate predictions of rapid pressure transients in pipelines using numerical simulations are critical. State of the art modelling of pressure transient in general, and water hammer in particular include unsteady friction in addition to the steady frictional pressure drop, and numerical simulations rely on the method of characteristics. Comparison of rapid pressure transient calculations by the method of characteristics and a selected high resolution finite volume method highlights issues related to modelling of pressure waves and illustrates that matches between numerical simulations and physics are purely coincidental.

Numerical simulation of a liquid propellant rocket motor

Science.gov (United States)

Salvador, Nicolas M. C.; Morales, Marcelo M.; Migueis, Carlos E. S. S.; Bastos-Netto, Demétrio

2001-03-01

This work presents a numerical simulation of the flow field in a liquid propellant rocket engine chamber and exit nozzle using techniques to allow the results to be taken as starting points for designing those propulsive systems. This was done using a Finite Volume method simulating the different flow regimes which usually take place in those systems. As the flow field has regions ranging from the low subsonic to the supersonic regimes, the numerical code used, initially developed for compressible flows only, was modified to work proficiently in the whole velocity range. It is well known that codes have been developed in CFD, for either compressible or incompressible flows, the joint treatment of both together being complex even today, given the small number of references available in this area. Here an existing code for compressible flow was used and primitive variables, the pressure, the Cartesian components of the velocity and the temperature instead of the conserved variables were introduced in the Euler and Navier-Stokes equations. This was done to permit the treatment at any Mach number. Unstructured meshes with adaptive refinements were employed here. The convective terms were treated with upwind first and second order methods. The numerical stability was kept with artificial dissipation and in the spatial coverage one used a five stage Runge-Kutta scheme for the Fluid Mechanics and the VODE (Value of Ordinary Differential Equations) scheme along with the Chemkin II in the chemical reacting solution. During the development of this code simulating the flow in a rocket engine, comparison tests were made with several different types of internal and external flows, at different velocities, seeking to establish the confidence level of the techniques being used. These comparisons were done with existing theoretical results and with other codes already validated and well accepted by the CFD community.

Numerical simulation in astrophysics

International Nuclear Information System (INIS)

Miyama, Shoken

1985-01-01

There have been many numerical simulations of hydrodynamical problems in astrophysics, e.g. processes of star formation, supernova explosion and formation of neutron stars, and general relativistic collapse of star to form black hole. The codes are made to be suitable for computing such problems. In astrophysical hydrodynamical problems, there are the characteristics: problems of self-gravity or external gravity acting, objects of scales very large or very short, objects changing by short period or long time scale, problems of magnetic force and/or centrifugal force acting. In this paper, we present one of methods of numerical simulations which may satisfy these requirements, so-called smoothed particle methods. We then introduce the methods briefly. Then, we show one of the applications of the methods to astrophysical problem (fragmentation and collapse of rotating isothermal cloud). (Mori, K.)

Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses

Science.gov (United States)

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.

Numerical simulation of pseudoelastic shape memory alloys using the large time increment method

Science.gov (United States)

Gu, Xiaojun; Zhang, Weihong; Zaki, Wael; Moumni, Ziad

2017-04-01

The paper presents a numerical implementation of the large time increment (LATIN) method for the simulation of shape memory alloys (SMAs) in the pseudoelastic range. The method was initially proposed as an alternative to the conventional incremental approach for the integration of nonlinear constitutive models. It is adapted here for the simulation of pseudoelastic SMA behavior using the Zaki-Moumni model and is shown to be especially useful in situations where the phase transformation process presents little or lack of hardening. In these situations, a slight stress variation in a load increment can result in large variations of strain and local state variables, which may lead to difficulties in numerical convergence. In contrast to the conventional incremental method, the LATIN method solve the global equilibrium and local consistency conditions sequentially for the entire loading path. The achieved solution must satisfy the conditions of static and kinematic admissibility and consistency simultaneously after several iterations. 3D numerical implementation is accomplished using an implicit algorithm and is then used for finite element simulation using the software Abaqus. Computational tests demonstrate the ability of this approach to simulate SMAs presenting flat phase transformation plateaus and subjected to complex loading cases, such as the quasi-static behavior of a stent structure. Some numerical results are contrasted to those obtained using step-by-step incremental integration.

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.

Numerical simulation of Higgs models

International Nuclear Information System (INIS)

Jaster, A.

1995-10-01

The SU(2) Higgs and the Schwinger model on the lattice were analysed. Numerical simulations of the SU(2) Higgs model were performed to study the finite temperature electroweak phase transition. With the help of the multicanonical method the distribution of an order parameter at the phase transition point was measured. This was used to obtain the order of the phase transition and the value of the interface tension with the histogram method. Numerical simulations were also performed at zero temperature to perform renormalization. The measured values for the Wilson loops were used to determine the static potential and from this the renormalized gauge coupling. The Schwinger model was simulated at different gauge couplings to analyse the properties of the Kaplan-Shamir fermions. The prediction that the mass parameter gets only multiplicative renormalization was tested and verified. (orig.)

Numerical simulation of solitary waves on deep water with constant vorticity

Science.gov (United States)

Dosaev, A. S.; Shishina, M. I.; Troitskaya, Yu I.

2018-01-01

Characteristics of solitary deep water waves on a flow with constant vorticity are investigated by numerical simulation within the framework of fully nonlinear equations of motion (Euler equations) using the method of surface-tracking conformal coordinates. To ensure that solutions observed are stable, soliton formation as a result of disintegration of an initial pulse-like disturbance is modeled. Evidence is obtained that solitary waves with height above a certain threshold are unstable.

Numerical simulation of ultrasonic wave propagation in elastically anisotropic media

International Nuclear Information System (INIS)

Jacob, Victoria Cristina Cheade; Jospin, Reinaldo Jacques; Bittencourt, Marcelo de Siqueira Queiroz

2013-01-01

The ultrasonic non-destructive testing of components may encounter considerable difficulties to interpret some inspections results mainly in anisotropic crystalline structures. A numerical method for the simulation of elastic wave propagation in homogeneous elastically anisotropic media, based on the general finite element approach, is used to help this interpretation. The successful modeling of elastic field associated with NDE is based on the generation of a realistic pulsed ultrasonic wave, which is launched from a piezoelectric transducer into the material under inspection. The values of elastic constants are great interest information that provide the application of equations analytical models, until small and medium complexity problems through programs of numerical analysis as finite elements and/or boundary elements. The aim of this work is the comparison between the results of numerical solution of an ultrasonic wave, which is obtained from transient excitation pulse that can be specified by either force or displacement variation across the aperture of the transducer, and the results obtained from a experiment that was realized in an aluminum block in the IEN Ultrasonic Laboratory. The wave propagation can be simulated using all the characteristics of the material used in the experiment valuation associated to boundary conditions and from these results, the comparison can be made. (author)

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

Science.gov (United States)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Introduction to the numerical solutions of Markov chains

CERN Document Server

Stewart, Williams J

1994-01-01

A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...

Numerical simulation of incidence and sweep effects on delta wing vortex breakdown

Science.gov (United States)

Ekaterinaris, J. A.; Schiff, Lewis B.

1994-01-01

The structure of the vortical flowfield over delta wings at high angles of attack was investigated. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics, including leading-edge separation, secondary separation, and vortex breakdown. Flows over a 75- and a 63-deg sweep delta wing with sharp leading edges were investigated and compared with available experimental data. The effect of variation of circumferential grid resolution grid resolution in the vicinity of the wing leading edge on the accuracy of the solutions was addressed. Furthermore, the effect of turbulence modeling on the solutions was investigated. The effects of variation of angle of attack on the computed vortical flow structure for the 75-deg sweep delta wing were examined. At moderate angles of attack no vortex breakdown was observed. When a critical angle of attack was reached, bubble-type vortex breakdown was found. With further increase in angle of attack, a change from bubble-type breakdown to spiral-type vortex breakdown was predicted by the numerical solution. The effects of variation of sweep angle and freestream Mach number were addressed with the solutions on a 63-deg sweep delta wing.

Direct Numerical Simulation of Passive Scalar Mixing in Shock Turbulence Interaction

Science.gov (United States)

Gao, Xiangyu; Bermejo-Moreno, Ivan; Larsson, Johan

2017-11-01

Passive scalar mixing in the canonical shock-turbulence interaction configuration is investigated through shock-capturing Direct Numerical Simulations (DNS). Scalar fields with different Schmidt numbers are transported by an initially isotropic turbulent flow field passing across a nominally planar shock wave. A solution-adaptive hybrid numerical scheme on Cartesian structured grids is used, that combines a fifth-order WENO scheme near shocks and a sixth-order central-difference scheme away from shocks. The simulations target variations in the shock Mach number, M (from 1.5 to 3), turbulent Mach number, Mt (from 0.1 to 0.4, including wrinkled- and broken-shock regimes), and scalar Schmidt numbers, Sc (from 0.5 to 2), while keeping the Taylor microscale Reynolds number constant (Reλ 40). The effects on passive scalar statistics are investigated, including the streamwise evolution of scalar variance budgets, pdfs and spectra, in comparison with their temporal evolution in decaying isotropic turbulence.

Rotationally symmetric numerical solutions to the sine-Gordon equation

DEFF Research Database (Denmark)

Olsen, O. H.; Samuelsen, Mogens Rugholm

1981-01-01

We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...

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 simulation of in-situ DNAPL remediation by alcohol flooding

Energy Technology Data Exchange (ETDEWEB)

Falta, R.W.; Brame, S.E. [Earth Science Department, Clemson, SC (United States)

1995-03-01

The removal of residual saturations of dense non-aqueous phase liquids (DNAPLs) from below the water table using alcohol solutions is under investigation as a potential remediation tool. Alcohol flooding reduces the interfacial tension (IFT) an density difference between the aqueous and DNAPL phases, and increases the chemical solubility in the aqueous phase. Depending on the partitioning behavior of the alcohol/chemical system, DNAPL can be removed by either mobilization as a separate phase or through enhanced dissolution. A new three dimensional multiphase numerical simulator has been developed for modeling this process. The code is based on the general TOUGH2 Integral Finite Difference formulation for multiphase transport with modifications to account for the complex behavior of an alcohol/water/DNAPL system. The alcohol flood code uses a special equation of state module for computing phase compositions, IFT, saturations, densities, viscosities, relative permeabilities, and capillary pressures during each time step. This equation of state is based on a numerical interpolation of experimentally determined ternary phase data. The code was designed so that it can readily be applied to other three-component, two-phase problems such as surfactant and solvent floods given appropriate ternary data. Comparisons of simulation results with column experiments performed at Clemson University were used to validate the simulator.

Experimentation and numerical simulation of steel fibre reinforced concrete pipes

International Nuclear Information System (INIS)

Fuente, A. de la; Domingues de Figueiredo, A.; Aguado, A.; Molins, C.; Chama Neto, P. J.

2011-01-01

The results concerning on an experimental and a numerical study related to SFRCP are presented. Eighteen pipes with an internal diameter of 600 mm and fibre dosages of 10, 20 and 40 kg/m3 were manufactured and tested. Some technological aspects were concluded. Likewise, a numerical parameterized model was implemented. With this model, the simulation of the resistant behaviour of SFRCP can be performed. In this sense, the results experimentally obtained were contrasted with those suggested by means MAP reaching very satisfactory correlations. Taking it into account, it could be said that the numerical model is a useful tool for the optimal design of the SFRCP fibre dosages, avoiding the need of the systematic employment of the test as an indirect design method. Consequently, the use of this model would reduce the overall cost of the pipes and would give fibres a boost as a solution for this structural typology. (Author) 27 refs.

Direct numerical simulation of electrokinetic instability and transition to chaotic motion

Science.gov (United States)

Demekhin, E. A.; Nikitin, N. V.; Shelistov, V. S.

2013-12-01

A new type of instability—electrokinetic instability—and an unusual transition to chaotic motion near a charge-selective surface (semiselective electric membrane, electrode, or system of micro-/nanochannels) was studied by the numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. A special finite-difference method was used for the space discretization along with a semi-implicit 31/3-step Runge-Kutta scheme for the integration in time. Two kinds of initial conditions were considered: (a) white-noise initial conditions to mimic "room disturbances" and subsequent natural evolution of the solution, and (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. Our weakly nonlinear analysis and numerical integration of the entire system predict possibility of both kinds of bifurcations at the critical point, supercritical and subcritical, depending on the system parameters. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution, two-dimensional steady electroconvective vortices (stationary point in a proper phase space), unsteady vortices aperiodically changing their parameters (homoclinic contour), periodic motion (limit cycle), and chaotic motion. The transition to chaotic motion does not include Hopf bifurcation. The numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the

Direct numerical simulation of electrokinetic instability and transition to chaotic motion

International Nuclear Information System (INIS)

Demekhin, E. A.; Nikitin, N. V.; Shelistov, V. S.

2013-01-01

A new type of instability—electrokinetic instability—and an unusual transition to chaotic motion near a charge-selective surface (semiselective electric membrane, electrode, or system of micro-/nanochannels) was studied by the numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. A special finite-difference method was used for the space discretization along with a semi-implicit 31/3 -step Runge-Kutta scheme for the integration in time. Two kinds of initial conditions were considered: (a) white-noise initial conditions to mimic “room disturbances” and subsequent natural evolution of the solution, and (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. Our weakly nonlinear analysis and numerical integration of the entire system predict possibility of both kinds of bifurcations at the critical point, supercritical and subcritical, depending on the system parameters. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution, two-dimensional steady electroconvective vortices (stationary point in a proper phase space), unsteady vortices aperiodically changing their parameters (homoclinic contour), periodic motion (limit cycle), and chaotic motion. The transition to chaotic motion does not include Hopf bifurcation. The numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the

Direct numerical simulation of electrokinetic instability and transition to chaotic motion

Energy Technology Data Exchange (ETDEWEB)

Demekhin, E. A., E-mail: edemekhi@gmail.com [Laboratory of Micro- and Nanofluidics, Moscow State University, Moscow 119192 (Russian Federation); Department of Computation Mathematics and Computer Science, Kuban State University, Krasnodar 350040 (Russian Federation); Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Nikitin, N. V. [Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Shelistov, V. S. [Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Scientific Research Department, Kuban State University, Krasnodar 350040 (Russian Federation)

2013-12-15

A new type of instability—electrokinetic instability—and an unusual transition to chaotic motion near a charge-selective surface (semiselective electric membrane, electrode, or system of micro-/nanochannels) was studied by the numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. A special finite-difference method was used for the space discretization along with a semi-implicit 31/3 -step Runge-Kutta scheme for the integration in time. Two kinds of initial conditions were considered: (a) white-noise initial conditions to mimic “room disturbances” and subsequent natural evolution of the solution, and (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. Our weakly nonlinear analysis and numerical integration of the entire system predict possibility of both kinds of bifurcations at the critical point, supercritical and subcritical, depending on the system parameters. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution, two-dimensional steady electroconvective vortices (stationary point in a proper phase space), unsteady vortices aperiodically changing their parameters (homoclinic contour), periodic motion (limit cycle), and chaotic motion. The transition to chaotic motion does not include Hopf bifurcation. The numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the

Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

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 methods for the simulation of continuous sedimentation in ideal clarifier-thickener units

Energy Technology Data Exchange (ETDEWEB)

Buerger, R.; Karlsen, K.H.; Risebro, N.H.; Towers, J.D.

2001-10-01

We consider a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value problem for a nonlinear hyperbolic partial differential equation with a flux function that depends discontinuously on height. The purpose of this contribution is to present and demonstrate two numerical methods for simulating continuous sedimentation: a front tracking method and a finite finite difference method. The basic building blocks in the front tracking method are the solutions of a finite number of certain Riemann problems and a procedure for tracking local collisions of shocks. The solutions of the Riemann problems are recalled herein and the front tracking algorithm is described. As an alternative to the front tracking method, a simple scalar finite difference algorithm is proposed. This method is based on discretizing the spatially varying flux parameters on a mesh that is staggered with respect to that of the conserved variable, resulting in a straightforward generalization of the well-known Engquist-Osher upwind finite difference method. The result is an easily implemented upwind shock capturing method. Numerical examples demonstrate that the front tracking and finite difference methods can be used as efficient and accurate simulation tools for continuous sedimentation. The numerical results for the finite difference method indicate that discontinuities in the local solids concentration are resolved sharply and agree with those produced by the front tracking method. The latter is free of numerical dissipation, which leads to sharply resolved concentration discontinuities, but is more complicated to implement than the former. Available mathematical results for the proposed numerical methods are also briefly reviewed. (author)

Numerical modelling of coupled fluid, heat, and solute transport in deformable fractured rock

International Nuclear Information System (INIS)

Chan, T.; Reid, J.A.K.

1987-01-01

This paper reports on a three-dimensional (3D) finite-element code, MOTIF (model of transport in fractured/porous media), developed to model the coupled processes of groundwater flow, heat transport, brine transport, and one-species radionuclide transport in geological media. Three types of elements are available: a 3D continuum element, a planar fracture element that can be oriented in any arbitrary direction in 3D space or pipe flow in 3D space, and a line element for simulating fracture flow in 2D space or pipe flow in 3D space. As a quality-assurance measure, the MOTIF code was verified by comparison of its results with analytical solutions and other published numerical solutions

Numerical simulation of long-term radiation effects for MOSFETs

International Nuclear Information System (INIS)

Wei Yuan; Xie Honggang; Gong Ding; Zhu Jinhui; Niu Shengli; Huang Liuxing

2013-01-01

A coupled algorithm is introduced to simulate the long-term radiation effects of MOSFETs, which combines particle transport with semiconductor governing equations. The former is dealt with Monte-Carlo method, and the latter is solved by finite-volume method. The trapped charge in SiO 2 and the free charge in Si are both described by the drift-diffusion model, and the deposited energy by incident particles can be coupled with the continuous equations of charge, acting as a source item. The discrete form of governing equations is obtained using the finite-volume method, and the numerical solutions of these equations are the long-term radiation response result of MOSFETs. The threshold voltage shift and off-state leakage current of an irradiated MOSFET are simulated with the coupled algorithm respectively, showing a good accordance with results by other calculations. (authors)

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

Directory of Open Access Journals (Sweden)

Moutassem El Rafei

2017-12-01

Full Text Available The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES. The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier–Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor–Green Vortex (TGV test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT. All combinations of numerical methods produce a k − 4 spectrum

Advanced numerical simulation based on a non-local micromorphic model for metal forming processes

Directory of Open Access Journals (Sweden)

Diamantopoulou Evangelia

2016-01-01

Full Text Available An advanced numerical methodology is developed for metal forming simulation based on thermodynamically-consistent nonlocal constitutive equations accounting for various fully coupled mechanical phenomena under finite strain in the framework of micromorphic continua. The numerical implementation into ABAQUS/Explicit is made for 2D quadrangular elements thanks to the VUEL users’ subroutine. Simple examples with presence of a damaged area are made in order to show the ability of the proposed methodology to describe the independence of the solution from the space discretization.

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

Energy Technology Data Exchange (ETDEWEB)

Franceschini, Andrea; Ferronato, Massimiliano, E-mail: massimiliano.ferronato@unipd.it; Janna, Carlo; Teatini, Pietro

2016-06-01

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

International Nuclear Information System (INIS)

Franceschini, Andrea; Ferronato, Massimiliano; Janna, Carlo; Teatini, Pietro

2016-01-01

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.

Numerical simulation of wave-induced scour and backfilling processes beneath submarine pipelines

DEFF Research Database (Denmark)

Fuhrman, David R.; Baykal, Cüneyt; Sumer, B. Mutlu

2014-01-01

A fully-coupled hydrodynamic/morphodynamic numerical model is presented and utilized for the simulation of wave-induced scour and backfilling processes beneath submarine pipelines. The model is based on solutions to Reynolds-averaged Navier–Stokes equations, coupled with k−ω turbulence closure......≤30 demonstrate reasonable match with previous experiments, both in terms of the equilibrium scour depth as well as the scour time scale. Wave-induced backfilling processes are additionally studied by subjecting initial conditions taken from scour simulations with larger KC to new wave climates...... characterized by lower KC values. The simulations considered demonstrate the ability of the model to predict backfilling toward expected equilibrium scour depths based on the new wave climate, in line with experimental expectations. The simulated backfilling process is characterized by two stages: (1...

Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method

Science.gov (United States)

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian-Ping

2018-03-01

In this paper, we present a first direct numerical simulation (DNS) of a turbulent pipe flow using the mesoscopic lattice Boltzmann method (LBM) on both a D3Q19 lattice grid and a D3Q27 lattice grid. DNS of turbulent pipe flows using LBM has never been reported previously, perhaps due to inaccuracy and numerical stability associated with the previous implementations of LBM in the presence of a curved solid surface. In fact, it was even speculated that the D3Q19 lattice might be inappropriate as a DNS tool for turbulent pipe flows. In this paper, we show, through careful implementation, accurate turbulent statistics can be obtained using both D3Q19 and D3Q27 lattice grids. In the simulation with D3Q19 lattice, a few problems related to the numerical stability of the simulation are exposed. Discussions and solutions for those problems are provided. The simulation with D3Q27 lattice, on the other hand, is found to be more stable than its D3Q19 counterpart. The resulting turbulent flow statistics at a friction Reynolds number of Reτ = 180 are compared systematically with both published experimental and other DNS results based on solving the Navier-Stokes equations. The comparisons cover the mean-flow profile, the r.m.s. velocity and vorticity profiles, the mean and r.m.s. pressure profiles, the velocity skewness and flatness, and spatial correlations and energy spectra of velocity and vorticity. Overall, we conclude that both D3Q19 and D3Q27 simulations yield accurate turbulent flow statistics. The use of the D3Q27 lattice is shown to suppress the weak secondary flow pattern in the mean flow due to numerical artifacts.

Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

Science.gov (United States)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

Science.gov (United States)

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 simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

Science.gov (United States)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow

Go with the Flow. Moving meshes and solution monitoring for compressible flow simulation

NARCIS (Netherlands)

van Dam, A.

2009-01-01

The simulation of time-dependent physical problems, such as flows of some kind, places high demands on the domain discretization in order to obtain high accuracy of the numerical solution. We present a moving mesh method in which the mesh points automatically move towards regions where high spatial

COMSOL-PHREEQC: a tool for high performance numerical simulation of reactive transport phenomena

International Nuclear Information System (INIS)

Nardi, Albert; Vries, Luis Manuel de; Trinchero, Paolo; Idiart, Andres; Molinero, Jorge

2012-01-01

Document available in extended abstract form only. Comsol Multiphysics (COMSOL, from now on) is a powerful Finite Element software environment for the modelling and simulation of a large number of physics-based systems. The user can apply variables, expressions or numbers directly to solid and fluid domains, boundaries, edges and points, independently of the computational mesh. COMSOL then internally compiles a set of equations representing the entire model. The availability of extremely powerful pre and post processors makes COMSOL a numerical platform well known and extensively used in many branches of sciences and engineering. On the other hand, PHREEQC is a freely available computer program for simulating chemical reactions and transport processes in aqueous systems. It is perhaps the most widely used geochemical code in the scientific community and is openly distributed. The program is based on equilibrium chemistry of aqueous solutions interacting with minerals, gases, solid solutions, exchangers, and sorption surfaces, but also includes the capability to model kinetic reactions with rate equations that are user-specified in a very flexible way by means of Basic statements directly written in the input file. Here we present COMSOL-PHREEQC, a software interface able to communicate and couple these two powerful simulators by means of a Java interface. The methodology is based on Sequential Non Iterative Approach (SNIA), where PHREEQC is compiled as a dynamic subroutine (iPhreeqc) that is called by the interface to solve the geochemical system at every element of the finite element mesh of COMSOL. The numerical tool has been extensively verified by comparison with computed results of 1D, 2D and 3D benchmark examples solved with other reactive transport simulators. COMSOL-PHREEQC is parallelized so that CPU time can be highly optimized in multi-core processors or clusters. Then, fully 3D detailed reactive transport problems can be readily simulated by means of

Analysis of the flamelet concept in the numerical simulation of laminar partially premixed flames

Energy Technology Data Exchange (ETDEWEB)

Consul, R.; Oliva, A.; Perez-Segarra, C.D.; Carbonell, D. [Centre Tecnologic de Transferencia de Calor (CTTC), Universitat Politecnica de Catalunya (UPC), Colom 11, E-08222, Terrassa, Barcelona (Spain); de Goey, L.P.H. [Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, 5600 MB Eindhoven (Netherlands)

2008-04-15

The aim of this work is to analyze the application of flamelet models based on the mixture fraction variable and its dissipation rate to the numerical simulation of partially premixed flames. Although the main application of these models is the computation of turbulent flames, this work focuses on the performance of flamelet concept in laminar flame simulations removing, in this way, turbulence closure interactions. A well-known coflow methane/air laminar flame is selected. Five levels of premixing are taken into account from an equivalence ratio {phi}={infinity} (nonpremixed) to {phi}=2.464. Results obtained using the flamelet approaches are compared to data obtained from the detailed solution of the complete transport equations using primitive variables. Numerical simulations of a counterflow flame are also presented to support the discussion of the results. Special emphasis is given to the analysis of the scalar dissipation rate modeling. (author)

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

Continuous limit of a crowd motion and herding model: Analysis and numerical simulations

KAUST Repository

Pietschmann, Jan-Frederik; Markowich, Peter Alexander; Burger, Martin

2011-01-01

In this paper we study the continuum limit of a cellular automaton model used for simulating human crowds with herding behaviour. We derive a system of non-linear partial differential equations resembling the Keller-Segel model for chemotaxis, however with a non-monotone interaction. The latter has interesting consequences on the behaviour of the model's solutions, which we highlight in its analysis. In particular we study the possibility of stationary states, the formation of clusters and explore their connection to congestion. We also introduce an efficient numerical simulation approach based on an appropriate hybrid discontinuous Galerkin method, which in particular allows flexible treatment of complicated geometries. Extensive numerical studies also provide a better understanding of the strengths and shortcomings of the herding model, in particular we examine trapping effects of crowds behind nonconvex obstacles. © American Institute of Mathematical Sciences.

Continuous limit of a crowd motion and herding model: Analysis and numerical simulations

KAUST Repository

Pietschmann, Jan-Frederik

2011-11-01

In this paper we study the continuum limit of a cellular automaton model used for simulating human crowds with herding behaviour. We derive a system of non-linear partial differential equations resembling the Keller-Segel model for chemotaxis, however with a non-monotone interaction. The latter has interesting consequences on the behaviour of the model\\'s solutions, which we highlight in its analysis. In particular we study the possibility of stationary states, the formation of clusters and explore their connection to congestion. We also introduce an efficient numerical simulation approach based on an appropriate hybrid discontinuous Galerkin method, which in particular allows flexible treatment of complicated geometries. Extensive numerical studies also provide a better understanding of the strengths and shortcomings of the herding model, in particular we examine trapping effects of crowds behind nonconvex obstacles. © American Institute of Mathematical Sciences.

Automatic validation of numerical solutions

DEFF Research Database (Denmark)

Stauning, Ole

1997-01-01

This thesis is concerned with ``Automatic Validation of Numerical Solutions''. The basic theory of interval analysis and self-validating methods is introduced. The mean value enclosure is applied to discrete mappings for obtaining narrow enclosures of the iterates when applying these mappings...... differential equations, but in this thesis, we describe how to use the methods for enclosing iterates of discrete mappings, and then later use them for discretizing solutions of ordinary differential equations. The theory of automatic differentiation is introduced, and three methods for obtaining derivatives...... are described: The forward, the backward, and the Taylor expansion methods. The three methods have been implemented in the C++ program packages FADBAD/TADIFF. Some examples showing how to use the three metho ds are presented. A feature of FADBAD/TADIFF not present in other automatic differentiation packages...

Numerical simulation of low pressure die-casting aluminum wheel

Directory of Open Access Journals (Sweden)

Mi Guofa

2009-02-01

Full Text Available The FDM numerical simulation software, ViewCast system, was employed to simulate the low pressure die casting (LPDC of an aluminum wheel. By analyzing the mold-fi lling and solidifi cation stage of the LPDC process, the distribution of liquid fraction, temperature field and solidification pattern of castings were studied. The potential shrinkage defects were predicted to be formed at the rim/spoke junctions, which is in consistence with the X-ray detection result. The distribution pattern of the defects has also been studied. A solution towards reducing such defects has been presented. The cooling capacity of the mold was improved by installing water pipes both in the side mold and the top mold. Analysis on the shrinkage defects under forced cooling mode proved that adding the cooling system in the mold is an effective method for reduction of shrinkage defects.

Developing a numerical simulation for fading in feldspar

International Nuclear Information System (INIS)

Larsen, A.; Greilich, S.; Jain, M.; Murray, A.S.

2009-01-01

Most models describing anomalous fading in feldspars are based on analytical solutions. As an alternative approach we present an entirely numerical model based on statistical sampling that simulates stepwise the charge creation/trapping and recombination in a given phosphor. We assume the number density of electrons and holes at any time to be equal, although the model is not bound to that assumption. The model is flexible enough to be used on any combination of geological and laboratory timescales and for any defined configuration of defects. Using this approach we observed reorganization of nearest-neighbor distances with time. The best agreement with experimental data is achieved if we assume the crystal to consist of small subvolumes (nanocrystals) only within which charge carriers are allowed to recombine.

Numerical simulations of time-resolved quantum electronics

International Nuclear Information System (INIS)

Gaury, Benoit; Weston, Joseph; Santin, Matthieu; Houzet, Manuel; Groth, Christoph; Waintal, Xavier

2014-01-01

Numerical simulation has become a major tool in quantum electronics both for fundamental and applied purposes. While for a long time those simulations focused on stationary properties (e.g. DC currents), the recent experimental trend toward GHz frequencies and beyond has triggered a new interest for handling time-dependent perturbations. As the experimental frequencies get higher, it becomes possible to conceive experiments which are both time-resolved and fast enough to probe the internal quantum dynamics of the system. This paper discusses the technical aspects–mathematical and numerical–associated with the numerical simulations of such a setup in the time domain (i.e. beyond the single-frequency AC limit). After a short review of the state of the art, we develop a theoretical framework for the calculation of time-resolved observables in a general multiterminal system subject to an arbitrary time-dependent perturbation (oscillating electrostatic gates, voltage pulses, time-varying magnetic fields, etc.) The approach is mathematically equivalent to (i) the time-dependent scattering formalism, (ii) the time-resolved non-equilibrium Green’s function (NEGF) formalism and (iii) the partition-free approach. The central object of our theory is a wave function that obeys a simple Schrödinger equation with an additional source term that accounts for the electrons injected from the electrodes. The time-resolved observables (current, density, etc.) and the (inelastic) scattering matrix are simply expressed in terms of this wave function. We use our approach to develop a numerical technique for simulating time-resolved quantum transport. We find that the use of this wave function is advantageous for numerical simulations resulting in a speed up of many orders of magnitude with respect to the direct integration of NEGF equations. Our technique allows one to simulate realistic situations beyond simple models, a subject that was until now beyond the simulation

Robustness of numerical TIG welding simulation of 3D structures in stainless steel 316L

International Nuclear Information System (INIS)

El-Ahmar, W.

2007-04-01

The numerical welding simulation is considered to be one of those mechanical problems that have the great level of nonlinearity and which requires a good knowledge in various scientific fields. The 'Robustness Analysis' is a suitable tool to control the quality and guarantee the reliability of numerical welding results. The robustness of a numerical simulation of welding is related to the sensitivity of the modelling assumptions on the input parameters. A simulation is known as robust if the result that it produces is not very sensitive to uncertainties of the input data. The term 'Robust' was coined in statistics by G.E.P. Box in 1953. Various definitions of greater or lesser mathematical rigor are possible for the term, but in general, referring to a statistical estimator, it means 'insensitive to small deviation from the idealized assumptions for which the estimator is optimized. In order to evaluate the robustness of numerical welding simulation, sensitivity analyses on thermomechanical models and parameters have been conducted. At the first step, we research a reference solution which gives the best agreement with the thermal and mechanical experimental results. The second step consists in determining through numerical simulations which parameters have the largest influence on residual stresses induced by the welding process. The residual stresses were predicted using finite element method performed with Code-Aster of EDF and SYSWELD of ESI-GROUP. An analysis of robustness can prove to be heavy and expensive making it an unjustifiable route. However, only with development such tool of analysis can predictive methods become a useful tool for industry. (author)

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

Science.gov (United States)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

Mitigation of numerical noise for beam loss simulations

CERN Document Server

Kesting, Frederik

2017-01-01

Numerical noise emerges in self-consistent simulations of charged particles, and its mitigation is investigated since the first numerical studies in plasma physics. In accelerator physics, recent studies find an artificial diffusion of the particle beam due to numerical noise in particle-in-cell tracking, which is of particular importance for high intensity machines with a long storage time, as the SIS100 at FAIR or in context of the LIU upgrade at CERN. In beam loss simulations for these projects artificial effects must be distinguished from physical beam loss. Therefore, it is important to relate artificial diffusion to artificial beam loss, and to choose simulation parameters such that physical beam loss is well resolved. As a practical tool, we therefore suggest a scaling law to find optimal simulation parameters for a given maximum percentage of acceptable artificial beam loss.

A Numerical Simulation for a Deterministic Compartmental ...

African Journals Online (AJOL)

In this work, an earlier deterministic mathematical model of HIV/AIDS is revisited and numerical solutions obtained using Eulers numerical method. Using hypothetical values for the parameters, a program was written in VISUAL BASIC programming language to generate series for the system of difference equations from the ...

Computational Enhancements for Direct Numerical Simulations of Statistically Stationary Turbulent Premixed Flames

KAUST Repository

Mukhadiyev, Nurzhan

2017-05-01

Combustion at extreme conditions, such as a turbulent flame at high Karlovitz and Reynolds numbers, is still a vast and an uncertain field for researchers. Direct numerical simulation of a turbulent flame is a superior tool to unravel detailed information that is not accessible to most sophisticated state-of-the-art experiments. However, the computational cost of such simulations remains a challenge even for modern supercomputers, as the physical size, the level of turbulence intensity, and chemical complexities of the problems continue to increase. As a result, there is a strong demand for computational cost reduction methods as well as in acceleration of existing methods. The main scope of this work was the development of computational and numerical tools for high-fidelity direct numerical simulations of premixed planar flames interacting with turbulence. The first part of this work was KAUST Adaptive Reacting Flow Solver (KARFS) development. KARFS is a high order compressible reacting flow solver using detailed chemical kinetics mechanism; it is capable to run on various types of heterogeneous computational architectures. In this work, it was shown that KARFS is capable of running efficiently on both CPU and GPU. The second part of this work was numerical tools for direct numerical simulations of planar premixed flames: such as linear turbulence forcing and dynamic inlet control. DNS of premixed turbulent flames conducted previously injected velocity fluctuations at an inlet. Turbulence injected at the inlet decayed significantly while reaching the flame, which created a necessity to inject higher than needed fluctuations. A solution for this issue was to maintain turbulence strength on the way to the flame using turbulence forcing. Therefore, a linear turbulence forcing was implemented into KARFS to enhance turbulence intensity. Linear turbulence forcing developed previously by other groups was corrected with net added momentum removal mechanism to prevent mean

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

Science.gov (United States)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

On the numerical simulation of population dynamics with density-dependent migrations and the Allee effects

International Nuclear Information System (INIS)

Sweilam, H N; Khader, M M; Al-Bar, F R

2008-01-01

In this paper, the variational iteration method (VIM) and the Adomian decomposition method (ADM) are presented for the numerical simulation of the population dynamics model with density-dependent migrations and the Allee effects. The convergence of ADM is proved for the model problem. The results obtained by these methods are compared to the exact solution. It is found that these methods are always converges to the right solutions with high accuracy. Furthermore, VIM needs relative less computational work than ADM

Mathematical study and numerical simulations of bi-kinetic plasma sheaths

International Nuclear Information System (INIS)

Badsi, Mehdi

2016-01-01

This thesis focuses on the construction and the numerical simulation theoretical models of plasmas in interaction with an absorbing wall. These models are based on two species Vlasov-Poisson or Vlasov-Ampere systems in the presence of boundary conditions. The expected stationary solutions must verify the balance of the flux of charges in the orthogonal direction to the wall. This feature is called the ambi-polarity. Through the study of a non linear Poisson equation, we prove the well-posedness of 1d-1v stationary Vlasov-Poisson system, for which we determine incoming particles distributions and a wall potential that induces the ambi-polarity as well as a non negative charge density hold. We also give a quantitative estimates of the thickness of the boundary layer that develops at the wall. These results are illustrated numerically. We prove the linear stability of the electronic stationary solution for a non-stationary Vlasov-Ampere system. Finally, we study a 1d-3v stationary Vlasov-Poisson system in the presence of a constant and parallel to the wall magnetic field. We determine incoming particles distributions and a wall potential so that the ambi-polarity holds. We study a non linear Poisson equation through a non linear functional energy that admits minimizers. We established some bounds on the numerical parameters inside which, our model is relevant and we propose an interpretation of the results. (author)

Direct numerical simulations of evaporating droplets in turbulence

Science.gov (United States)

Palmore, John; Desjardins, Olivier

2015-11-01

This work demonstrates direct numerical simulations of evaporating two phase flows, with applications to studying combustion in aircraft engines. Inside the engine, liquid fuel is injected into the combustion chamber where it atomizes into droplets and evaporates. Combustion occurs as the fuel vapor mixes with the surrounding flow of turbulent gas. Understanding combustion, therefore, requires studying evaporation in a turbulent flow and the resulting vapor distribution. We study the problem using a finite volume framework to solve the Navier-Stokes and scalar transport equations under a low-Mach assumption [Desjardins et al., J. Comp. Phys., 2008]. The liquid-gas interface is tracked using a conservative level-set method [Desjardins et al., J. Comp. Phys., 2008] which allows for a sharp reconstruction of the discontinuity across the interface. Special care is taken in the discretization of cells near the liquid-gas interface to ensure the stability and accuracy of the solution. Results are discussed for non-reacting simulations of liquid droplets evaporating into a turbulent field of inert gas.

Rippled shock front solutions for testing hydrodynamic stability simulations

International Nuclear Information System (INIS)

Munro, D.H.

1989-01-01

The response of a shock front to arbitrary small perturbations can be calculated analytically. Such rippled shock front solutions are useful for determining the accuracy of hydrodynamic simulation codes such as LASNEX [Comments Plasma Phys. Controlled Fusion 2, 51 (1977)], which are used to compute perturbation growth in inertial fusion targets. The LASNEX fractional errors are of order κ 2 L 2 , where κ is the transverse wavenumber of the perturbation, and L is the largest zone dimension. Numerical errors are about 25% for a calculation using 26 zones per transverse wavelength

Spurious solutions in few-body equations. II. Numerical investigations

International Nuclear Information System (INIS)

Adhikari, S.K.

1979-01-01

A recent analytic study of spurious solutions in few-body equations by Adhikari and Gloeckle is here complemented by numerical investigations. As proposed by Adhikari and Gloeckle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence, if proven convenient, the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations

Numerical Hydrodynamics in General Relativity

Directory of Open Access Journals (Sweden)

Font José A.

2003-01-01

Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.

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

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.

Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

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.)

Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

Energy Technology Data Exchange (ETDEWEB)

Kotler, Z.; Neria, E.; Nitzan, A. (Tel Aviv Univ. (Israel). School of Chemistry)

1991-02-01

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 soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

Fluid-structure-interaction of the pressurized water reactor core internals during blowdown - numerical simulation with a homogenization model

International Nuclear Information System (INIS)

Benner, J.

1984-03-01

A method for the numerical simulation of the Pressurized Water Reactor (PWR) core internal's behaviour during a blowdown accident is described, by which the motion of the reactor core and the interaction of the fuel elements with the core barrel and the coolant medium is calculated. Furthermore, some simple models for the support columns, lower and upper core support and the grid plate are provided. All these models have been implemented into the code Flux-4. For the solution of the very complex, coupled equations of motions for fluid and fuel rods an efficient numerical solution technique has been developed. With the new code-version Flux-5 the PWR-blowdown is parametically investigated. The calculated core barrel loadings are compared with Flux-4 results, simulating the core's inertia by a mass ring of HDR type. (orig.) [de

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

International Nuclear Information System (INIS)

Pappas, George

2009-01-01

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R ISCO ), the rotation frequency and the epicyclic frequencies Ω ρ , Ω z . Finally we present some results of the comparison.

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

Energy Technology Data Exchange (ETDEWEB)

Pappas, George, E-mail: gpappas@phys.uoa.g [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)

2009-10-01

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R{sub ISCO}), the rotation frequency and the epicyclic frequencies {Omega}{sub {rho}}, {Omega}{sub z}. Finally we present some results of the comparison.

Numerical simulation of flow fields and particle trajectories

DEFF Research Database (Denmark)

Mayer, Stefan

2000-01-01

. The time-dependent flow is approximated with a continuous sequence of steady state creeping flow fields, where metachronously beating ciliary bands are modelled by linear combinations of singularity solutions to the Stokes equations. Generally, the computed flow fields can be divided into an unsteady......A model describing the ciliary driven flow and motion of suspended particles in downstream suspension feeders is developed. The quasi-steady Stokes equations for creeping flow are solved numerically in an unbounded fluid domain around cylindrical bodies using a boundary integral formulation...... in the simulated unsteady ciliary driven flow. A fraction of particles appear to follow trajectories, that resemble experimentally observed particle capture events in the downstream feeding system of the polycheate Sabella penicillus, indicating that particles can be captured by ciliary systems without mechanical...

GITTAM program for numerical simulation of one-dimensional targets TIS. Part 3

International Nuclear Information System (INIS)

Basko, M.M.; Sokolovskij, M.V.

1989-01-01

Results of testing calculations according to GITTAM program, developed for numeric simulation of one-dimensional thermonuclear targets of heavy-ion synthesis are presented. Finite-difference method for solving a system of one-dimensional hydrodynamics equations with heat conductivity, radiation diffusion and thermonuclear combustion is used in the GITTAM program. In the tests presented, based on simple automodel solutions, adiabatic motion as well as distribution of shock, thermal and radial waves in gas with simple polytron state equation is investigated. 3 refs.; 6 figs

Confidence in Numerical Simulations

Energy Technology Data Exchange (ETDEWEB)

Hemez, Francois M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-02-23

This PowerPoint presentation offers a high-level discussion of uncertainty, confidence and credibility in scientific Modeling and Simulation (M&S). It begins by briefly evoking M&S trends in computational physics and engineering. The first thrust of the discussion is to emphasize that the role of M&S in decision-making is either to support reasoning by similarity or to “forecast,” that is, make predictions about the future or extrapolate to settings or environments that cannot be tested experimentally. The second thrust is to explain that M&S-aided decision-making is an exercise in uncertainty management. The three broad classes of uncertainty in computational physics and engineering are variability and randomness, numerical uncertainty and model-form uncertainty. The last part of the discussion addresses how scientists “think.” This thought process parallels the scientific method where by a hypothesis is formulated, often accompanied by simplifying assumptions, then, physical experiments and numerical simulations are performed to confirm or reject the hypothesis. “Confidence” derives, not just from the levels of training and experience of analysts, but also from the rigor with which these assessments are performed, documented and peer-reviewed.

Development of Three-Layer Simulation Model for Freezing Process of Food Solution Systems

Science.gov (United States)

Kaminishi, Koji; Araki, Tetsuya; Shirakashi, Ryo; Ueno, Shigeaki; Sagara, Yasuyuki

A numerical model has been developed for simulating freezing phenomena of food solution systems. The cell model was simplified to apply to food solution systems, incorporating with the existence of 3 parts such as unfrozen, frozen and moving boundary layers. Moreover, the moving rate of freezing front model was also introduced and calculated by using the variable space network method proposed by Murray and Landis (1957). To demonstrate the validity of the model, it was applied to the freezing processes of coffee solutions. Since the model required the phase diagram of the material to be frozen, the initial freezing temperatures of 1-55 % coffee solutions were measured by the DSC method. The effective thermal conductivity for coffee solutions was determined as a function of temperature and solute concentration by using the Maxwell - Eucken model. One-dimensional freezing process of 10 % coffee solution was simulated based on its phase diagram and thermo-physical properties. The results were good agreement with the experimental data and then showed that the model could accurately describe the change in the location of the freezing front and the distributions of temperature as well as ice fraction during a freezing process.

Numerical solution of distributed order fractional differential equations

Science.gov (United States)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Numerical simulation of hypersonic flight experiment vehicle

OpenAIRE

Yamamoto, Yukimitsu; Yoshioka, Minako; 山本　行光; 吉岡　美菜子

1994-01-01

Hypersonic aerodynamic characteristics of Hypersonic FLight EXperiment (HYFLEX vehicle were investigated by numerical simulations using Navier-Stokes CFD (Computational Fluid Dynamics) code of NAL. Numerical results were compared with experimental data obtained at Hypersonic Wind Tunnel at NAL. In order to investigate real flight aerodynamic characteristics. numerical calculations corresponding to the flight conditions suffering from maximum aero thermodynamic heating were also made and the d...

Numerical simulation of mechatronic sensors and actuators

CERN Document Server

Kaltenbacher, Manfred

2007-01-01

Focuses on the physical modeling of mechatronic sensors and actuators and their precise numerical simulation using the Finite Element Method (FEM). This book discusses the physical modeling as well as numerical computation. It also gives a comprehensive introduction to finite elements, including their computer implementation.

Numerical solution of ordinary differential equations. For classical, relativistic and nano systems

International Nuclear Information System (INIS)

Greenspan, D.

2006-01-01

An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)

Numerical simulation methods to richtmyer-meshkov instabilities

International Nuclear Information System (INIS)

Zhou Ning; Yu Yan; Tang Weijun

2003-01-01

Front tracking algorithms have generally assumed that the computational medium is divided into piece-wise smooth subdomains bounded by interfaces and that strong wave interactions are solved via Riemann solutions. However, in multi-dimensional cases, the Riemann solution of multiple shock wave interactions are far more complicated and still subject to analytical study. For this reason, it is very desirable to be able to track contact discontinuities only. A new numerical algorithm to couple a tracked contact surface and an untracked strong shock wave are described. The new tracking algorithm reduces the complication of computation, and maintains the sharp resolution of the contact surface. The numerical results are good. (authors)

Numerical simulation of plasmas

International Nuclear Information System (INIS)

Dnestrovskii, Y.N.; Kostomarov, D.P.

1986-01-01

This book contains a modern consistent and systematic presentation of numerical computer simulation of plasmas in controlled thermonuclear fusion. The authors focus on the Soviet research in mathematical modelling of Tokamak plasmas, and present kinetic hydrodynamic and transport models with special emphasis on the more recent hybrid models. Compared with the first edition (in Russian) this book has been greatly revised and updated. (orig./WL)

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)

Parallel 3-D numerical simulation of dielectric barrier discharge plasma actuators

Science.gov (United States)

Houba, Tomas

Dielectric barrier discharge plasma actuators have shown promise in a range of applications including flow control, sterilization and ozone generation. Developing numerical models of plasma actuators is of great importance, because a high-fidelity parallel numerical model allows new design configurations to be tested rapidly. Additionally, it provides a better understanding of the plasma actuator physics which is useful for further innovation. The physics of plasma actuators is studied numerically. A loosely coupled approach is utilized for the coupling of the plasma to the neutral fluid. The state of the art in numerical plasma modeling is advanced by the development of a parallel, three-dimensional, first-principles model with detailed air chemistry. The model incorporates 7 charged species and 18 reactions, along with a solution of the electron energy equation. To the author's knowledge, a parallel three-dimensional model of a gas discharge with a detailed air chemistry model and the solution of electron energy is unique. Three representative geometries are studied using the gas discharge model. The discharge of gas between two parallel electrodes is used to validate the air chemistry model developed for the gas discharge code. The gas discharge model is then applied to the discharge produced by placing a dc powered wire and grounded plate electrodes in a channel. Finally, a three-dimensional simulation of gas discharge produced by electrodes placed inside a riblet is carried out. The body force calculated with the gas discharge model is loosely coupled with a fluid model to predict the induced flow inside the riblet.

Implementation of numerical integration schemes for the simulation of magnetic SMA constitutive response

International Nuclear Information System (INIS)

Kiefer, B; Bartel, T; Menzel, A

2012-01-01

Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic variant reorientation to limit complexity. The first updating scheme is based on the numerical integration of the reorientation strain evolution equation and represents a classical predictor–corrector-type general return mapping algorithm. In the second approach, the inequality-constrained optimization problem associated with internal variable evolution is converted into an unconstrained problem via Fischer–Burmeister complementarity functions and then iteratively solved in standard Newton–Raphson format. Simulations are verified by comparison to closed-form solutions for experimentally relevant loading cases. (paper)

Numerical simulation of single-phase and multiphase non-Darcy flowin porous and fractured reservoirs

Energy Technology Data Exchange (ETDEWEB)

Wu, Yu-Shu

2000-06-02

A numerical method as well as a theoretical study of non-Darcy fluid flow of through porous and fractured reservoirs is described. The non-Darcy flow is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in geothermal reservoirs.

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

Science.gov (United States)

Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

Numerical Simulation of 3D Solid-Liquid Turbulent Flow in a Low Specific Speed Centrifugal Pump: Flow Field Analysis

Directory of Open Access Journals (Sweden)

Baocheng Shi

2014-06-01

Full Text Available For numerically simulating 3D solid-liquid turbulent flow in low specific speed centrifugal pumps, the iteration convergence problem caused by complex internal structure and high rotational speed of pump is always a problem for numeral simulation researchers. To solve this problem, the combination of three measures of dynamic underrelaxation factor adjustment, step method, and rotational velocity control means according to residual curves trends of operating parameters was used to improve the numerical convergence. Numeral simulation of 3D turbulent flow in a low specific speed solid-liquid centrifugal pump was performed, and the results showed that the improved solution strategy is greatly helpful to the numerical convergence. Moreover, the 3D turbulent flow fields in pumps have been simulated for the bottom ash-particles with the volume fraction of 10%, 20%, and 30% at the same particle diameter of 0.1 mm. The two-phase calculation results are compared with those of single-phase clean water flow. The calculated results gave the main region of the abrasion of the impeller and volute casing and improve the hydraulic design of the impeller in order to decrease the abrasion and increase the service life of the pump.

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2008-01-01

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Numerical solution of boundary-integral equations for molecular electrostatics.

Science.gov (United States)

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Dynamic load synthesis for shock numerical simulation in space structure design

Science.gov (United States)

Monti, Riccardo; Gasbarri, Paolo

2017-08-01

Pyroshock loads are the most stressing environments that a space equipment experiences during its operating life from a mechanical point of view. In general, the mechanical designer considers the pyroshock analysis as a very demanding constraint. Unfortunately, due to the non-linear behaviour of the structure under such loads, only the experimental tests can demonstrate if it is able to withstand these dynamic loads. By taking all the previous considerations into account, some preliminary information about the design correctness could be done by performing ;ad-hoc; numerical simulations, for example via commercial finite element software (i.e. MSC Nastran). Usually these numerical tools face the shock solution in two ways: 1) a direct mode, by using a time dependent enforcement and by evaluating the time-response and space-response as well as the internal forces; 2) a modal basis approach, by considering a frequency dependent load and of course by evaluating internal forces in the frequency domain. This paper has the main aim to develop a numerical tool to synthetize the time dependent enforcement based on deterministic and/or genetic algorithm optimisers. In particular starting from a specified spectrum in terms of SRS (Shock Response Spectrum) a time dependent discrete function, typically an acceleration profile, will be obtained to force the equipment by simulating the shock event. The synthetizing time and the interface with standards numerical codes will be two of the main topics dealt with in the paper. In addition a congruity and consistency methodology will be presented to ensure that the identified time dependent loads fully match the specified spectrum.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark’s Method with Netwon-Raphson Iteration Revisited

Directory of Open Access Journals (Sweden)

Markou A.A.

2018-03-01

Full Text Available Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Numerical simulation of boron injection in a BWR

Energy Technology Data Exchange (ETDEWEB)

Tinoco, Hernan, E-mail: htb@forsmark.vattenfall.s [Forsmarks Kraftgrupp AB, SE-742 03 Osthammar (Sweden); Buchwald, Przemyslaw [Reactor Technology, Royal Institute of Technology, SE-100 44 Stockholm (Sweden); Frid, Wiktor, E-mail: wiktor@reactor.sci.kth.s [Reactor Technology, Royal Institute of Technology, SE-100 44 Stockholm (Sweden)

2010-02-15

The present study constitutes a first step to understand the process of boron injection, transport and mixing in a BWR. It consists of transient CFD simulations of boron injection in a model of the downcomer of Forsmark's Unit 3 containing about 6 million elements. The two cases studied are unintentional start of boron injection under normal operation and loss of offsite power with partial ATWS leaving 10% of the core power uncontrolled. The flow conditions of the second case are defined by means of an analysis with RELAP5, assuming boron injection start directly after the first ECCS injection. Recent publications show that meaningful conservative results may be obtained for boron or thermal mixing in PWRs with grids as coarse as that utilized here, provided that higher order discretization schemes are used to minimize numerical diffusion. The obtained results indicate an apparently strong influence of the scenario in the behavior of the injection process. The normal operation simulation shows that virtually all boron solution flows down to the Main Recirculation Pump inlet located directly below the boron inlet nozzle. The loss of offsite power simulation shows initially a spread of the boron solution over the entire sectional area of the lower part of the downcomer filled with colder water. This remaining effect of the ECCS injection lasts until all this water has left the downcomer. Above this region, the boron injection jet develops in a vertical streak, eventually resembling the injection of the normal operation scenario. Due to the initial spread, this boron injection will probably cause larger temporal and spatial concentration variations in the core. In both cases, these variations may cause reactivity transients and fuel damage due to local power escalation. To settle this issue, an analysis using an extended model containing the downcomer, the MRPs and the Lower Plenum will be carried out. Also, the simulation time will be extended to a scale of

Numerical simulation of boron injection in a BWR

International Nuclear Information System (INIS)

Tinoco, Hernan; Buchwald, Przemyslaw; Frid, Wiktor

2010-01-01

The present study constitutes a first step to understand the process of boron injection, transport and mixing in a BWR. It consists of transient CFD simulations of boron injection in a model of the downcomer of Forsmark's Unit 3 containing about 6 million elements. The two cases studied are unintentional start of boron injection under normal operation and loss of offsite power with partial ATWS leaving 10% of the core power uncontrolled. The flow conditions of the second case are defined by means of an analysis with RELAP5, assuming boron injection start directly after the first ECCS injection. Recent publications show that meaningful conservative results may be obtained for boron or thermal mixing in PWRs with grids as coarse as that utilized here, provided that higher order discretization schemes are used to minimize numerical diffusion. The obtained results indicate an apparently strong influence of the scenario in the behavior of the injection process. The normal operation simulation shows that virtually all boron solution flows down to the Main Recirculation Pump inlet located directly below the boron inlet nozzle. The loss of offsite power simulation shows initially a spread of the boron solution over the entire sectional area of the lower part of the downcomer filled with colder water. This remaining effect of the ECCS injection lasts until all this water has left the downcomer. Above this region, the boron injection jet develops in a vertical streak, eventually resembling the injection of the normal operation scenario. Due to the initial spread, this boron injection will probably cause larger temporal and spatial concentration variations in the core. In both cases, these variations may cause reactivity transients and fuel damage due to local power escalation. To settle this issue, an analysis using an extended model containing the downcomer, the MRPs and the Lower Plenum will be carried out. Also, the simulation time will be extended to a scale of several

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

Energy Technology Data Exchange (ETDEWEB)

Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com

2008-04-14

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Numerical simulation of 3D unsteady flow in a rotating pump by dynamic mesh technique

International Nuclear Information System (INIS)

Huang, S; Guo, J; Yang, F X

2013-01-01

In this paper, the numerical simulation of unsteady flow for three kinds of typical rotating pumps, roots blower, roto-jet pump and centrifugal pump, were performed using the three-dimensional Dynamic Mesh technique. In the unsteady simulation, all the computational domains, as stationary, were set in one inertial reference frame. The motions of the solid boundaries were defined by the Profile file in FLUENT commercial code, in which the rotational orientation and speed of the rotors were specified. Three methods (Spring-based Smoothing, Dynamic Layering and Local Re-meshing) were used to achieve mesh deformation and re-meshing. The unsteady solutions of flow field and pressure distribution were solved. After a start-up stage, the flow parameters exhibit time-periodic behaviour corresponding to blade passing frequency of rotor. This work shows that Dynamic Mesh technique could achieve numerical simulation of three-dimensional unsteady flow field in various kinds of rotating pumps and have a strong versatility and broad application prospects

Numerical simulation of edge plasma in tokamak

International Nuclear Information System (INIS)

Chen Yiping; Qiu Lijian

1996-02-01

The transport process and transport property of plasma in edge layer of Tokamak are simulated by solving numerically two-dimensional and multi-fluid plasma transport equations using suitable simulation code. The simulation results can show plasma parameter distribution characteristics in the area of edge layer, especially the characteristics near the first wall and divertor target plate. The simulation results play an important role in the design of divertor and first wall of Tokamak. (2 figs)

Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz

KAUST Repository

Yuan, Xuefei

2012-07-01

Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of . r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the . x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated. © 2012 Elsevier Inc.

Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz

KAUST Repository

Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E.

2012-01-01

Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of . r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the . x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated. © 2012 Elsevier Inc.

Numerical Simulation of Cylindrical Solitary Waves in Periodic Media

KAUST Repository

Quezada de Luna, Manuel; Ketcheson, David I.

2013-01-01

We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.

Numerical Simulation of Cylindrical Solitary Waves in Periodic Media

KAUST Repository

Quezada de Luna, Manuel

2013-07-14

We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

International Nuclear Information System (INIS)

Jo, Jong Chull; Shin, Won Ky

1997-01-01

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available

Numerical simulation of radial compressor stage

Science.gov (United States)

Syka, T.; Luňáček, O.

2013-04-01

Article describes numerical simulations of air flow in radial compressor stage in NUMECA CFD software. In simulations geometry variants with and without seals are used. During tasks evaluating was observed seals influence on flow field and performance parameters of compressor stage. Also is described CFDresults comparison with results from design software based on experimental measurements and monitoring of influence of seals construction on compressor stage efficiency.

Numerical simulation of radial compressor stage

OpenAIRE

Luňáček O.; Syka T.

2013-01-01

Article describes numerical simulations of air flow in radial compressor stage in NUMECA CFD software. In simulations geometry variants with and without seals are used. During tasks evaluating was observed seals influence on flow field and performance parameters of compressor stage. Also is described CFDresults comparison with results from design software based on experimental measurements and monitoring of influence of seals construction on compressor stage efficiency.

Non-dissipative kinetic simulation and analytical solution of three-mode equations of ion temperature gradient instability

International Nuclear Information System (INIS)

Watanabe, T.-H.; Sugama, H.; Sato, T.

1999-12-01

A non-dissipative drift kinetic simulation scheme, which rigorously satisfies the time-reversibility, is applied to the three-mode coupling problem of the ion temperature gradient (ITG) instability. It is found from the simulation that the three-mode ITG system repeats growth and decay with a period which shows a logarithmic divergence for infinitesimal initial perturbations. Accordingly, time average of the mode amplitude vanishes, as the initial amplitude approaches to zero. An exact solution is analytically given for a class of initial conditions. An excellent agreement is confirmed between the analytical solution and numerical results. The results obtained here provide a useful reference for basic benchmarking of theories and simulation of the ITG modes. (author)

Simulation of ground-water flow and solute transport in the Glen Canyon aquifer, East-Central Utah

Science.gov (United States)

Freethey, Geoffrey W.; Stolp, Bernard J.

2010-01-01

The extraction of methane from coal beds in the Ferron coal trend in central Utah started in the mid-1980s. Beginning in 1994, water from the extraction process was pressure injected into the Glen Canyon aquifer. The lateral extent of the aquifer that could be affected by injection is about 7,600 square miles. To address regional-scale effects of injection over a decadal time frame, a conceptual model of ground-water movement and transport of dissolved solids was formulated. A numerical model that incorporates aquifer concepts was then constructed and used to simulate injection.The Glen Canyon aquifer within the study area is conceptualized in two parts—an active area of ground-water flow and solute transport that exists between recharge areas in the San Rafael Swell and Desert, Waterpocket Fold, and Henry Mountains and discharge locations along the Muddy, Dirty Devil, San Rafael, and Green Rivers. An area of little or negligible ground-water flow exists north of Price, Utah, and beneath the Wasatch Plateau. Pressurized injection of coal-bed methane production water occurs in this area where dissolved-solids concentrations can be more than 100,000 milligrams per liter. Injection has the potential to increase hydrologic interaction with the active flow area, where dissolved-solids concentrations are generally less than 3,000 milligrams per liter.Pressurized injection of coal-bed methane production water in 1994 initiated a net addition of flow and mass of solutes into the Glen Canyon aquifer. To better understand the regional scale hydrologic interaction between the two areas of the Glen Canyon aquifer, pressurized injection was numerically simulated. Data constraints precluded development of a fully calibrated simulation; instead, an uncalibrated model was constructed that is a plausible representation of the conceptual flow and solute-transport processes. The amount of injected water over the 36-year simulation period is about 25,000 acre-feet. As a result

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.

Numerical simulation of "an American haboob"

OpenAIRE

Vukovic, A.; Vujadinovic, M.; Pejanovic, G.; Andric, J.; Kumjian, M. R.; Djurdjevic, V.; Dacic, M.; Prasad, A. K.; El-Askary, H. M.; Paris, B. C.; Petkovic, S.; Nickovic, S.; Sprigg, W. A.

2014-01-01

A dust storm of fearful proportions hit Phoenix in the early evening hours of 5 July 2011. This storm, an American haboob, was predicted hours in advance because numerical, land–atmosphere modeling, computing power and remote sensing of dust events have improved greatly over the past decade. High-resolution numerical models are required for accurate simulation of the small scales of the haboob process, with high velocity surface winds produced by strong convection and severe...

Confidence in Numerical Simulations

International Nuclear Information System (INIS)

Hemez, Francois M.

2015-01-01

This PowerPoint presentation offers a high-level discussion of uncertainty, confidence and credibility in scientific Modeling and Simulation (M&S). It begins by briefly evoking M&S trends in computational physics and engineering. The first thrust of the discussion is to emphasize that the role of M&S in decision-making is either to support reasoning by similarity or to ''forecast,'' that is, make predictions about the future or extrapolate to settings or environments that cannot be tested experimentally. The second thrust is to explain that M&S-aided decision-making is an exercise in uncertainty management. The three broad classes of uncertainty in computational physics and engineering are variability and randomness, numerical uncertainty and model-form uncertainty. The last part of the discussion addresses how scientists ''think.'' This thought process parallels the scientific method where by a hypothesis is formulated, often accompanied by simplifying assumptions, then, physical experiments and numerical simulations are performed to confirm or reject the hypothesis. ''Confidence'' derives, not just from the levels of training and experience of analysts, but also from the rigor with which these assessments are performed, documented and peer-reviewed.

Direct Numerical Simulations of Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Livescu, D; Wei, T; Petersen, M R

2011-01-01

The development of the Rayleigh-Taylor mixing layer is studied using data from an extensive new set of Direct Numerical Simulations (DNS), performed on the 0.5 Petaflops, 150k compute cores BG/L Dawn supercomputer at Lawrence Livermore National Laboratory. This includes a suite of simulations with grid size of 1024 2 × 4608 and Atwood number ranging from 0.04 to 0.9, in order to examine small departures from the Boussinesq approximation as well as large Atwood number effects, and a high resolution simulation of grid size 4096 2 × 4032 and Atwood number of 0.75. After the layer width had developed substantially, additional branched simulations have been run under reversed and zero gravity conditions. While the bulk of the results will be published elsewhere, here we present preliminary results on: 1) the long-standing open question regarding the discrepancy between the numerically and experimentally measured mixing layer growth rates and 2) mixing characteristics.

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.

Numerical simulation of ventilation air movement in partitioned offices

Energy Technology Data Exchange (ETDEWEB)

Plett, E.G.; Soultogiannis, A.A.; Jouini, D.B. (Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, Ontario (Canada))

1993-01-01

Good air quality can only be assured throughout an office complex if each workspace receives an adequate supply of ventilation air. The likelihood of achieving this situation would be increased if the building engineer had a means of easily predicting the air movement in each office configuration. A simple computer-based solution to this need is proposed. To this end, the development and validation testing of a numerical solution technique to simulate the ventilation air movement in a room or office is described. The predictions of the two-dimensional, isothermal, inviscid formulation are seen to be in good agreement with experimentally measured airflows in configurations of interest. The computer code is then used to illustrate the airflow in offices served by a single row of supply air diffusers, when partitions are used to divide the space into smaller workspaces. It is observed that the partitions distort the airflow patterns to the extent that it would be difficult to provide desirable ventilation airflows to all the workspaces formed by the partitions. (au) (26 refs.)

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 simulation of heat transfer in metal foams

Science.gov (United States)

Gangapatnam, Priyatham; Kurian, Renju; Venkateshan, S. P.

2018-02-01

This paper reports a numerical study of forced convection heat transfer in high porosity aluminum foams. Numerical modeling is done considering both local thermal equilibrium and non local thermal equilibrium conditions in ANSYS-Fluent. The results of the numerical model were validated with experimental results, where air was forced through aluminum foams in a vertical duct at different heat fluxes and velocities. It is observed that while the LTE model highly under predicts the heat transfer in these foams, LTNE model predicts the Nusselt number accurately. The novelty of this study is that once hydrodynamic experiments are conducted the permeability and porosity values obtained experimentally can be used to numerically simulate heat transfer in metal foams. The simulation of heat transfer in foams is further extended to find the effect of foam thickness on heat transfer in metal foams. The numerical results indicate that though larger foam thicknesses resulted in higher heat transfer coefficient, this effect weakens with thickness and is negligible in thick foams.

Application of CPML to two-dimension numerical simulation of nuclear electromagnetic pulse from air explosions

International Nuclear Information System (INIS)

Gao Chunxia; Wang Lianghou

2005-01-01

The characteristics of different types of PML were analyzed and the convolutional PML was chosen to truncate the open boundaries in numerical simulation of nuclear electromagnetic pulse from air explosions. On the basis of the split-field PML and the plane-wave solution of electromagnetic field in free space, the unsplit-field PML was constructed. By applying the convolutional theorem of Fourier transform, the discrete iterative equations of electromagnetic field components were presented in the CPML media under the two-dimension prolate-spheroidal coordinate system. The numerical results indicate that the method of CPML can largely decrease calculation errors of boundary fields. (authors)

Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ

DEFF Research Database (Denmark)

Kutanaai, S Soleimani; Roshan, Naeem; Vosoughi, A

2012-01-01

This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation of der...... in solution of partial differential equations (PDEs).......This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation...... is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method...

Numerical simulation of radial compressor stage

Directory of Open Access Journals (Sweden)

Luňáček O.

2013-04-01

Full Text Available Article describes numerical simulations of air flow in radial compressor stage in NUMECA CFD software. In simulations geometry variants with and without seals are used. During tasks evaluating was observed seals influence on flow field and performance parameters of compressor stage. Also is described CFDresults comparison with results from design software based on experimental measurements and monitoring of influence of seals construction on compressor stage efficiency.

Numerical Simulation Of Silicon-Ribbon Growth

Science.gov (United States)

Woda, Ben K.; Kuo, Chin-Po; Utku, Senol; Ray, Sujit Kumar

1987-01-01

Mathematical model includes nonlinear effects. In development simulates growth of silicon ribbon from melt. Takes account of entire temperature and stress history of ribbon. Numerical simulations performed with new model helps in search for temperature distribution, pulling speed, and other conditions favoring growth of wide, flat, relatively defect-free silicon ribbons for solar photovoltaic cells at economically attractive, high production rates. Also applicable to materials other than silicon.

Experiments and Numerical Simulations of Electrodynamic Tether

Science.gov (United States)

Iki, Kentaro; Kawamoto, Satomi; Takahashi, Ayaka; Ishimoto, Tomori; Yanagida, Atsushi; Toda, Susumu

As an effective means of suppressing space debris growth, the Aerospace Research and Development Directorate of the Japan Aerospace Exploration Agency (JAXA) has been investigating an active space debris removal system that employs highly efficient electrodynamic tether (EDT) technology for orbital transfer. This study investigates tether deployment dynamics by means of on-ground experiments and numerical simulations of an electrodynamic tether system. Some key parameters used in the numerical simulations, such as the elastic modulus and damping ratio of the tether, the spring constant of the coiling of the tether, and deployment friction, must be estimated, and various experiments are conducted to determine these values. As a result, the following values were obtained: The elastic modulus of the tether was 40 GPa, and the damping ratio of the tether was 0.02. The spring constant and the damping ratio of the tether coiling were 10-4 N/m and 0.025 respectively. The deployment friction was 0.038ν + 0.005 N. In numerical simulations using a multiple mass tether model, tethers with lengths of several kilometers are deployed and the attitude dynamics of satellites attached to the end of the tether and tether libration are calculated. As a result, the simulations confirmed successful deployment of the tether with a length of 500 m using the electrodynamic tether system.

Direct Numerical Simulation of Driven Cavity Flows

NARCIS (Netherlands)

Verstappen, R.; Wissink, J.G.; Veldman, A.E.P.

Direct numerical simulations of 2D driven cavity flows have been performed. The simulations exhibit that the flow converges to a periodically oscillating state at Re=11,000, and reveal that the dynamics is chaotic at Re=22,000. The dimension of the attractor and the Kolmogorov entropy have been

Direct numerical simulation and modeling of turbulent natural convection in a vertical differentially heated slot; Simulation numerique directe et modelisation de la convection naturelle turbulente dans un canal differentiellement chauffe

Energy Technology Data Exchange (ETDEWEB)

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{sup 5} and 5.4*10{sup 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.

Numerical simulation of the effects of variation of angle of attack and sweep angle on vortex breakdown over delta wings

Science.gov (United States)

Ekaterinaris, J. A.; Schiff, Lewis B.

1990-01-01

In the present investigation of the vortical flowfield structure over delta wings at high angles of attack, three-dimensional Navier-Stokes numerical simulations were conducted to predict the complex leeward flowfield characteristics; these encompass leading-edge separation, secondary separation, and vortex breakdown. Attention is given to the effect on solution accuracy of circumferential grid-resolution variations in the vicinity of the wing leading edge, and well as to the effect of turbulence modeling on the solutions. When a critical angle-of-attack was reached, bubble-type vortex breakdown was found. With further angle-of-attack increase, a change from bubble-type to spiral-type vortex breakdown was predicted by the numerical solution.

Numerical simulation of filamentation in laser-plasma interactions

International Nuclear Information System (INIS)

Nicholas, D.J.; Sajjadi, S.G.

1986-01-01

Numerical studies of beam filamentation in laser-produced plasma are presented. This involves the numerical solution of the parabolic wave equation, known as the Schroedinger equation, coupled with the thermal transport equations for both ions and electrons, in two dimensions. The solution of the resulting equation with non-linear refractive index due to thermal and pondermotive forces, shows self-focusing and a variety of strong aberration effects. Intensity amplification at the final focus is found to be between one and two orders of magnitude greater than the initial beam intensity, governed in general by diffraction and aberration effects within the beam. (author)

Numerical simulation of filamentation in laser-plasma interactions

Energy Technology Data Exchange (ETDEWEB)

Nicholas, D.J.; Sajjadi, S.G.

1986-05-14

Numerical studies of beam filamentation in laser-produced plasma are presented. This involves the numerical solution of the parabolic wave equation, known as the Schroedinger equation, coupled with the thermal transport equations for both ions and electrons, in two dimensions. The solution of the resulting equation with non-linear refractive index due to thermal and pondermotive forces, shows self-focusing and a variety of strong aberration effects. Intensity amplification at the final focus is found to be between one and two orders of magnitude greater than the initial beam intensity, governed in general by diffraction and aberration effects within the beam.

Numerical simulation of avascular tumor growth

Energy Technology Data Exchange (ETDEWEB)

Slezak, D Fernandez; Suarez, C; Soba, A; Risk, M; Marshall, G [Laboratorio de Sistemas Complejos, Departamento de Computacion, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires (C1428EGA) Buenos Aires (Argentina)

2007-11-15

A mathematical and numerical model for the description of different aspects of microtumor development is presented. The model is based in the solution of a system of partial differential equations describing an avascular tumor growth. A detailed second-order numeric algorithm for solving this system is described. Parameters are swiped to cover a range of feasible physiological values. While previous published works used a single set of parameters values, here we present a wide range of feasible solutions for tumor growth, covering a more realistic scenario. The model is validated by experimental data obtained with a multicellular spheroid model, a specific type of in vitro biological model which is at present considered to be optimum for the study of complex aspects of avascular microtumor physiology. Moreover, a dynamical analysis and local behaviour of the system is presented, showing chaotic situations for particular sets of parameter values at some fixed points. Further biological experiments related to those specific points may give potentially interesting results.

Limit Theorems and Their Relation to Solute Transport in Simulated Fractured Media

Science.gov (United States)

Reeves, D. M.; Benson, D. A.; Meerschaert, M. M.

2003-12-01

Solute particles that travel through fracture networks are subject to wide velocity variations along a restricted set of directions. This may result in super-Fickian dispersion along a few primary scaling directions. The fractional advection-dispersion equation (FADE), a modification of the original advection-dispersion equation in which a fractional derivative replaces the integer-order dispersion term, has the ability to model rapid, non-Gaussian solute transport. The FADE assumes that solute particle motions converge to either α -stable or operator stable densities, which are modeled by spatial fractional derivatives. In multiple dimensions, the multi-fractional dispersion derivative dictates the order and weight of differentiation in all directions, which correspond to the statistics of large particle motions in all directions. This study numerically investigates the presence of super- Fickian solute transport through simulated two-dimensional fracture networks. An ensemble of networks is gen

Chrystal and Proudman resonances simulated with three numerical models

Science.gov (United States)

Bubalo, Maja; Janeković, Ivica; Orlić, Mirko

2018-05-01

The aim of this work was to study Chrystal and Proudman resonances in a simple closed basin and to explore and compare how well the two resonant mechanisms are reproduced with different, nowadays widely used, numerical ocean models. The test case was based on air pressure disturbances of two commonly used shapes (a sinusoidal and a boxcar), having various wave lengths, and propagating at different speeds. Our test domain was a closed rectangular basin, 300 km long with a uniform depth of 50 m, with the theoretical analytical solution available for benchmark. In total, 2250 simulations were performed for each of the three different numerical models: ADCIRC, SCHISM and ROMS. During each of the simulations, we recorded water level anomalies and computed the integral of the energy density spectrum for a number of points distributed along the basin. We have successfully documented the transition from Proudman to Chrystal resonance that occurs for a sinusoidal air pressure disturbance having a wavelength between one and two basin lengths. An inter-model comparison of the results shows that different models represent the two resonant phenomena in a slightly different way. For Chrystal resonance, all the models showed similar behavior; however, ADCIRC model providing slightly higher values of the mean resonant period than the other two models. In the case of Proudman resonance, the most consistent results, closest to the analytical solution, were obtained using ROMS model, which reproduced the mean resonant speed equal to 22.00 m/s— i.e., close to the theoretical value of 22.15 m/s. ADCIRC and SCHISM models showed small deviations from that value, with the mean speed being slightly lower—21.97 m/s (ADCIRC) and 21.93 m/s (SCHISM). The findings may seem small but could play an important role when resonance is a crucial process producing enhancing effects by two orders of magnitude (i.e., meteotsunamis).

Comparison of GPU-Based Numerous Particles Simulation and Experiment

International Nuclear Information System (INIS)

Park, Sang Wook; Jun, Chul Woong; Sohn, Jeong Hyun; Lee, Jae Wook

2014-01-01

The dynamic behavior of numerous grains interacting with each other can be easily observed. In this study, this dynamic behavior was analyzed based on the contact between numerous grains. The discrete element method was used for analyzing the dynamic behavior of each particle and the neighboring-cell algorithm was employed for detecting their contact. The Hertzian and tangential sliding friction contact models were used for calculating the contact force acting between the particles. A GPU-based parallel program was developed for conducting the computer simulation and calculating the numerous contacts. The dam break experiment was performed to verify the simulation results. The reliability of the program was verified by comparing the results of the simulation with those of the experiment

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

On mesh refinement and accuracy of numerical solutions

NARCIS (Netherlands)

Zhou, Hong; Peters, Maria; van Oosterom, Adriaan

1993-01-01

This paper investigates mesh refinement and its relation with the accuracy of the boundary element method (BEM) and the finite element method (FEM). TO this end an isotropic homogeneous spherical volume conductor, for which the analytical solution is available, wag used. The numerical 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

A new unconditionally stable and consistent quasi-analytical in-stream water quality solution scheme for CSTR-based water quality simulators

Science.gov (United States)

Woldegiorgis, Befekadu Taddesse; van Griensven, Ann; Pereira, Fernando; Bauwens, Willy

2017-06-01

Most common numerical solutions used in CSTR-based in-stream water quality simulators are susceptible to instabilities and/or solution inconsistencies. Usually, they cope with instability problems by adopting computationally expensive small time steps. However, some simulators use fixed computation time steps and hence do not have the flexibility to do so. This paper presents a novel quasi-analytical solution for CSTR-based water quality simulators of an unsteady system. The robustness of the new method is compared with the commonly used fourth-order Runge-Kutta methods, the Euler method and three versions of the SWAT model (SWAT2012, SWAT-TCEQ, and ESWAT). The performance of each method is tested for different hypothetical experiments. Besides the hypothetical data, a real case study is used for comparison. The growth factors we derived as stability measures for the different methods and the R-factor—considered as a consistency measure—turned out to be very useful for determining the most robust method. The new method outperformed all the numerical methods used in the hypothetical comparisons. The application for the Zenne River (Belgium) shows that the new method provides stable and consistent BOD simulations whereas the SWAT2012 model is shown to be unstable for the standard daily computation time step. The new method unconditionally simulates robust solutions. Therefore, it is a reliable scheme for CSTR-based water quality simulators that use first-order reaction formulations.

Correction of MHS Viscosimetric Constants upon Numerical Simulation of Temperature Induced Degradation Kinetic of Chitosan Solutions

Directory of Open Access Journals (Sweden)

Vincenzo Maria De Benedictis

2016-05-01

Full Text Available The Mark–Houwink–Sakurada (MHS equation allows for estimation of rheological properties, if the molecular weight is known along with good understanding of the polymer conformation. The intrinsic viscosity of a polymer solution is related to the polymer molecular weight according to the MHS equation, where the value of the constants is related to the specific solvent and its concentration. However, MHS constants do not account for other characteristics of the polymeric solutions, i.e., Deacetilation Degree (DD when the solute is chitosan. In this paper, the degradation of chitosan in different acidic environments by thermal treatment is addressed. In particular, two different solutions are investigated (used as solvent acetic or hydrochloric acid with different concentrations used for the preparation of chitosan solutions. The samples were treated at different temperatures (4, 30, and 80 °C and time points (3, 6 and 24 h. Rheological, Gel Permeation Chromatography (GPC, Fourier Transform Infrared Spectroscopy (FT-IR, Differential Scanning Calorimetry (DSC and Thermal Gravimetric Analyses (TGA were performed in order to assess the degradation rate of the polymer backbones. Measured values of molecular weight have been integrated in the simulation of the batch degradation of chitosan solutions for evaluating MHS coefficients to be compared with their corresponding experimental values. Evaluating the relationship between the different parameters used in the preparation of chitosan solutions (e.g., temperature, time, acid type and concentration, and their contribution to the degradation of chitosan backbone, it is important to have a mathematical frame that could account for phenomena involved in polymer degradation that go beyond the solvent-solute combination. Therefore, the goal of the present work is to propose an integration of MHS coefficients for chitosan solutions that contemplate a deacetylation degree for chitosan systems or a more

Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

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 second-order stochastic differential equations with Gaussian random parameters

Directory of Open Access Journals (Sweden)

Rahman Farnoosh

2014-07-01

Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1998-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1997-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

Science.gov (United States)

Nixon, D. D.

2001-01-01

Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

Numerical simulation of scour by a wall jet downstream of a solid apron

Energy Technology Data Exchange (ETDEWEB)

Barron, R.M. [Univ. of Windsor, Fluid Dynamics Research Inst., Windsor, Ontario (Canada)]. E-mail: az3@uwindsor.ca; Neyshabouri, S.A.A.S. [Univ. of Tarbiat Modarres, Dept. of Civil Engineering, Tehran (Iran, Islamic Republic of)]. E-mail: salehi@modares.ac.ir

2003-07-01

The time consuming and expensive nature of experimental research on scouring processes caused by flowing water makes it attractive to develop numerical tools for the prediction of the interaction of the fluid flow and the movable bed. In this paper the numerical simulation of scour caused by a wall jet flowing over a solid apron is presented. The flow is assumed to be two-dimensional, and the alluvium is cohesionless. The solution process, repeated at each time step, involves simulation of a turbulent wall jet flow, determination of the convection-diffusion of sand concentration, and prediction of the bed deformation. For simulation of the jet flow, the governing equations for momentum, mass balance and turbulent parameters are solved by the finite volume method. The SIMPLE scheme with momentum interpolation is used for pressure correction. A convection-diffusion equation is solved for sediment concentration. A boundary condition for concentration at the bed, which takes into account the effect of bed-load, is implemented. The time rate of deposition and scour at the bed is obtained by solving the continuity equation for sediment. A meshing technique is devised to deal with the movement of the bed adjacent to the rigid apron. Comparison of the simulation results with available experimental data shows favorable agreement for the time evolution of the scour hole and for the maximum scour depth. (author)

Numerical simulation of airfoil trailing edge serration noise

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong

In the present work, numerical simulations are carried out for a low noise airfoil with and without serrated Trailing Edge. The Ffowcs Williams-Hawkings acoustic analogy is implemented into the in-house incompressible flow solver EllipSys3D. The instantaneous hydrodynamic pressure and velocity...... field are obtained using Large Eddy Simulation. To obtain the time history data of sound pressure, the flow quantities are integrated around the airfoil surface through the FW-H approach. The extended length of the serration is about 16.7% of the airfoil chord and the geometric angle of the serration...... is 28 degrees. The chord based Reynolds number is around 1.5x106. Simulations are compared with existing wind tunnel experiments at various angles of attack. Even though the airfoil under investigation is already optimized for low noise emission, numerical simulations and wind tunnel experiments show...

Direct numerical simulation of granular flows with fluid; Simulation numerique directe d'ecoulements granulaires en presence de fluide

Energy Technology Data Exchange (ETDEWEB)

Komiwes, V.

1999-09-01

Numerical models applied to simulation of granular flow with fluid are developed. The physical model selected to describe particles flow is a discrete approach. Particle trajectories are calculated by the Newton law and collision is describe by a soft-sphere approach. The fluid flow is modelled by Navier-Stokes equations. The modelling of the momentum transfer depends on the resolution scale: for a scale of the order of the particle diameter, it is modelled by a drag-law and for a scale smaller than the particle diameter, it is directly calculated by stress tensor computation around particles. The direct model is used to find representative elementary volume and prove the local character of the Ergun's law. This application shows the numerical (mesh size), physical (Reynolds number) and computational (CPU time and memory consumptions) limitations. The drag law model and the direct model are validated with analytical and empirical solutions and compared. For the two models, the CPU time and the memory consumptions are discussed. The drag law model is applied to the simulation of gas-solid dense fluidized-beds. In the case of uniform gas distribution, the fluidized-bed simulation heights are compared to experimental data for particle of group A and B of the Geldart classification. (author)

Processing biobased polymers using plasticizers: Numerical simulations versus experiments

Science.gov (United States)

Desplentere, Frederik; Cardon, Ludwig; Six, Wim; Erkoç, Mustafa

2016-03-01

In polymer processing, the use of biobased products shows lots of possibilities. Considering biobased materials, biodegradability is in most cases the most important issue. Next to this, bio based materials aimed at durable applications, are gaining interest. Within this research, the influence of plasticizers on the processing of the bio based material is investigated. This work is done for an extrusion grade of PLA, Natureworks PLA 2003D. Extrusion through a slit die equipped with pressure sensors is used to compare the experimental pressure values to numerical simulation results. Additional experimental data (temperature and pressure data along the extrusion screw and die are recorded) is generated on a dr. Collin Lab extruder producing a 25mm diameter tube. All these experimental data is used to indicate the appropriate functioning of the numerical simulation tool Virtual Extrusion Laboratory 6.7 for the simulation of both the industrial available extrusion grade PLA and the compound in which 15% of plasticizer is added. Adding the applied plasticizer, resulted in a 40% lower pressure drop over the extrusion die. The combination of different experiments allowed to fit the numerical simulation results closely to the experimental values. Based on this experience, it is shown that numerical simulations also can be used for modified bio based materials if appropriate material and process data are taken into account.

Modelling and numerical simulation of liquid-vapor phase transitions; Modelisation et simulation numerique des transitions de phase liquide-vapeur

Energy Technology Data Exchange (ETDEWEB)

Caro, F

2004-11-15

This work deals with the modelling and numerical simulation of liquid-vapor phase transition phenomena. The study is divided into two part: first we investigate phase transition phenomena with a Van Der Waals equation of state (non monotonic equation of state), then we adopt an alternative approach with two equations of state. In the first part, we study the classical viscous criteria for selecting weak solutions of the system used when the equation of state is non monotonic. Those criteria do not select physical solutions and therefore we focus a more recent criterion: the visco-capillary criterion. We use this criterion to exactly solve the Riemann problem (which imposes solving an algebraic scalar non linear equation). Unfortunately, this step is quite costly in term of CPU which prevent from using this method as a ground for building Godunov solvers. That is why we propose an alternative approach two equations of state. Using the least action principle, we propose a phase changing two-phase flow model which is based on the second thermodynamic principle. We shall then describe two equilibrium submodels issued from the relaxations processes when instantaneous equilibrium is assumed. Despite the weak hyperbolicity of the last sub-model, we propose stable numerical schemes based on a two-step strategy involving a convective step followed by a relaxation step. We show the ability of the system to simulate vapor bubbles nucleation. (author)

Numerical simulation code for combustion of sodium liquid droplet and its verification

International Nuclear Information System (INIS)

Okano, Yasushi

1997-11-01

The computer programs for sodium leak and burning phenomena had been developed based on mechanistic approach. Direct numerical simulation code for sodium liquid droplet burning had been developed for numerical analysis of droplet combustion in forced convection air flow. Distributions of heat generation and temperature and reaction rate of chemical productions, such as sodium oxide and hydroxide, are calculated and evaluated with using this numerical code. Extended MAC method coupled with a higher-order upwind scheme had been used for combustion simulation of methane-air mixture. In the numerical simulation code for combustion of sodium liquid droplet, chemical reaction model of sodium was connected with the extended MAC method. Combustion of single sodium liquid droplet was simulated in this report for the verification of developed numerical simulation code. The changes of burning rate and reaction product with droplet diameter and inlet wind velocity were investigated. These calculation results were qualitatively and quantitatively conformed to the experimental and calculation observations in combustion engineering. It was confirmed that the numerical simulation code was available for the calculation of sodium liquid droplet burning. (author)

Numerical simulation of anisotropic preheating ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Wang Lifeng; Ye Wenhua; Li Yingjun

2010-01-01

The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability (ARTI) is studied by numerical simulations. The preheating model κ(T)=κ SH [1+f(T)] is applied, where f(T) is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse. (authors)

Numerical Simulation of Antennae by Discrete Exterior Calculus

International Nuclear Information System (INIS)

Xie Zheng; Ye Zheng; Ma Yujie

2009-01-01

Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Numerical simulation in plasma physics

International Nuclear Information System (INIS)

Samarskii, A.A.

1980-01-01

Plasma physics is not only a field for development of physical theories and mathematical models but also an object of application of the computational experiment comprising analytical and numerical methods adapted for computers. The author considers only MHD plasma physics problems. Examples treated are dissipative structures in plasma; MHD model of solar dynamo; supernova explosion simulation; and plasma compression by a liner. (Auth.)

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

International Nuclear Information System (INIS)

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

3D numerical simulations of multiphase continental rifting

Science.gov (United States)

Naliboff, J.; Glerum, A.; Brune, S.

2017-12-01

Observations of rifted margin architecture suggest continental breakup occurs through multiple phases of extension with distinct styles of deformation. The initial rifting stages are often characterized by slow extension rates and distributed normal faulting in the upper crust decoupled from deformation in the lower crust and mantle lithosphere. Further rifting marks a transition to higher extension rates and coupling between the crust and mantle lithosphere, with deformation typically focused along large-scale detachment faults. Significantly, recent detailed reconstructions and high-resolution 2D numerical simulations suggest that rather than remaining focused on a single long-lived detachment fault, deformation in this phase may progress toward lithospheric breakup through a complex process of fault interaction and development. The numerical simulations also suggest that an initial phase of distributed normal faulting can play a key role in the development of these complex fault networks and the resulting finite deformation patterns. Motivated by these findings, we will present 3D numerical simulations of continental rifting that examine the role of temporal increases in extension velocity on rifted margin structure. The numerical simulations are developed with the massively parallel finite-element code ASPECT. While originally designed to model mantle convection using advanced solvers and adaptive mesh refinement techniques, ASPECT has been extended to model visco-plastic deformation that combines a Drucker Prager yield criterion with non-linear dislocation and diffusion creep. To promote deformation localization, the internal friction angle and cohesion weaken as a function of accumulated plastic strain. Rather than prescribing a single zone of weakness to initiate deformation, an initial random perturbation of the plastic strain field combined with rapid strain weakening produces distributed normal faulting at relatively slow rates of extension in both 2D and

Numerical solution of the radionuclide transport equation

International Nuclear Information System (INIS)

Hadermann, J.; Roesel, F.

1983-11-01

A numerical solution of the one-dimensional geospheric radionuclide chain transport equation based on the pseudospectral method is developed. The advantages of this approach are flexibility in incorporating space and time dependent migration parameters, arbitrary boundary conditions and solute rock interactions as well as efficiency and reliability. As an application the authors investigate the impact of non-linear sorption isotherms on migration in crystalline rock. It is shown that non-linear sorption, in the present case a Freundlich isotherm, may reduce concentration at the geosphere outlet by orders of magnitude provided the migration time is comparable or larger than the half-life of the nuclide in question. The importance of fixing dispersivity within the continuum approach is stressed. (Auth.)

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 solution of the polymer system

Energy Technology Data Exchange (ETDEWEB)

Haugse, V.; Karlsen, K.H.; Lie, K.-A.; Natvig, J.R.

1999-05-01

The paper describes the application of front tracking to the polymer system, an example of a nonstrictly hyperbolic system. Front tracking computes piecewise constant approximations based on approximate Remain solutions and exact tracking of waves. It is well known that the front tracking method may introduce a blow-up of the initial total variation for initial data along the curve where the two eigenvalues of the hyperbolic system are identical. It is demonstrated by numerical examples that the method converges to the correct solution after a finite time that decreases with the discretization parameter. For multidimensional problems, front tracking is combined with dimensional splitting and numerical experiments indicate that large splitting steps can be used without loss of accuracy. Typical CFL numbers are in the range of 10 to 20 and comparisons with the Riemann free, high-resolution method confirm the high efficiency of front tracking. The polymer system, coupled with an elliptic pressure equation, models two-phase, tree-component polymer flooding in an oil reservoir. Two examples are presented where this model is solved by a sequential time stepping procedure. Because of the approximate Riemann solver, the method is non-conservative and CFL members must be chosen only moderately larger than unity to avoid substantial material balance errors generated in near-well regions after water breakthrough. Moreover, it is demonstrated that dimensional splitting may introduce severe grid orientation effects for unstable displacements that are accentuated for decreasing discretization parameters. 9 figs., 2 tabs., 26 refs.

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

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 solution of field theories using random walks

International Nuclear Information System (INIS)

Barnes, T.; Daniell, G.J.

1985-01-01

We show how random walks in function space can be employed to evaluate field theoretic vacuum expectation values numerically. Specific applications which we study are the two-point function, mass gap, magnetization and classical solutions. This technique offers the promise of faster calculations using less computer memory than current methods. (orig.)

Numerical Simulation of Steady Supercavitating Flows

OpenAIRE

Ali Jafarian; Ahmad-Reza Pishevar

2016-01-01

In this research, the Supercavitation phenomenon in compressible liquid flows is simulated. The one-fluid method based on a new exact two-phase Riemann solver is used for modeling. The cavitation is considered as an isothermal process and a consistent equation of state with the physical behavior of the water is used. High speed flow of water over a cylinder and a projectile are simulated and the results are compared with the previous numerical and experimental results. The cavitation bubble p...

Optimal design of a composite space shield based on numerical simulations

International Nuclear Information System (INIS)

Son, Byung Jin; Yoo, Jeong Hoon; Lee, Min Hyung

2015-01-01

In this study, optimal design of a stuffed Whipple shield is proposed by using numerical simulations and new penetration criterion. The target model was selected based on the shield model used in the Columbus module of the international space station. Because experimental results can be obtained only in the low velocity region below 7 km/s, it is required to derive the Ballistic limit curve (BLC) in the high velocity region above 7 km/s by numerical simulation. AUTODYN-2D, the commercial hydro-code package, was used to simulate the nonlinear transient analysis for the hypervelocity impact. The Smoothed particle hydrodynamics (SPH) method was applied to projectile and bumper modeling to represent the debris cloud generated after the impact. Numerical simulation model and selected material properties were validated through a quantitative comparison between numerical and experimental results. A new criterion to determine whether the penetration occurs or not is proposed from kinetic energy analysis by numerical simulation in the velocity region over 7 km/s. The parameter optimization process was performed to improve the protection ability at a specific condition through the Design of experiment (DOE) method and the Response surface methodology (RSM). The performance of the proposed optimal design was numerically verified.

Behavioral modeling of SRIM tables for numerical simulation

Energy Technology Data Exchange (ETDEWEB)

Martinie, S., E-mail: sebastien.martinie@cea.fr; Saad-Saoud, T.; Moindjie, S.; Munteanu, D.; Autran, J.L., E-mail: jean-luc.autran@univ-amu.fr

2014-03-01

Highlights: • Behavioral modeling of SRIM data is performed on the basis of power polynomial fitting functions. • Fast and continuous numerical functions are proposed for the stopping power and projected range. • Functions have been successfully tested for a wide variety of ions and targets. • Typical accuracies below the percent have been obtained in the range 1 keV–1 GeV. - Abstract: This work describes a simple way to implement SRIM stopping power and range tabulated data in the form of fast and continuous numerical functions for intensive simulation. We provide here the methodology of this behavioral modeling as well as the details of the implementation and some numerical examples for ions in silicon target. Developed functions have been successfully tested and used for the simulation of soft errors in microelectronics circuits.

Behavioral modeling of SRIM tables for numerical simulation

International Nuclear Information System (INIS)

Martinie, S.; Saad-Saoud, T.; Moindjie, S.; Munteanu, D.; Autran, J.L.

2014-01-01

Highlights: • Behavioral modeling of SRIM data is performed on the basis of power polynomial fitting functions. • Fast and continuous numerical functions are proposed for the stopping power and projected range. • Functions have been successfully tested for a wide variety of ions and targets. • Typical accuracies below the percent have been obtained in the range 1 keV–1 GeV. - Abstract: This work describes a simple way to implement SRIM stopping power and range tabulated data in the form of fast and continuous numerical functions for intensive simulation. We provide here the methodology of this behavioral modeling as well as the details of the implementation and some numerical examples for ions in silicon target. Developed functions have been successfully tested and used for the simulation of soft errors in microelectronics circuits

Numerical double layer solutions with ionization

International Nuclear Information System (INIS)

Andersson, D.; Soerensen, J.

1982-08-01

Maxwell's equation div D = ro in one dimension is solved numerically, taking ionization into account. Time independent anode sheath and double layer solutions are obtained. By varying voltage, neutral gas pressure, temperature of the trapped ions on the cathode side and density and temperature of the trapped electrones on the anode side, diagrams are constructed that show permissible combinations of these parameters. Results from a recent experiment form a subset. Distribution functions, the Langmuir condition, some scaling laws and a possible application to the lower ionosphere are discussed. (Authors)

Numerical Simulation of Anisotropic Preheating Ablative Rayleigh–Taylor Instability

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Ying-Jun, Li

2010-01-01

The linear growth rate of the anisotropic preheating ablative Rayleigh–Taylor instability (ARTI) is studied by numerical simulations. The preheating model κ(T) = κ SH [1 + f(T)] is applied, where f(T) is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 (2007) 245001]. (physics of gases, plasmas, and electric discharges)

Three-Dimensional Numerical Simulation to Mud Turbine for LWD

Science.gov (United States)

Yao, Xiaojiang; Dong, Jingxin; Shang, Jie; Zhang, Guanqi

Hydraulic performance analysis was discussed for a type of turbine on generator used for LWD. The simulation models were built by CFD analysis software FINE/Turbo, and full three-dimensional numerical simulation was carried out for impeller group. The hydraulic parameter such as power, speed and pressure drop, were calculated in two kinds of medium water and mud. Experiment was built in water environment. The error of numerical simulation was less than 6%, verified by experiment. Based on this rationalization proposals would be given to choice appropriate impellers, and the rationalization of methods would be explored.

Numerical simulation support to the ESA/THOR mission

Science.gov (United States)

Valentini, F.; Servidio, S.; Perri, S.; Perrone, D.; De Marco, R.; Marcucci, M. F.; Daniele, B.; Bruno, R.; Camporeale, E.

2016-12-01

THOR is a spacecraft concept currently undergoing study phase as acandidate for the next ESA medium size mission M4. THOR has been designedto solve the longstanding physical problems of particle heating andenergization in turbulent plasmas. It will provide high resolutionmeasurements of electromagnetic fields and particle distribution functionswith unprecedented resolution, with the aim of exploring the so-calledkinetic scales. We present the numerical simulation framework which is supporting the THOR mission during the study phase. The THOR teamincludes many scientists developing and running different simulation codes(Eulerian-Vlasov, Particle-In-Cell, Gyrokinetics, Two-fluid, MHD, etc.),addressing the physics of plasma turbulence, shocks, magnetic reconnectionand so on.These numerical codes are being used during the study phase, mainly withthe aim of addressing the following points:(i) to simulate the response of real particle instruments on board THOR, byemploying an electrostatic analyser simulator which mimics the response ofthe CSW, IMS and TEA instruments to the particle velocity distributions ofprotons, alpha particle and electrons, as obtained from kinetic numericalsimulations of plasma turbulence.(ii) to compare multi-spacecraft with single-spacecraft configurations inmeasuring current density, by making use of both numerical models ofsynthetic turbulence and real data from MMS spacecraft.(iii) to investigate the validity of the Taylor hypothesis indifferent configurations of plasma turbulence

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 retar...... 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....

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

Numerical simulation of mass and energy transport phenomena in solid oxide fuel cells

Energy Technology Data Exchange (ETDEWEB)

Arpino, F. [Dipartimento di Meccanica, Strutture, Ambiente e Territorio (DiMSAT), University of Cassino, via Di Biasio 43, Cassino (Italy); Massarotti, N. [Dipertimento per le Tecnologie (DiT), University of Naples ' ' Parthenope' ' , Centro Direzionale, isola C4, 80143 Napoli (Italy)

2009-12-15

Solid Oxide Fuel Cells (SOFCs) represent a very promising technology for near future energy conversion thanks to a number of advantages, including the possibility of using different fuels. In this paper, a detailed numerical model, based on a general mathematical description and on a finite element Characteristic based Split (CBS) algorithm code is employed to simulate mass and energy transport phenomena in SOFCs. The model predicts the thermodynamic quantity of interest in the fuel cell. Full details of the numerical solution obtained are presented both in terms of heat and mass transfer in the cell and in terms of electro-chemical reactions that occur in the system considered. The results obtained with the present algorithm is compared with the experimental data available in the literature for validation, showing an excellent agreement. (author)

Solutions manual to accompany An introduction to numerical methods and analysis

CERN Document Server

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

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.

Underestimation of nuclear fuel burnup – theory, demonstration and solution in numerical models

Directory of Open Access Journals (Sweden)

Gajda Paweł

2016-01-01

Full Text Available Monte Carlo methodology provides reference statistical solution of neutron transport criticality problems of nuclear systems. Estimated reaction rates can be applied as an input to Bateman equations that govern isotopic evolution of reactor materials. Because statistical solution of Boltzmann equation is computationally expensive, it is in practice applied to time steps of limited length. In this paper we show that simple staircase step model leads to underprediction of numerical fuel burnup (Fissions per Initial Metal Atom – FIMA. Theoretical considerations indicates that this error is inversely proportional to the length of the time step and origins from the variation of heating per source neutron. The bias can be diminished by application of predictor-corrector step model. A set of burnup simulations with various step length and coupling schemes has been performed. SERPENT code version 1.17 has been applied to the model of a typical fuel assembly from Pressurized Water Reactor. In reference case FIMA reaches 6.24% that is equivalent to about 60 GWD/tHM of industrial burnup. The discrepancies up to 1% have been observed depending on time step model and theoretical predictions are consistent with numerical results. Conclusions presented in this paper are important for research and development concerning nuclear fuel cycle also in the context of Gen4 systems.

Towards numerical simulations of supersonic liquid jets using ghost fluid method

International Nuclear Information System (INIS)

Majidi, Sahand; Afshari, Asghar

2015-01-01

Highlights: • A ghost fluid method based solver is developed for numerical simulation of compressible multiphase flows. • The performance of the numerical tool is validated via several benchmark problems. • Emergence of supersonic liquid jets in quiescent gaseous environment is simulated using ghost fluid method for the first time. • Bow-shock formation ahead of the liquid jet is clearly observed in the obtained numerical results. • Radiation of mach waves from the phase-interface witnessed experimentally is evidently captured in our numerical simulations. - Abstract: A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid

Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

International Nuclear Information System (INIS)

Inc, Mustafa; Ugurlu, Yavuz

2007-01-01

In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions

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)

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

Energy Technology Data Exchange (ETDEWEB)

Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

2017-02-01

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.

Direct numerical simulation of noninvasive channel healing in electrical field

KAUST Repository

Wang, Yi

2017-11-25

Noninvasive channel healing is a new idea to repair the broken pipe wall, using external electric fields to drive iron particles to the destination. The repair can be done in the normal operation of the pipe flow without any shutdown of the pipeline so that this method can be a potentially efficient and safe technology of pipe healing. However, the real application needs full knowledge of healing details. Numerical simulation is an effective method. Thus, in this research, we first established a numerical model for noninvasive channel healing technology to represent fluid–particle interaction. The iron particles can be attached to a cracking area by external electrostatic forces or can also be detached by mechanical forces from the fluid. When enough particles are permanently attached on the cracking area, the pipe wall can be healed. The numerical criterion of the permanent attachment is discussed. A fully three-dimensional finite difference framework of direct numerical simulation is established and applied to different cases to simulate the full process of channel healing. The impact of Reynolds number and particle concentration on the healing process is discussed. This numerical investigation provides valuable reference and tools for further simulation of real pipe healing in engineering.

Numerical simulation of small scale soft impact tests

International Nuclear Information System (INIS)

Varpasuo, Pentti

2008-01-01

This paper describes the small scale soft missile impact tests. The purpose of the test program is to provide data for the calibration of the numerical simulation models for impact simulation. In the experiments, both dry and fluid filled missiles are used. The tests with fluid filled missiles investigate the release speed and the droplet size of the fluid release. This data is important in quantifying the fire hazard of flammable liquid after the release. The spray release velocity and droplet size are also input data for analytical and numerical simulation of the liquid spread in the impact. The behaviour of the impact target is the second investigative goal of the test program. The response of reinforced and pre-stressed concrete walls is studied with the aid of displacement and strain monitoring. (authors)

Numerical simulation of large deformation polycrystalline plasticity

International Nuclear Information System (INIS)

Inal, K.; Neale, K.W.; Wu, P.D.; MacEwen, S.R.

2000-01-01

A finite element model based on crystal plasticity has been developed to simulate the stress-strain response of sheet metal specimens in uniaxial tension. Each material point in the sheet is considered to be a polycrystalline aggregate of FCC grains. The Taylor theory of crystal plasticity is assumed. The numerical analysis incorporates parallel computing features enabling simulations of realistic models with large number of grains. Simulations have been carried out for the AA3004-H19 aluminium alloy and the results are compared with experimental data. (author)

Numerical simulations of progressive hardening by using ABAQUS FEA software

Directory of Open Access Journals (Sweden)

Domański Tomasz

2018-01-01

Full Text Available The paper concerns numerical simulations of progressive hardening include phase transformations in solid state of steel. Abaqus FEA software is used for numerical analysis of temperature field and phase transformations. Numerical subroutines, written in fortran programming language are used in computer simulations where models of the distribution of movable heat source, kinetics of phase transformations in solid state as well as thermal and structural strain are implemented. Model for evaluation of fractions of phases and their kinetics is based on continuous heating diagram and continuous cooling diagram. The numerical analysis of thermal fields, phase fractions and strain associated progressive hardening of elements made of steel were done.

INCREASE OF QUEUING SYSTEM EFFECTIVENESS OF TRADING ENTERPRISE BY MEANS OF NUMERICAL STATISTICAL SIMULATION

Directory of Open Access Journals (Sweden)

Knyazheva Yu. V.

2014-06-01

Full Text Available The market economy causes need of development of the economic analysis first of all at microlevel, that is at the level of the separate enterprises as the enterprises are basis for market economy. Therefore improvement of the queuing system trading enterprise is an important economic problem. Analytical solutions of problems of the mass servicing are in described the theory, don’t correspond to real operating conditions of the queuing systems. Therefore in this article optimization of customer service process and improvement of settlement and cash service system trading enterprise are made by means of numerical statistical simulation of the queuing system trading enterprise. The article describe integrated statistical numerical simulation model of queuing systems trading enterprise working in nonstationary conditions with reference to different distribution laws of customers input stream. This model takes account of various behavior customers output stream, includes checkout service model which takes account of cashier rate of working, also this model includes staff motivation model, profit earning and profit optimization models that take into account possible revenue and costs. The created statistical numerical simulation model of queuing systems trading enterprise, at its realization in the suitable software environment, allows to perform optimization of the most important parameters of system. And when developing the convenient user interface, this model can be a component of support decision-making system for rationalization of organizational structure and for management optimization by trading enterprise.

A numerical simulation of pre-big bang cosmology

CERN Document Server

Maharana, J P; Veneziano, Gabriele

1998-01-01

We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($\\Omega \\to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.

Numerical Simulation of Transitional, Hypersonic Flows using a Hybrid Particle-Continuum Method

Science.gov (United States)

Verhoff, Ashley Marie

Analysis of hypersonic flows requires consideration of multiscale phenomena due to the range of flight regimes encountered, from rarefied conditions in the upper atmosphere to fully continuum flow at low altitudes. At transitional Knudsen numbers there are likely to be localized regions of strong thermodynamic nonequilibrium effects that invalidate the continuum assumptions of the Navier-Stokes equations. Accurate simulation of these regions, which include shock waves, boundary and shear layers, and low-density wakes, requires a kinetic theory-based approach where no prior assumptions are made regarding the molecular distribution function. Because of the nature of these types of flows, there is much to be gained in terms of both numerical efficiency and physical accuracy by developing hybrid particle-continuum simulation approaches. The focus of the present research effort is the continued development of the Modular Particle-Continuum (MPC) method, where the Navier-Stokes equations are solved numerically using computational fluid dynamics (CFD) techniques in regions of the flow field where continuum assumptions are valid, and the direct simulation Monte Carlo (DSMC) method is used where strong thermodynamic nonequilibrium effects are present. Numerical solutions of transitional, hypersonic flows are thus obtained with increased physical accuracy relative to CFD alone, and improved numerical efficiency is achieved in comparison to DSMC alone because this more computationally expensive method is restricted to those regions of the flow field where it is necessary to maintain physical accuracy. In this dissertation, a comprehensive assessment of the physical accuracy of the MPC method is performed, leading to the implementation of a non-vacuum supersonic outflow boundary condition in particle domains, and more consistent initialization of DSMC simulator particles along hybrid interfaces. The relative errors between MPC and full DSMC results are greatly reduced as a

Pitfall in quantum mechanical/molecular mechanical molecular dynamics simulation of small solutes in solution.

Science.gov (United States)

Hu, Hao; Liu, Haiyan

2013-05-30

Developments in computing hardware and algorithms have made direct molecular dynamics simulation with the combined quantum mechanical/molecular mechanical methods affordable for small solute molecules in solution, in which much improved accuracy can be obtained via the quantum mechanical treatment of the solute molecule and even sometimes water molecules in the first solvation shell. However, unlike the conventional molecular mechanical simulations of large molecules, e.g., proteins, in solutions, special care must be taken in the technical details of the simulation, including the thermostat of the solute/solvent system, so that the conformational space of the solute molecules can be properly sampled. We show here that the common setup for classical molecular mechanical molecular dynamics simulations, such as the Berendsen or single Nose-Hoover thermostat, and/or rigid water models could lead to pathological sampling of the solutes' conformation. In the extreme example of a methanol molecule in aqueous solution, improper and sluggish setups could generate two peaks in the distribution of the O-H bond length. We discuss the factors responsible for this somewhat unexpected result and evoke a simple and ancient technical fix-up to resolve this problem.

On the numerical solution of the neutron fractional diffusion equation

International Nuclear Information System (INIS)

Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto

2014-01-01

Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative

Adaptive and dynamic meshing methods for numerical simulations

Science.gov (United States)

Acikgoz, Nazmiye

For the numerical simulation of many problems of engineering interest, it is desirable to have an automated mesh adaption tool capable of producing high quality meshes with an affordably low number of mesh points. This is important especially for problems, which are characterized by anisotropic features of the solution and require mesh clustering in the direction of high gradients. Another significant issue in meshing emerges in the area of unsteady simulations with moving boundaries or interfaces, where the motion of the boundary has to be accommodated by deforming the computational grid. Similarly, there exist problems where current mesh needs to be adapted to get more accurate solutions because either the high gradient regions are initially predicted inaccurately or they change location throughout the simulation. To solve these problems, we propose three novel procedures. For this purpose, in the first part of this work, we present an optimization procedure for three-dimensional anisotropic tetrahedral grids based on metric-driven h-adaptation. The desired anisotropy in the grid is dictated by a metric that defines the size, shape, and orientation of the grid elements throughout the computational domain. Through the use of topological and geometrical operators, the mesh is iteratively adapted until the final mesh minimizes a given objective function. In this work, the objective function measures the distance between the metric of each simplex and a target metric, which can be either user-defined (a-priori) or the result of a-posteriori error analysis. During the adaptation process, one tries to decrease the metric-based objective function until the final mesh is compliant with the target within a given tolerance. However, in regions such as corners and complex face intersections, the compliance condition was found to be very difficult or sometimes impossible to satisfy. In order to address this issue, we propose an optimization process based on an ad

Numerical simulation of baseflow modification due to effects of ...

African Journals Online (AJOL)

Numerical simulation of baseflow modification due to effects of sediment yield. ... Physically-based mathematical modelling affords the opportunity to look at this kind of interaction, which should be simulated by deterministic responses of both water and fluvial processes. In addition to simulating the streamflow and ...

A Dynamic Operation Permission Technique Based on an MFM Model and Numerical Simulation

International Nuclear Information System (INIS)

Akio, Gofuku; Masahiro, Yonemura

2011-01-01

It is important to support operator activities to an abnormal plant situation where many counter actions are taken in relatively short time. The authors proposed a technique called dynamic operation permission to decrease human errors without eliminating creative idea of operators to cope with an abnormal plant situation by checking if the counter action taken is consistent with emergency operation procedure. If the counter action is inconsistent, a dynamic operation permission system warns it to operators. It also explains how and why the counter action is inconsistent and what influence will appear on the future plant behavior by a qualitative influence inference technique based on a model by the Mf (Multilevel Flow Modeling). However, the previous dynamic operation permission is not able to explain quantitative effects on plant future behavior. Moreover, many possible influence paths are derived because a qualitative reasoning does not give a solution when positive and negative influences are propagated to the same node. This study extends the dynamic operation permission by combining the qualitative reasoning and the numerical simulation technique. The qualitative reasoning based on an Mf model of plant derives all possible influence propagation paths. Then, a numerical simulation gives a prediction of plant future behavior in the case of taking a counter action. The influence propagation that does not coincide with the simulation results is excluded from possible influence paths. The extended technique is implemented in a dynamic operation permission system for an oil refinery plant. An MFM model and a static numerical simulator are developed. The results of dynamic operation permission for some abnormal plant situations show the improvement of the accuracy of dynamic operation permission and the quality of explanation for the effects of the counter action taken

Validation of accuracy and stability of numerical simulation for 2-D heat transfer system by an entropy production approach

Directory of Open Access Journals (Sweden)

Brohi Ali Anwar

2017-01-01

Full Text Available The entropy production in 2-D heat transfer system has been analyzed systematically by using the finite volume method, to develop new criteria for the numerical simulation in case of multidimensional systems, with the aid of the CFD codes. The steady-state heat conduction problem has been investigated for entropy production, and the entropy production profile has been calculated based upon the current approach. From results for 2-D heat conduction, it can be found that the stability of entropy production profile exhibits a better agreement with the exact solution accordingly, and the current approach is effective for measuring the accuracy and stability of numerical simulations for heat transfer problems.

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 simulation on chain-die forming of an AHSS top-hat section

Science.gov (United States)

Majji, Raju; Xiang, Yang; Ding, Scott; Yang, Chunhui

2018-05-01

The applications of Advanced High-Strength Steels (AHSS) in the automotive industry are rapidly increasing due to a demand for a lightweight material that significantly reduces fuel consumption without compromising passenger safety. Automotive industries and material suppliers are expected by consumers to deliver reliable and affordable products, thus stimulating these manufacturers to research solutions to meet these customer requirements. The primary advantage of AHSS is its extremely high strength to weight ratio, an ideal material for the automotive industry. However, its low ductility is a major disadvantage, in particular, when using traditional cold forming processes such as roll forming and deep drawing process to form profiles. Consequently, AHSS parts frequently fail to form. Thereby, in order to improve quality and reliability on manufacturing AHSS products, a recently-developed incremental cold sheet metal forming technology called Chain-die Forming (CDF) is recognised as a potential solution to the forming process of AHSS. The typical CDF process is a combination of bending and roll forming processes which is equivalent to a roll with a large deforming radius, and incrementally forms the desired shape with split die and segments. This study focuses on manufacturing an AHSS top-hat section with minimum passes without geometrical or surface defects by using finite element modelling and simulations. The developed numerical simulation is employed to investigate the influences on the main control parameter of the CDF process while forming AHSS products and further develop new die-punch sets of compensation design via a numerical optimal process. In addition, the study focuses on the tool design to compensate spring-back and reduce friction between tooling and sheet-metal. This reduces the number of passes, thereby improving productivity and reducing energy consumption and material waste. This numerical study reveals that CDF forms AHSS products of complex

Numerical and analytical solutions for problems relevant for quantum computers

International Nuclear Information System (INIS)

Spoerl, Andreas

2008-01-01

Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)

Physical modeling and numerical simulation of subcooled boiling in one- and three-dimensional representation of bundle geometry

International Nuclear Information System (INIS)

Bottoni, M.; Lyczkowski, R.; Ahuja, S.

1995-01-01

Numerical simulation of subcooled boiling in one-dimensional geometry with the Homogeneous Equilibrium Model (HEM) may yield difficulties related to the very low sonic velocity associated with the HEM. These difficulties do not arise with subcritical flow. Possible solutions of the problem include introducing a relaxation of the vapor production rate. Three-dimensional simulations of subcooled boiling in bundle geometry typical of fast reactors can be performed by using two systems of conservation equations, one for the HEM and the other for a Separated Phases Model (SPM), with a smooth transition between the two models

GPU based numerical simulation of core shooting process

Directory of Open Access Journals (Sweden)

Yi-zhong Zhang

2017-11-01

Full Text Available Core shooting process is the most widely used technique to make sand cores and it plays an important role in the quality of sand cores. Although numerical simulation can hopefully optimize the core shooting process, research on numerical simulation of the core shooting process is very limited. Based on a two-fluid model (TFM and a kinetic-friction constitutive correlation, a program for 3D numerical simulation of the core shooting process has been developed and achieved good agreements with in-situ experiments. To match the needs of engineering applications, a graphics processing unit (GPU has also been used to improve the calculation efficiency. The parallel algorithm based on the Compute Unified Device Architecture (CUDA platform can significantly decrease computing time by multi-threaded GPU. In this work, the program accelerated by CUDA parallelization method was developed and the accuracy of the calculations was ensured by comparing with in-situ experimental results photographed by a high-speed camera. The design and optimization of the parallel algorithm were discussed. The simulation result of a sand core test-piece indicated the improvement of the calculation efficiency by GPU. The developed program has also been validated by in-situ experiments with a transparent core-box, a high-speed camera, and a pressure measuring system. The computing time of the parallel program was reduced by nearly 95% while the simulation result was still quite consistent with experimental data. The GPU parallelization method can successfully solve the problem of low computational efficiency of the 3D sand shooting simulation program, and thus the developed GPU program is appropriate for engineering applications.

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 modeling and numerical simulation of Czochralski Crystal Growth

Energy Technology Data Exchange (ETDEWEB)

Jaervinen, J.; Nieminen, R. [Center for Scientific Computing, Espoo (Finland)

1996-12-31

A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)

Mathematical modeling and numerical simulation of Czochralski Crystal Growth

Energy Technology Data Exchange (ETDEWEB)

Jaervinen, J; Nieminen, R [Center for Scientific Computing, Espoo (Finland)

1997-12-31

A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)

Numerical simulation of random stresses on an annular turbulent flow

International Nuclear Information System (INIS)

Marti-Moreno, Marta

2000-01-01

The flow along a circular cylinder may induce structural vibrations. For the predictive analysis of such vibrations, the turbulent forcing spectrum needs to be characterized. The aim of this work is to study the turbulent fluid forces acting on a single tube in axial flow. More precisely we have performed numerical simulations of an annular flow. These simulations were carried out on a cylindrical staggered mesh by a finite difference method. We consider turbulent flow with Reynolds number up to 10 6 . The Large Eddy Simulation Method has been used. A survey of existent experiments showed that hydraulic diameter acts as an important parameter. We first showed the accuracy of the numerical code by reproducing the experiments of Mulcahy. The agreement between pressure spectra from computations and from experiments is good. Then, we applied this code to simulate new numerical experiments varying the hydraulic diameter and the flow velocity. (author) [fr

2nd International Workshop on the Numerical Solution of Markov Chains

CERN Document Server

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 simulation investigation on centrifugal compressor performance of turbocharger

International Nuclear Information System (INIS)

Li, Jie; Yin, Yuting; Li, Shuqi; Zhang, Jizhong

2013-01-01

In this paper, the mathematical model of the flow filed in centrifugal compressor of turbocharger was studied. Based on the theory of computational fluid dynamics (CFD), performance curves and parameter distributions of the compressor were obtained from the 3-D numerical simulation by using CFX. Meanwhile, the influences of grid number and distribution on compressor performance were investigated, and numerical calculation method was analyzed and validated, through combining with test data. The results obtained show the increase of the grid number has little influence on compressor performance while the grid number of single-passage is above 300,000. The results also show that the numerical calculation mass flow rate of compressor choke situation has a good consistent with test results, and the maximum difference of the diffuser exit pressure between simulation and experiment decrease to 3.5% with the assumption of 6 kPa additional total pressure loss at compressor inlet. The numerical simulation method in this paper can be used to predict compressor performance, and the difference of total pressure ratio between calculation and test is less than 7%, and the total-to-total efficiency also have a good consistent with test.

Numerical simulation investigation on centrifugal compressor performance of turbocharger

Energy Technology Data Exchange (ETDEWEB)

Li, Jie [China Iron and Steel Research Institute Group, Beijing (China); Yin, Yuting [China North Engine Research Institute, Datong (China); Li, Shuqi; Zhang, Jizhong [Science and Technology Diesel Engine Turbocharging Laboratory, Datong (China)

2013-06-15

In this paper, the mathematical model of the flow filed in centrifugal compressor of turbocharger was studied. Based on the theory of computational fluid dynamics (CFD), performance curves and parameter distributions of the compressor were obtained from the 3-D numerical simulation by using CFX. Meanwhile, the influences of grid number and distribution on compressor performance were investigated, and numerical calculation method was analyzed and validated, through combining with test data. The results obtained show the increase of the grid number has little influence on compressor performance while the grid number of single-passage is above 300,000. The results also show that the numerical calculation mass flow rate of compressor choke situation has a good consistent with test results, and the maximum difference of the diffuser exit pressure between simulation and experiment decrease to 3.5% with the assumption of 6 kPa additional total pressure loss at compressor inlet. The numerical simulation method in this paper can be used to predict compressor performance, and the difference of total pressure ratio between calculation and test is less than 7%, and the total-to-total efficiency also have a good consistent with test.

Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

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.

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 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

Parallel numerical simulation of oscillating airfoil NACA0015 in the channel due to flutter instability

Directory of Open Access Journals (Sweden)

Řidký Václav

2014-03-01

Full Text Available The work is devoted to 3D and 2D parallel numerical computation of pressure and velocity fields around an elastically supported airfoil self-oscillating due to interaction with the airflow. Numerical solution is computed in the OpenFOAM package, an open-source software package based on finite volume method. Movement of airfoil is described by translation and rotation, identified from experimental data. A new boundary condition for the 2DOF motion of the airfoil was implemented. The results of numerical simulations (velocity are compared with data measured in a wind tunnel, where a physical model of NACA0015 airfoil was mounted and tuned to exhibit the flutter instability. The experimental results were obtained previously in the Institute of Thermomechanics by interferographic measurements in a subsonic wind tunnel in Nový Knín.

A model for the numerical simulations of ion cyclotron heating of tokamak plasmas

International Nuclear Information System (INIS)

Brambilla, M.

1986-05-01

We present a complete set of equations for the numerical simulation of ion cyclotron heating of tokamak plasmas. The model includes the full geometry of the tokamak equilibrium, full parallel dispersion, and perpendicular dispersion to second order in the Larmor radius. It is therefore capable of describing correctly ion cyclotron damping at the fundamental and first harmonic, as well as mode conversion to the ion Bernstein wave and/or the shear Alfven wave, depending on the heating scenario. It includes also electron magnitude pumping and Landau damping, the latter to lowest order in msub(e)/msub(i). Relying on the knowledge gained from slab and ray tracing analysis, we also situate with respect to this standard model some of the further approximations which are commonly encountered in the literature. Finally, two procedures for the numerical solution of the standard model are proposed. (orig.)

NUMERICAL SIMULATION OF ELECTRICAL IMPEDANCE TOMOGRAPHY PROBLEM AND STUDY OF APPROACH BASED ON FINITE VOLUME METHOD

Directory of Open Access Journals (Sweden)

Ye. S. Sherina

2014-01-01

Full Text Available This research has been aimed to carry out a study of peculiarities that arise in a numerical simulation of the electrical impedance tomography (EIT problem. Static EIT image reconstruction is sensitive to a measurement noise and approximation error. A special consideration has been given to reducing of the approximation error, which originates from numerical implementation drawbacks. This paper presents in detail two numerical approaches for solving EIT forward problem. The finite volume method (FVM on unstructured triangular mesh is introduced. In order to compare this approach, the finite element (FEM based forward solver was implemented, which has gained the most popularity among researchers. The calculated potential distribution with the assumed initial conductivity distribution has been compared to the analytical solution of a test Neumann boundary problem and to the results of problem simulation by means of ANSYS FLUENT commercial software. Two approaches to linearized EIT image reconstruction are discussed. Reconstruction of the conductivity distribution is an ill-posed problem, typically requiring a large amount of computation and resolved by minimization techniques. The objective function to be minimized is constructed of measured voltage and calculated boundary voltage on the electrodes. A classical modified Newton type iterative method and the stochastic differential evolution method are employed. A software package has been developed for the problem under investigation. Numerical tests were conducted on simulated data. The obtained results could be helpful to researches tackling the hardware and software issues for medical applications of EIT.

acme: The Amendable Coal-Fire Modeling Exercise. A C++ Class Library for the Numerical Simulation of Coal-Fires

Science.gov (United States)

Wuttke, Manfred W.

2017-04-01

At LIAG, we use numerical models to develop and enhance understanding of coupled transport processes and to predict the dynamics of the system under consideration. Topics include geothermal heat utilization, subrosion processes, and spontaneous underground coal fires. Although the details make it inconvenient if not impossible to apply a single code implementation to all systems, their investigations go along similar paths: They all depend on the solution of coupled transport equations. We thus saw a need for a modular code system with open access for the various communities to maximize the shared synergistic effects. To this purpose we develop the oops! ( open object-oriented parallel solutions) - toolkit, a C++ class library for the numerical solution of mathematical models of coupled thermal, hydraulic and chemical processes. This is used to develop problem-specific libraries like acme( amendable coal-fire modeling exercise), a class library for the numerical simulation of coal-fires and applications like kobra (Kohlebrand, german for coal-fire), a numerical simulation code for standard coal-fire models. Basic principle of the oops!-code system is the provision of data types for the description of space and time dependent data fields, description of terms of partial differential equations (pde), their discretisation and solving methods. Coupling of different processes, described by their particular pde is modeled by an automatic timescale-ordered operator-splitting technique. acme is a derived coal-fire specific application library, depending on oops!. If specific functionalities of general interest are implemented and have been tested they will be assimilated into the main oops!-library. Interfaces to external pre- and post-processing tools are easily implemented. Thus a construction kit which can be arbitrarily amended is formed. With the kobra-application constructed with acme we study the processes and propagation of shallow coal seam fires in particular in

Numerical investigations of solute transport in bimodal porous media under dynamic boundary conditions

Science.gov (United States)

Cremer, Clemens; Neuweiler, Insa; Bechtold, Michel; Vanderborght, Jan

2016-04-01

Quantification of flow and solute transport in the shallow subsurface adjacent to the atmosphere is decisive to prevent groundwater pollution and conserve groundwater quality, to develop successful remediation strategies and to understand nutrient cycling. In nature, due to erratic precipitation-evaporation patterns, soil moisture content and related hydraulic conductivity in the vadose zone are not only variable in space but also in time. Flow directions and flow paths locally change between precipitation and evaporation periods. This makes the identification and description of solute transport processes in the vadose zone a complex problem. Recent studies (Lehmann and Or, 2009; Bechtold et al., 2011a) focused on the investigation of upward transport of solutes during evaporation in heterogeneous soil columns, where heterogeneity was introduced by a sharp vertical material interface between two types of sand. Lateral solute transport through the interface in both (lateral) directions was observed at different depths of the investigated soil columns. Following recent approaches, we conduct two-dimensional numerical simulations in a similar setup which is composed of two sands with a sharp vertical material interface. The investigation is broadened from the sole evaporation to combined precipitation-evaporation cycles in order to quantify transport processes resulting from the combined effects of heterogeneous soil structure and dynamic flow conditions. Simulations are performed with a coupled finite volume and random walk particle tracking algorithm (Ippisch et al., 2006; Bechtold et al., 2011b). By comparing scenarios with cyclic boundary conditions and stationary counterparts with the same net flow rate, we found that duration and intensity of precipitation and evaporation periods potentially have an influence on lateral redistribution of solutes and thus leaching rates. Whether or not dynamic boundary conditions lead to significant deviations in the transport

On the elimination of numerical Cerenkov radiation in PIC simulations

International Nuclear Information System (INIS)

Greenwood, Andrew D.; Cartwright, Keith L.; Luginsland, John W.; Baca, Ernest A.

2004-01-01

Particle-in-cell (PIC) simulations are a useful tool in modeling plasma in physical devices. The Yee finite difference time domain (FDTD) method is commonly used in PIC simulations to model the electromagnetic fields. However, in the Yee FDTD method, poorly resolved waves at frequencies near the cut off frequency of the grid travel slower than the physical speed of light. These slowly traveling, poorly resolved waves are not a problem in many simulations because the physics of interest are at much lower frequencies. However, when high energy particles are present, the particles may travel faster than the numerical speed of their own radiation, leading to non-physical, numerical Cerenkov radiation. Due to non-linear interaction between the particles and the fields, the numerical Cerenkov radiation couples into the frequency band of physical interest and corrupts the PIC simulation. There are two methods of mitigating the effects of the numerical Cerenkov radiation. The computational stencil used to approximate the curl operator can be altered to improve the high frequency physics, or a filtering scheme can be introduced to attenuate the waves that cause the numerical Cerenkov radiation. Altering the computational stencil is more physically accurate but is difficult to implement while maintaining charge conservation in the code. Thus, filtering is more commonly used. Two previously published filters by Godfrey and Friedman are analyzed and compared to ideally desired filter properties

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.

Direct numerical simulations of premixed turbulent flames with flamelet-generated manifolds

NARCIS (Netherlands)

Oijen, van J.A.; Bastiaans, R.J.M.; Goey, de L.P.H.

2005-01-01

Direct numerical simulation is a very powerful tool to evaluate the validity of new models and theories for turbulent combustion. In this paper, direct numerical simulations of spherically expanding premixed turbulent flames in the thin reaction zone regime and in the broken reaction zone regime are

Method for numerical simulation of two-term exponentially correlated colored noise

International Nuclear Information System (INIS)

Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.

2006-01-01

A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications

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...

Graphics interfaces and numerical simulations: Mexican Virtual Solar Observatory

Science.gov (United States)

Hernández, L.; González, A.; Salas, G.; Santillán, A.

2007-08-01

Preliminary results associated to the computational development and creation of the Mexican Virtual Solar Observatory (MVSO) are presented. Basically, the MVSO prototype consists of two parts: the first, related to observations that have been made during the past ten years at the Solar Observation Station (EOS) and at the Carl Sagan Observatory (OCS) of the Universidad de Sonora in Mexico. The second part is associated to the creation and manipulation of a database produced by numerical simulations related to solar phenomena, we are using the MHD ZEUS-3D code. The development of this prototype was made using mysql, apache, java and VSO 1.2. based GNU and `open source philosophy'. A graphic user interface (GUI) was created in order to make web-based, remote numerical simulations. For this purpose, Mono was used, because it is provides the necessary software to develop and run .NET client and server applications on Linux. Although this project is still under development, we hope to have access, by means of this portal, to other virtual solar observatories and to be able to count on a database created through numerical simulations or, given the case, perform simulations associated to solar phenomena.

Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom

Science.gov (United States)

Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.

2017-01-01

We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

International Nuclear Information System (INIS)

Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjoegreen, Bjoern; Yee, H.C.; Zhong Xiaolin; Lele, Sanjiva K.

2010-01-01

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

Science.gov (United States)

Franceschini, Andrea; Ferronato, Massimiliano; Janna, Carlo; Teatini, Pietro

2016-06-01

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions.

FOLDER: A numerical tool to simulate the development of structures in layered media

Science.gov (United States)

Adamuszek, Marta; Dabrowski, Marcin; Schmid, Daniel W.

2015-04-01

FOLDER is a numerical toolbox for modelling deformation in layered media during layer parallel shortening or extension in two dimensions. FOLDER builds on MILAMIN [1], a finite element method based mechanical solver, with a range of utilities included from the MUTILS package [2]. Numerical mesh is generated using the Triangle software [3]. The toolbox includes features that allow for: 1) designing complex structures such as multi-layer stacks, 2) accurately simulating large-strain deformation of linear and non-linear viscous materials, 3) post-processing of various physical fields such as velocity (total and perturbing), rate of deformation, finite strain, stress, deviatoric stress, pressure, apparent viscosity. FOLDER is designed to ensure maximum flexibility to configure model geometry, define material parameters, specify range of numerical parameters in simulations and choose the plotting options. FOLDER is an open source MATLAB application and comes with a user friendly graphical interface. The toolbox additionally comprises an educational application that illustrates various analytical solutions of growth rates calculated for the cases of folding and necking of a single layer with interfaces perturbed with a single sinusoidal waveform. We further derive two novel analytical expressions for the growth rate in the cases of folding and necking of a linear viscous layer embedded in a linear viscous medium of a finite thickness. We use FOLDER to test the accuracy of single-layer folding simulations using various 1) spatial and temporal resolutions, 2) time integration schemes, and 3) iterative algorithms for non-linear materials. The accuracy of the numerical results is quantified by: 1) comparing them to analytical solution, if available, or 2) running convergence tests. As a result, we provide a map of the most optimal choice of grid size, time step, and number of iterations to keep the results of the numerical simulations below a given error for a given time

VS2DRTI: Simulating Heat and Reactive Solute Transport in Variably Saturated Porous Media.

Science.gov (United States)

Healy, Richard W; Haile, Sosina S; Parkhurst, David L; Charlton, Scott R

2018-01-29

Variably saturated groundwater flow, heat transport, and solute transport are important processes in environmental phenomena, such as the natural evolution of water chemistry of aquifers and streams, the storage of radioactive waste in a geologic repository, the contamination of water resources from acid-rock drainage, and the geologic sequestration of carbon dioxide. Up to now, our ability to simulate these processes simultaneously with fully coupled reactive transport models has been limited to complex and often difficult-to-use models. To address the need for a simple and easy-to-use model, the VS2DRTI software package has been developed for simulating water flow, heat transport, and reactive solute transport through variably saturated porous media. The underlying numerical model, VS2DRT, was created by coupling the flow and transport capabilities of the VS2DT and VS2DH models with the equilibrium and kinetic reaction capabilities of PhreeqcRM. Flow capabilities include two-dimensional, constant-density, variably saturated flow; transport capabilities include both heat and multicomponent solute transport; and the reaction capabilities are a complete implementation of geochemical reactions of PHREEQC. The graphical user interface includes a preprocessor for building simulations and a postprocessor for visual display of simulation results. To demonstrate the simulation of multiple processes, the model is applied to a hypothetical example of injection of heated waste water to an aquifer with temperature-dependent cation exchange. VS2DRTI is freely available public domain software. © 2018, National Ground Water Association.

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

Science.gov (United States)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

Numerical Simulation of a Tornado Generating Supercell

Science.gov (United States)

Proctor, Fred H.; Ahmad, Nashat N.; LimonDuparcmeur, Fanny M.

2012-01-01

The development of tornadoes from a tornado generating supercell is investigated with a large eddy simulation weather model. Numerical simulations are initialized with a sounding representing the environment of a tornado producing supercell that affected North Carolina and Virginia during the Spring of 2011. The structure of the simulated storm was very similar to that of a classic supercell, and compared favorably to the storm that affected the vicinity of Raleigh, North Carolina. The presence of mid-level moisture was found to be important in determining whether a supercell would generate tornadoes. The simulations generated multiple tornadoes, including cyclonic-anticyclonic pairs. The structure and the evolution of these tornadoes are examined during their lifecycle.

A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.

Science.gov (United States)

Ling, Hong; Luo, Ercang; Dai, Wei

2006-12-22

Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.

Direct numerical simulations of turbulent lean premixed combustion

International Nuclear Information System (INIS)

Sankaran, Ramanan; Hawkes, Evatt R; Chen, Jacqueline H; Lu Tianfeng; Law, Chung K

2006-01-01

In recent years, due to the advent of high-performance computers and advanced numerical algorithms, direct numerical simulation (DNS) of combustion has emerged as a valuable computational research tool, in concert with experimentation. The role of DNS in delivering new Scientific insight into turbulent combustion is illustrated using results from a recent 3D turbulent premixed flame simulation. To understand the influence of turbulence on the flame structure, a 3D fully-resolved DNS of a spatially-developing lean methane-air turbulent Bunsen flame was performed in the thin reaction zones regime. A reduced chemical model for methane-air chemistry consisting of 13 resolved species, 4 quasi-steady state species and 73 elementary reactions was developed specifically for the current simulation. The data is analyzed to study possible influences of turbulence on the flame thickness. The results show that the average flame thickness increases, in qualitative agreement with several experimental results

Simple Numerical Simulation of Strain Measurement

Science.gov (United States)

Tai, H.

2002-01-01

By adopting the basic principle of the reflection (and transmission) of a plane polarized electromagnetic wave incident normal to a stack of films of alternating refractive index, a simple numerical code was written to simulate the maximum reflectivity (transmittivity) of a fiber optic Bragg grating corresponding to various non-uniform strain conditions including photo-elastic effect in certain cases.

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)

Concatenating algorithms for parallel numerical simulations coupling radiation hydrodynamics with neutron transport

International Nuclear Information System (INIS)

Mo Zeyao

2004-11-01

Multiphysics parallel numerical simulations are usually essential to simplify researches on complex physical phenomena in which several physics are tightly coupled. It is very important on how to concatenate those coupled physics for fully scalable parallel simulation. Meanwhile, three objectives should be balanced, the first is efficient data transfer among simulations, the second and the third are efficient parallel executions and simultaneously developments of those simulation codes. Two concatenating algorithms for multiphysics parallel numerical simulations coupling radiation hydrodynamics with neutron transport on unstructured grid are presented. The first algorithm, Fully Loosely Concatenation (FLC), focuses on the independence of code development and the independence running with optimal performance of code. The second algorithm. Two Level Tightly Concatenation (TLTC), focuses on the optimal tradeoffs among above three objectives. Theoretical analyses for communicational complexity and parallel numerical experiments on hundreds of processors on two parallel machines have showed that these two algorithms are efficient and can be generalized to other multiphysics parallel numerical simulations. In especial, algorithm TLTC is linearly scalable and has achieved the optimal parallel performance. (authors)

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 simulation of gasket behaviour during severe accidents (ATHERMIP project)

International Nuclear Information System (INIS)

Castro Lopez, Fernando; Orden Martinez, Alfredo

1998-01-01

This paper summarises the work carried out to numerically simulate the thermo-mechanical behaviour of sealing gasket in large containment penetrations during a severe accident. The gasket material is an elastomeric material and the thermo-mechanical characterization was based on experimentation. The difficulty of numerical simulation lies in the high non-linearity of the analysis, due on one hand, to the high strain levels reached, and on the other, to stiffness changes introduced by contact/takeoff indicators. Also, the stiffness parameters of the gasket material are not constant, but are subject to changes, both regarding the strain level and the environmental conditions (temperature, radiation). The results obtained allow presenting a calculation model capable of simulating and explaining the behaviour of the sealing gasket during a severe accident. Also, the failure hypothesis numerically obtained was environmentally validated. (author)

Plasma modelling and numerical simulation

International Nuclear Information System (INIS)

Van Dijk, J; Kroesen, G M W; Bogaerts, A

2009-01-01

Plasma modelling is an exciting subject in which virtually all physical disciplines are represented. Plasma models combine the electromagnetic, statistical and fluid dynamical theories that have their roots in the 19th century with the modern insights concerning the structure of matter that were developed throughout the 20th century. The present cluster issue consists of 20 invited contributions, which are representative of the state of the art in plasma modelling and numerical simulation. These contributions provide an in-depth discussion of the major theories and modelling and simulation strategies, and their applications to contemporary plasma-based technologies. In this editorial review, we introduce and complement those papers by providing a bird's eye perspective on plasma modelling and discussing the historical context in which it has surfaced. (editorial review)

A calculation method for RF couplers design based on numerical simulation by microwave studio

International Nuclear Information System (INIS)

Wang Rong; Pei Yuanji; Jin Kai

2006-01-01

A numerical simulation method for coupler design is proposed. It is based on the matching procedure for the 2π/3 structure given by Dr. R.L. Kyhl. Microwave Studio EigenMode Solver is used for such numerical simulation. the simulation for a coupler has been finished with this method and the simulation data are compared with experimental measurements. The results show that this numerical simulation method is feasible for coupler design. (authors)

On the numerical solution of fault trees

International Nuclear Information System (INIS)

Demichela, M.; Piccinini, N.; Ciarambino, I.; Contini, S.

2003-01-01

In this paper an account will be given of the numerical solution of the logic trees directly extracted from the Recursive Operability Analysis. Particular attention will be devoted to the use of the NOT and INH logic gates for correct logical representation of Fault Trees prior to their quantitative resolution. The NOT gate is needed for correct logical representation of events when both non-intervention and correct intervention of a protective system may lead to a Top Event. The INH gate must be used to correctly represent the time link between two events that are both necessary, but must occur in sequence. Some numerical examples will be employed to show both the correct identification of the events entering the INH gates and how use of the AND gate instead of the INH gate leads to overestimation of the probability of occurrence of a Top Event

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

Science.gov (United States)

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.

Numerical Simulations of Kinetic Alfvén Waves to Study Spectral ...

Indian Academy of Sciences (India)

Numerical Simulations of Kinetic Alfvén Waves to Study Spectral. Index in Solar Wind Turbulence and Particle Heating. R. P. Sharma. ∗. & H. D. Singh. Center for Energy Studies, Indian Institute of Technology, Delhi 110 016, India. ∗ e-mail: rpsharma@ces.iitd.ernet.in. Abstract. We present numerical simulations of the ...

Contributions to reinforced concrete structures numerical simulations

International Nuclear Information System (INIS)

Badel, P.B.

2001-07-01

In order to be able to carry out simulations of reinforced concrete structures, it is necessary to know two aspects: the behaviour laws have to reflect the complex behaviour of concrete and a numerical environment has to be developed in order to avoid to the user difficulties due to the softening nature of the behaviour. This work deals with these two subjects. After an accurate estimation of two behaviour models (micro-plan and mesoscopic models), two damage models (the first one using a scalar variable, the other one a tensorial damage of the 2 order) are proposed. These two models belong to the framework of generalized standard materials, which renders their numerical integration easy and efficient. A method of load control is developed in order to make easier the convergence of the calculations. At last, simulations of industrial structures illustrate the efficiency of the method. (O.M.)

NUMERICAL METHODS FOR THE SIMULATION OF HIGH INTENSITY HADRON SYNCHROTRONS.

Energy Technology Data Exchange (ETDEWEB)

LUCCIO, A.; D' IMPERIO, N.; MALITSKY, N.

2005-09-12

Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented is SIMBAD, that can be run as stand alone or as part of the UAL (Unified Accelerator Libraries) package.

On the characteristics of a numerical fluid dynamics simulator

International Nuclear Information System (INIS)

Winkler, K.H.A.; Norman, M.L.; Norton, J.L.

1986-01-01

John von Neumann envisioned scientists and mathematicians analyzing and controlling their numerical experiments on nonlinear dynamic systems interactively. The authors describe their concept of a real-time Numerical Fluid Dynamics Simulator NFDS. The authors envision the NFDS to be composed of simulation processors, data storage devices, and image processing devices of extremely high power and capacity, interconnected by very high throughput communication channels. They present individual component performance requirements for both real-time and playback operating modes of the NFDS, using problems of current interest in fluid dynamics as examples. Scaling relations are derived showing the dependence of system requirements on the dimensionality and complexity of the numerical model. The authors conclude by extending their analysis to the system requirements posed in modeling the more involved physics of radiation hydrodynamics

Numerical simulations of earthquakes and the dynamics of fault systems using the Finite Element method.

Science.gov (United States)

Kettle, L. M.; Mora, P.; Weatherley, D.; Gross, L.; Xing, H.

2006-12-01

Simulations using the Finite Element method are widely used in many engineering applications and for the solution of partial differential equations (PDEs). Computational models based on the solution of PDEs play a key role in earth systems simulations. We present numerical modelling of crustal fault systems where the dynamic elastic wave equation is solved using the Finite Element method. This is achieved using a high level computational modelling language, escript, available as open source software from ACcESS (Australian Computational Earth Systems Simulator), the University of Queensland. Escript is an advanced geophysical simulation software package developed at ACcESS which includes parallel equation solvers, data visualisation and data analysis software. The escript library was implemented to develop a flexible Finite Element model which reliably simulates the mechanism of faulting and the physics of earthquakes. Both 2D and 3D elastodynamic models are being developed to study the dynamics of crustal fault systems. Our final goal is to build a flexible model which can be applied to any fault system with user-defined geometry and input parameters. To study the physics of earthquake processes, two different time scales must be modelled, firstly the quasi-static loading phase which gradually increases stress in the system (~100years), and secondly the dynamic rupture process which rapidly redistributes stress in the system (~100secs). We will discuss the solution of the time-dependent elastic wave equation for an arbitrary fault system using escript. This involves prescribing the correct initial stress distribution in the system to simulate the quasi-static loading of faults to failure; determining a suitable frictional constitutive law which accurately reproduces the dynamics of the stick/slip instability at the faults; and using a robust time integration scheme. These dynamic models generate data and information that can be used for earthquake forecasting.

Numerical simulation of gas metal arc welding parametrical study

International Nuclear Information System (INIS)

Szanto, M.; Gilad, I.; Shai, I.; Quinn, T.P.

2002-01-01

The Gas Metal Arc Welding (GMAW) is a widely used welding process in the industry. The process variables are usually determined through extensive experiments. Numerical simulation, reduce the cost and extends the understanding of the process. In the present work, a versatile model for numerical simulation of GMAW is presented. The model provides the basis for fundamental understanding of the process. The model solves the magneto-hydrodynamic equations for the flow and temperature fields of the molten electrode and the plasma simultaneously, to form a fully coupled model. A commercial CFD code was extended to include the effects of radiation, Lorentz forces, Joule heating and thermoelectric effects. The geometry of the numerical model assembled to fit an experimental apparatus. To demonstrate the method, an aluminum electrode was modeled in a pure argon arc. Material properties and welding parameters are the input variables in the numerical model. In a typical process, the temperature distribution of the plasma is over 15000 K, resulting high non-linearity of the material properties. Moreover, there is high uncertainty in the available property data, at that range of temperatures. Therefore, correction factors were derived for the material properties to adjust between the numerical and the experimental results. Using the compensated properties, parametric study was performed. The effects of the welding parameters on the process, such the working voltage, electrode feed rate and shielding gas flow, were derived. The principal result of the present work is the ability to predict, by numerical simulation, the mode, size and frequency of the metal transferred from the electrode, which is the main material and energy source for the welding pool in GMAW

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 MODEL APPLICATION IN ROWING SIMULATOR DESIGN

Directory of Open Access Journals (Sweden)

Petr Chmátal

2016-04-01

Full Text Available The aim of the research was to carry out a hydraulic design of rowing/sculling and paddling simulator. Nowadays there are two main approaches in the simulator design. The first one includes a static water with no artificial movement and counts on specially cut oars to provide the same resistance in the water. The second approach, on the other hand uses pumps or similar devices to force the water to circulate but both of the designs share many problems. Such problems are affecting already built facilities and can be summarized as unrealistic feeling, unwanted turbulent flow and bad velocity profile. Therefore, the goal was to design a new rowing simulator that would provide nature-like conditions for the racers and provide an unmatched experience. In order to accomplish this challenge, it was decided to use in-depth numerical modeling to solve the hydraulic problems. The general measures for the design were taken in accordance with space availability of the simulator ́s housing. The entire research was coordinated with other stages of the construction using BIM. The detailed geometry was designed using a numerical model in Ansys Fluent and parametric auto-optimization tools which led to minimum negative hydraulic phenomena and decreased investment and operational costs due to the decreased hydraulic losses in the system.

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.

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

Science.gov (United States)

Lewis, F.M.; Voss, C.I.; Rubin, Jacob

1986-01-01

A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

The numerical simulation of convection delayed dominated diffusion equation

Directory of Open Access Journals (Sweden)

Mohan Kumar P. Murali

2016-01-01

Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.

Multi-physics modeling and numerical simulation of weld pool in GTA welding

International Nuclear Information System (INIS)

Nguyen, Minh-Chien

2015-01-01

In this work, we develop a 3D physical and numerical model of the GTA (Gas Tungsten Arc) welding process in order to predict, for given welding parameters, useful quantities for the designer of welded assembly: weld bead shape, fluid flow in the weld pool as well as thermal distribution in the work piece. The model is developed in the Cast3M (http://www-cast3m.cea.fr/) finite element software and takes into account the main physical phenomena acting in the work piece and particularly in the weld pool, subject to source terms modeling the arc part of the welding process. A steady solution of this model is thought for and involves the coupling of the nonlinear thermohydraulics and electromagnetic equations together with the displacement of the deformable free surface of the weld pool. A first step in the development consisted in modeling the electromagnetic phenomena with two different numerical methods, in comparing the numerical results obtained with those of the literature and in quantifying the importance of the Lorentz force and the Joule effect compared to the other mechanical and thermal sources by computing power balances. Then, in order to assess the predictive capability of the model, simulations of various welding configurations are performed: variation in the chemical composition of the material, of the welding speed, of the prescribed arc pressure and of the welding positions, which is a focus of this work, are studied. A good agreement is obtained between the results of our model and other experimental and numerical results of the literature. Eventually, a model accounting for metal filling is proposed and its results are discussed. Thus, our complete model can be seen as a solid foundation towards future totally-coupled 3D welding models including the arc and it will be included in WPROCESS the in-house CEA software dedicated to the numerical simulation of welding. (author) [fr

Numerical discrepancy between serial and MPI parallel computations

Directory of Open Access Journals (Sweden)

Sang Bong Lee

2016-09-01

Full Text Available Numerical simulations of 1D Burgers equation and 2D sloshing problem were carried out to study numerical discrepancy between serial and parallel computations. The numerical domain was decomposed into 2 and 4 subdomains for parallel computations with message passing interface. The numerical solution of Burgers equation disclosed that fully explicit boundary conditions used on subdomains of parallel computation was responsible for the numerical discrepancy of transient solution between serial and parallel computations. Two dimensional sloshing problems in a rectangular domain were solved using OpenFOAM. After a lapse of initial transient time sloshing patterns of water were significantly different in serial and parallel computations although the same numerical conditions were given. Based on the histograms of pressure measured at two points near the wall the statistical characteristics of numerical solution was not affected by the number of subdomains as much as the transient solution was dependent on the number of subdomains.

EXTENDED SCALING LAWS IN NUMERICAL SIMULATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE

International Nuclear Information System (INIS)

Mason, Joanne; Cattaneo, Fausto; Perez, Jean Carlos; Boldyrev, Stanislav

2011-01-01

Magnetized turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the inertial range of scales. Numerical simulations serve to guide and test these theories. However, the computational power that is currently available restricts the simulations to Reynolds numbers that are significantly smaller than those in astrophysical settings. In order to increase computational efficiency and, therefore, probe a larger range of scales, one often takes into account the fundamental anisotropy of field-guided MHD turbulence, with gradients being much slower in the field-parallel direction. The simulations are then optimized by employing the reduced MHD equations and relaxing the field-parallel numerical resolution. In this work we explore a different possibility. We propose that there exist certain quantities that are remarkably stable with respect to the Reynolds number. As an illustration, we study the alignment angle between the magnetic and velocity fluctuations in MHD turbulence, measured as the ratio of two specially constructed structure functions. We find that the scaling of this ratio can be extended surprisingly well into the regime of relatively low Reynolds number. However, the extended scaling easily becomes spoiled when the dissipation range in the simulations is underresolved. Thus, taking the numerical optimization methods too far can lead to spurious numerical effects and erroneous representation of the physics of MHD turbulence, which in turn can affect our ability to identify correctly the physical mechanisms that are operating in astrophysical systems.

Numerical simulation of collision-free plasma using Vlasov hybrid simulation

International Nuclear Information System (INIS)

Nunn, D.

1990-01-01

A novel scheme for the numerical simulation of wave particle interactions in space plasmas has been developed. The method, termed VHS or Vlasov Hybrid Simulation, is applicable to hot collision free plasmas in which the unperturbed distribution functions is smooth and free of delta function singularities. The particle population is described as a continuous Vlasov fluid in phase space-granularity and collisional effects being ignored. In traditional PIC/CIC codes the charge/current due to each simulation particle is assigned to a fixed spatial grid. In the VHS method the simulation particles sample the Vlasov fluid and provide information about the value of distribution function (F(r,v) at random points in phase space. Values of F are interpolated from the simulation particles onto a fixed grid in velocity/position or phase space. With distribution function defined on a phase space grid the plasma charge/current field is quickly calculated. The simulation particles serve only to provide information, and thus the particle population may be dynamic. Particles no longer resonant with the wavefield may be discarded from the simulation, and new particles may be inserted into the Vlasov fluid where required

Can numerical simulations accurately predict hydrodynamic instabilities in liquid films?

Science.gov (United States)

Denner, Fabian; Charogiannis, Alexandros; Pradas, Marc; van Wachem, Berend G. M.; Markides, Christos N.; Kalliadasis, Serafim

2014-11-01

Understanding the dynamics of hydrodynamic instabilities in liquid film flows is an active field of research in fluid dynamics and non-linear science in general. Numerical simulations offer a powerful tool to study hydrodynamic instabilities in film flows and can provide deep insights into the underlying physical phenomena. However, the direct comparison of numerical results and experimental results is often hampered by several reasons. For instance, in numerical simulations the interface representation is problematic and the governing equations and boundary conditions may be oversimplified, whereas in experiments it is often difficult to extract accurate information on the fluid and its behavior, e.g. determine the fluid properties when the liquid contains particles for PIV measurements. In this contribution we present the latest results of our on-going, extensive study on hydrodynamic instabilities in liquid film flows, which includes direct numerical simulations, low-dimensional modelling as well as experiments. The major focus is on wave regimes, wave height and wave celerity as a function of Reynolds number and forcing frequency of a falling liquid film. Specific attention is paid to the differences in numerical and experimental results and the reasons for these differences. The authors are grateful to the EPSRC for their financial support (Grant EP/K008595/1).

Numerical Simulation of Polynomial-Speed Convergence Phenomenon

Science.gov (United States)

Li, Yao; Xu, Hui

2017-11-01

We provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for Markov processes. The hybrid method that we introduce is based on the coupling technique and renewal theory. We propose to replace some estimates in classical results about the ergodicity of Markov processes by numerical simulations when the corresponding analytical proof is difficult. After that, all remaining conclusions can be derived from rigorous analysis. Then we apply our results to seek numerical justification for the ergodicity of two 1D microscopic heat conduction models. The mixing rate of these two models are expected to be polynomial but very difficult to prove. In both examples, our numerical results match the expected polynomial mixing rate well.

Numerical simulation of travelling wave induced electrothermal fluid flow

International Nuclear Information System (INIS)

Perch-Nielsen, Ivan R; Green, Nicolas G; Wolff, Anders

2004-01-01

Many microdevices for manipulating particles and cells use electric fields to produce a motive force on the particles. The movement of particles in non-uniform electric fields is called dielectrophoresis, and the usual method of applying this effect is to pass the particle suspension over a microelectrode structure. If the suspension has a noticeable conductivity, one important side effect is that the electric field drives a substantial conduction current through the fluid, causing localized Joule-heating. The resulting thermal gradient produces local conductivity and permittivity changes in the fluid. Dielectrophoretic forces acting upon these pockets of fluid will then produce motion of both the fluid and the particles. This paper presents a numerical solution of the electrical force and the resulting electrothermal driven fluid flow on a travelling wave structure. This common electrode geometry consists of interdigitated electrodes laid down in a long array, with the phase of the applied potential shifted by 90 0 on each subsequent electrode. The resulting travelling electric field was simulated and the thermal field and electrical body force on the fluid calculated, for devices constructed from two typical materials: silicon and glass. The electrothermal fluid flow in the electrolyte over the electrode array was then numerically simulated. The model predicts that the thermal field depends on the conductivity and applied voltage, but more importantly on the geometry of the system and the material used in the construction of the device. The velocity of the fluid flow depends critically on the same parameters, with slight differences in the thermal field for glass and silicon leading to diametrically opposite flow direction with respect to the travelling field for the two materials. In addition, the imposition of slight external temperature gradients is shown to have a large effect on the fluid flow in the device, under certain conditions leading to a reversal of

Numerical Relativity Simulations for Black Hole Merger Astrophysics

Science.gov (United States)

Baker, John G.

2010-01-01

Massive black hole mergers are perhaps the most energetic astronomical events, establishing their importance as gravitational wave sources for LISA, and also possibly leading to observable influences on their local environments. Advances in numerical relativity over the last five years have fueled the development of a rich physical understanding of general relativity's predictions for these events. Z will overview the understanding of these event emerging from numerical simulation studies. These simulations elucidate the pre-merger dynamics of the black hole binaries, the consequent gravitational waveform signatures ' and the resulting state, including its kick velocity, for the final black hole produced by the merger. Scenarios are now being considered for observing each of these aspects of the merger, involving both gravitational-wave and electromagnetic astronomy.

Sensitivity of the solution of the Elder problem to density, velocity and numerical perturbations

Science.gov (United States)

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

Numerical simulation of a mistral wind event occuring

Science.gov (United States)

Guenard, V.; Caccia, J. L.; Tedeschi, G.

2003-04-01

The experimental network of the ESCOMPTE field experiment (june-july 2001) is turned into account to investigate the Mistral wind affecting the Marseille area (South of France). Mistral wind is a northerly flow blowing across the Rhône valley and toward the Mediterranean sea resulting from the dynamical low pressure generated in the wake of the Alps ridge. It brings cold, dry air masses and clear sky conditions over the south-eastern part of France. Up to now, few scientific studies have been carried out on the Mistral wind especially the evolution of its 3-D structure so that its mesoscale numerical simulation is still relevant. Non-hydrostatic RAMS model is performed to better investigate this mesoscale phenomena. Simulations at a 12 km horizontal resolution are compared to boundary layer wind profilers and ground measurements. Preliminary results suit quite well with the Mistral statistical studies carried out by the operational service of Météo-France and observed wind profiles are correctly reproduced by the numerical model RAMS which appears to be an efficient tool for its understanding of Mistral. Owing to the absence of diabatic effect in Mistral events which complicates numerical simulations, the present work is the first step for the validation of RAMS model in that area. Further works will consist on the study of the interaction of Mistral wind with land-sea breeze. Also, RAMS simulations will be combined with aerosol production and ocean circulation models to supply chemists and oceanographers with some answers for their studies.

Experimental investigations and numerical simulations of methane cup-burner flame

Directory of Open Access Journals (Sweden)

Kubát P.

2013-04-01

Full Text Available Pulsation frequency of the cup-burner flame was determined by means of experimental investigations and numerical simulations. Simplified chemical kinetics was successfully implemented into a laminar fluid flow model applied to the complex burner geometry. Our methodical approach is based on the monitoring of flame emission, fast Fourier transformation and reproduction of measured spectral features by numerical simulations. Qualitative agreement between experimental and predicted oscillatory behaviour was obtained by employing a two-step methane oxidation scheme.

Fast numerical solution of KKR-CPA equations: Testing new algorithms

Energy Technology Data Exchange (ETDEWEB)

Bruno, E.; Florio, G.M.; Ginatempo, B.; Giuliano, E.S. (Universita di Messina (Italy))

1994-04-01

Some numerical methods for the solution of KKR-CPA equations are discussed and tested. New, efficient, computational algorithms are proposed, allowing a remarkable reduction of computing time and a good reliability in evaluating spectral quantities. 16 refs., 7 figs.

Numerical simulation of real-world flows

Energy Technology Data Exchange (ETDEWEB)

Hayase, Toshiyuki, E-mail: hayase@ifs.tohoku.ac.jp [Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 (Japan)

2015-10-15

Obtaining real flow information is important in various fields, but is a difficult issue because measurement data are usually limited in time and space, and computational results usually do not represent the exact state of real flows. Problems inherent in the realization of numerical simulation of real-world flows include the difficulty in representing exact initial and boundary conditions and the difficulty in representing unstable flow characteristics. This article reviews studies dealing with these problems. First, an overview of basic flow measurement methodologies and measurement data interpolation/approximation techniques is presented. Then, studies on methods of integrating numerical simulation and measurement, namely, four-dimensional variational data assimilation (4D-Var), Kalman filters (KFs), state observers, etc are discussed. The first problem is properly solved by these integration methodologies. The second problem can be partially solved with 4D-Var in which only initial and boundary conditions are control parameters. If an appropriate control parameter capable of modifying the dynamical structure of the model is included in the formulation of 4D-Var, unstable modes are properly suppressed and the second problem is solved. The state observer and KFs also solve the second problem by modifying mathematical models to stabilize the unstable modes of the original dynamical system by applying feedback signals. These integration methodologies are now applied in simulation of real-world flows in a wide variety of research fields. Examples are presented for basic fluid dynamics and applications in meteorology, aerospace, medicine, etc. (topical review)

A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

International Nuclear Information System (INIS)

Trogdon, Thomas; Deconinck, Bernard

2014-01-01

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg–de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t. (paper)

Simulation of Wave Overtopping of Maritime Structures in a Numerical Wave Flume

Directory of Open Access Journals (Sweden)

Tiago C. A. Oliveira

2012-01-01

Full Text Available A numerical wave flume based on the particle finite element method (PFEM is applied to simulate wave overtopping for impermeable maritime structures. An assessment of the performance and robustness of the numerical wave flume is carried out for two different cases comparing numerical results with experimental data. In the first case, a well-defined benchmark test of a simple low-crested structure overtopped by regular nonbreaking waves is presented, tested in the lab, and simulated in the numerical wave flume. In the second case, state-of-the-art physical experiments of a trapezoidal structure placed on a sloping beach overtopped by regular breaking waves are simulated in the numerical wave flume. For both cases, main overtopping events are well detected by the numerical wave flume. However, nonlinear processes controlling the tests proposed, such as nonlinear wave generation, energy losses along the wave propagation track, wave reflection, and overtopping events, are reproduced with more accuracy in the first case. Results indicate that a numerical wave flume based on the PFEM can be applied as an efficient tool to supplement physical models, semiempirical formulations, and other numerical techniques to deal with overtopping of maritime structures.

Dynamics of the east India coastal current. 2. Numerical solutions

Digital Repository Service at National Institute of Oceanography (India)

McCreary, J.P.; Han, W.; Shankar, D.; Shetye, S.R.

A linear, continuously stratified model is used to investigate the dynamics of the East India Coastal Current (EICC). Solutions are found numerically in a basin that resembles the Indian Ocean basin north of 29 degrees S, and they are forced...

Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

Energy Technology Data Exchange (ETDEWEB)

Paster, Amir, E-mail: paster@tau.ac.il [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); School of Mechanical Engineering, Tel Aviv University, Tel Aviv, 69978 (Israel); Bolster, Diogo [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); Benson, David A. [Hydrologic Science and Engineering, Colorado School of Mines, Golden, CO, 80401 (United States)

2014-04-15

We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. - Graphical abstract:.

Efficient numerical simulation of heat storage in subsurface georeservoirs

Science.gov (United States)

Boockmeyer, A.; Bauer, S.

2015-12-01

The transition of the German energy market towards renewable energy sources, e.g. wind or solar power, requires energy storage technologies to compensate for their fluctuating production. Large amounts of energy could be stored in georeservoirs such as porous formations in the subsurface. One possibility here is to store heat with high temperatures of up to 90°C through borehole heat exchangers (BHEs) since more than 80 % of the total energy consumption in German households are used for heating and hot water supply. Within the ANGUS+ project potential environmental impacts of such heat storages are assessed and quantified. Numerical simulations are performed to predict storage capacities, storage cycle times, and induced effects. For simulation of these highly dynamic storage sites, detailed high-resolution models are required. We set up a model that accounts for all components of the BHE and verified it using experimental data. The model ensures accurate simulation results but also leads to large numerical meshes and thus high simulation times. In this work, we therefore present a numerical model for each type of BHE (single U, double U and coaxial) that reduces the number of elements and the simulation time significantly for use in larger scale simulations. The numerical model includes all BHE components and represents the temporal and spatial temperature distribution with an accuracy of less than 2% deviation from the fully discretized model. By changing the BHE geometry and using equivalent parameters, the simulation time is reduced by a factor of ~10 for single U-tube BHEs, ~20 for double U-tube BHEs and ~150 for coaxial BHEs. Results of a sensitivity study that quantify the effects of different design and storage formation parameters on temperature distribution and storage efficiency for heat storage using multiple BHEs are then shown. It is found that storage efficiency strongly depends on the number of BHEs composing the storage site, their distance and

Decoupled numerical simulation of a solid fuel fired retort boiler

International Nuclear Information System (INIS)

Ryfa, Arkadiusz; Buczynski, Rafal; Chabinski, Michal; Szlek, Andrzej; Bialecki, Ryszard A.

2014-01-01

The paper deals with numerical simulation of the retort boiler fired with solid fuel. Such constructions are very popular for heating systems and their development is mostly based on the designer experience. The simulations have been done in ANSYS/Fluent package and involved two numerical models. The former deals with a fixed-bed combustion of the solid fuel and free-board gas combustion. Solid fuel combustion is based on the coal kinetic parameters. This model encompasses chemical reactions, radiative heat transfer and turbulence. Coal properties have been defined with user defined functions. The latter model describes flow of water inside a water jacked that surrounds the combustion chamber and flue gas ducts. The novelty of the proposed approach is separating of the combustion simulation from the water flow. Such approach allows for reducing the number of degrees of freedom and thus lowering the necessary numerical effort. Decoupling combustion from water flow requires defining interface boundary condition. As this boundary condition is unknown it is adjusted iteratively. The results of the numerical simulation have been successfully validated against measurement data. - Highlights: • New decoupled modelling of small scale boiler is proposed. • Fixed-bed combustion model based on kinetic parameters is introduced. • Decoupling reduced the complexity of the model and computational time. • Simple and computationally inexpensive coupling algorithm is proposed. • Model is successfully validated against measurements

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).

Numerical simulation of tornado-borne missile impact

International Nuclear Information System (INIS)

Tu, D.K.; Murray, R.C.

1977-01-01

The feasibility of using a finite element procedure to examine the impact phenomenon of a tornado-borne missile impinging on a reinforced concrete barrier was assessed. The major emphasis of this study was to simulate the impact of a nondeformable missile. Several series of simulations were run, using an 8-in.-dia steel slug as the impacting missile. The numerical results were then compared with experimental field tests and empirical formulas. The work is in support of tornado design practices for fuel reprocessing and fuel fabrication plants

Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method

Science.gov (United States)

Krasnov, M. M.; Kuchugov, P. A.; E Ladonkina, M.; E Lutsky, A.; Tishkin, V. F.

2017-02-01

Detailed unstructured grids and numerical methods of high accuracy are frequently used in the numerical simulation of gasdynamic flows in areas with complex geometry. Galerkin method with discontinuous basis functions or Discontinuous Galerkin Method (DGM) works well in dealing with such problems. This approach offers a number of advantages inherent to both finite-element and finite-difference approximations. Moreover, the present paper shows that DGM schemes can be viewed as Godunov method extension to piecewise-polynomial functions. As is known, DGM involves significant computational complexity, and this brings up the question of ensuring the most effective use of all the computational capacity available. In order to speed up the calculations, operator programming method has been applied while creating the computational module. This approach makes possible compact encoding of mathematical formulas and facilitates the porting of programs to parallel architectures, such as NVidia CUDA and Intel Xeon Phi. With the software package, based on DGM, numerical simulations of supersonic flow past solid bodies has been carried out. The numerical results are in good agreement with the experimental ones.

Numerical simulations of subcritical reactor kinetics in thermal hydraulic transient phases

Energy Technology Data Exchange (ETDEWEB)

Yoo, J; Park, W S [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1999-12-31

A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute (KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons, external neutrons form spallation reactions are essentially required for operating the reactor in its steady state. Furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance to the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases. 5 refs., 8 figs. (Author)

Numerical simulations of subcritical reactor kinetics in thermal hydraulic transient phases

Energy Technology Data Exchange (ETDEWEB)

Yoo, J.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1998-12-31

A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute (KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons, external neutrons form spallation reactions are essentially required for operating the reactor in its steady state. Furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance to the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases. 5 refs., 8 figs. (Author)

Finite-difference numerical simulations of underground explosion cavity decoupling

Science.gov (United States)

Aldridge, D. F.; Preston, L. A.; Jensen, R. P.

2012-12-01

Earth models containing a significant portion of ideal fluid (e.g., air and/or water) are of increasing interest in seismic wave propagation simulations. Examples include a marine model with a thick water layer, and a land model with air overlying a rugged topographic surface. The atmospheric infrasound community is currently interested in coupled seismic-acoustic propagation of low-frequency signals over long ranges (~tens to ~hundreds of kilometers). Also, accurate and efficient numerical treatment of models containing underground air-filled voids (caves, caverns, tunnels, subterranean man-made facilities) is essential. In support of the Source Physics Experiment (SPE) conducted at the Nevada National Security Site (NNSS), we are developing a numerical algorithm for simulating coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite-differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within the fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via a finite-difference operator "order switching" formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Current modeling efforts are oriented toward quantifying the amount of atmospheric infrasound energy generated by various underground seismic sources (explosions and earthquakes). Source depth and orientation, and surface topography play obvious roles. The cavity decoupling problem, where an explosion is detonated within an air-filled void, is of special interest. A point explosion

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.

Numerical simulation of liquid film flow on revolution surfaces with momentum integral method

International Nuclear Information System (INIS)

Bottoni Maurizio

2005-01-01

The momentum integral method is applied in the frame of safety analysis of pressure water reactors under hypothetical loss of coolant accident (LOCA) conditions to simulate numerically film condensation, rewetting and vaporization on the inner surface of pressure water reactor containment. From the conservation equations of mass and momentum of a liquid film arising from condensation of steam upon the inner of the containment during a LOCA in a pressure water reactor plant, an integro-differential equation is derived, referring to an arbitrary axisymmetric surface of revolution. This equation describes the velocity distribution of the liquid film along a meridian of a surface of revolution. From the integro-differential equation and ordinary differential equation of first order for the film velocity is derived and integrated numerically. From the velocity distribution the film thickness distribution is obtained. The solution of the enthalpy equation for the liquid film yields the temperature distribution on the inner surface of the containment. (authors)

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

Direct numerical simulation of annular flows

Science.gov (United States)

Batchvarov, Assen; Kahouadji, Lyes; Chergui, Jalel; Juric, Damir; Shin, Seungwon; Craster, Richard V.; Matar, Omar K.

2017-11-01

Vertical counter-current two-phase flows are investigated using direct numerical simulations. The computations are carried out using Blue, a front-tracking-based CFD solver. Preliminary results show good qualitative agreement with experimental observations in terms of interfacial phenomena; these include three-dimensional, large-amplitude wave formation, the development of long ligaments, and droplet entrainment. The flooding phenomena in these counter current systems are closely investigated. The onset of flooding in our simulations is compared to existing empirical correlations such as Kutateladze-type and Wallis-type. The effect of varying tube diameter and fluid properties on the flooding phenomena is also investigated in this work. EPSRC, UK, MEMPHIS program Grant (EP/K003976/1), RAEng Research Chair (OKM).

Numerical modelling of random walk one-dimensional diffusion

International Nuclear Information System (INIS)

Vamos, C.; Suciu, N.; Peculea, M.

1996-01-01

The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies

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.

Numerical simulation of transoceanic propagation and run-up of tsunami

Energy Technology Data Exchange (ETDEWEB)

Cho, Yong-Sik; Yoon Sung-Bum [Hanyang University, Seoul(Korea)

2001-04-30

The propagation and associated run-up process of tsunami are numerically investigated in this study. A transoceanic propagation model is first used to simulate the distant propagation of tsunamis. An inundation model is then employed to simulate the subsequent run-up process near coastline. A case study is done for the 1960 Chilean tsunami. A detailed maximum inundation map at Hilo Bay is obtained and compared with field observation and other numerical model, predictions. A very reasonable agreement is observed. (author). refs., tabs., figs.

A numerical solution of the coupled proton-H atom transport equations for the proton aurora

International Nuclear Information System (INIS)

Basu, B.; Jasperse, J.R.; Grossbard, N.J.

1990-01-01

A numerical code has been developed to solve the coupled proton-H atom linear transport equations for the proton aurora. The transport equations have been simplified by using plane-parallel geometry and the forward-scattering approximations only. Otherwise, the equations and their numerical solutions are exact. Results are presented for the particle fluxes and the energy deposition rates, and they are compared with the previous analytical results that were obtained by using additional simplifying approximations. It is found that although the analytical solutions for the particle fluxes differ somewhat from the numerical solutions, the energy deposition rates calculated by the two methods agree to within a few percent. The accurate particle fluxes given by the numerical code are useful for accurate calculation of the characteristic quantities of the proton aurora, such as the ionization rates and the emission rates

Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

Energy Technology Data Exchange (ETDEWEB)

Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)

2007-09-17

In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.

Analysis of numerical solutions for Bateman equations; Analise de solucoes numericas para as equacoes de Bateman

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)

Multiphysics Simulation of Welding-Arc and Nozzle-Arc System: Mathematical-Model, Solution-Methodology and Validation

Science.gov (United States)

Pawar, Sumedh; Sharma, Atul

2018-01-01

This work presents mathematical model and solution methodology for a multiphysics engineering problem on arc formation during welding and inside a nozzle. A general-purpose commercial CFD solver ANSYS FLUENT 13.0.0 is used in this work. Arc formation involves strongly coupled gas dynamics and electro-dynamics, simulated by solution of coupled Navier-Stoke equations, Maxwell's equations and radiation heat-transfer equation. Validation of the present numerical methodology is demonstrated with an excellent agreement with the published results. The developed mathematical model and the user defined functions (UDFs) are independent of the geometry and are applicable to any system that involves arc-formation, in 2D axisymmetric coordinates system. The high-pressure flow of SF6 gas in the nozzle-arc system resembles arc chamber of SF6 gas circuit breaker; thus, this methodology can be extended to simulate arcing phenomenon during current interruption.

Assessment of solute fluxes beneath an orchard irrigated with treated sewage water: A numerical study

Science.gov (United States)

Russo, David; Laufer, Asher; Shapira, Roi H.; Kurtzman, Daniel

2013-02-01

Detailed numerical simulations were used to analyze water flow and transport of nitrate, chloride, and a tracer solute in a 3-D, spatially heterogeneous, variably saturated soil, originating from a citrus orchard irrigated with treated sewage water (TSW) considering realistic features of the soil-water-plant-atmosphere system. Results of this study suggest that under long-term irrigation with TSW, because of nitrate uptake by the tree roots and nitrogen transformations, the vadose zone may provide more capacity for the attenuation of the nitrate load in the groundwater than for the chloride load in the groundwater. Results of the 3-D simulations were used to assess their counterparts based on a simplified, deterministic, 1-D vertical simulation and on limited soil monitoring. Results of the analyses suggest that the information that may be gained from a single sampling point (located close to the area active in water uptake by the tree roots) or from the results of the 1-D simulation is insufficient for a quantitative description of the response of the complicated, 3-D flow system. Both might considerably underestimate the movement and spreading of a pulse of a tracer solute and also the groundwater contamination hazard posed by nitrate and particularly by chloride moving through the vadose zone. This stems mainly from the rain that drove water through the flow system away from the rooted area and could not be represented by the 1-D model or by the single sampling point. It was shown, however, that an additional sampling point, located outside the area active in water uptake, may substantially improve the quantitative description of the response of the complicated, 3-D flow system.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

Science.gov (United States)

Horno, J; González-Caballero, F; González-Fernández, C F

1990-01-01

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

Two-fluid Numerical Simulations of Solar Spicules

Energy Technology Data Exchange (ETDEWEB)

Kuźma, Błażej; Murawski, Kris; Kayshap, Pradeep; Wójcik, Darek [Group of Astrophysics, University of Maria Curie-Skłodowska, ul. Radziszewskiego 10, 20-031 Lublin (Poland); Srivastava, Abhishek Kumar; Dwivedi, Bhola N., E-mail: blazejkuzma1@gmail.com [Department of Physics, Indian Institute of Technology (BHU), Varanasi-221005 (India)

2017-11-10

We aim to study the formation and evolution of solar spicules by means of numerical simulations of the solar atmosphere. With the use of newly developed JOANNA code, we numerically solve two-fluid (for ions + electrons and neutrals) equations in 2D Cartesian geometry. We follow the evolution of a spicule triggered by the time-dependent signal in ion and neutral components of gas pressure launched in the upper chromosphere. We use the potential magnetic field, which evolves self-consistently, but mainly plays a passive role in the dynamics. Our numerical results reveal that the signal is steepened into a shock that propagates upward into the corona. The chromospheric cold and dense plasma lags behind this shock and rises into the corona with a mean speed of 20–25 km s{sup −1}. The formed spicule exhibits the upflow/downfall of plasma during its total lifetime of around 3–4 minutes, and it follows the typical characteristics of a classical spicule, which is modeled by magnetohydrodynamics. The simulated spicule consists of a dense and cold core that is dominated by neutrals. The general dynamics of ion and neutral spicules are very similar to each other. Minor differences in those dynamics result in different widths of both spicules with increasing rarefaction of the ion spicule in time.

Numerical solution of the ekpyrotic scenario in the moduli space approximation

International Nuclear Information System (INIS)

Soerensen, Torquil MacDonald

2005-01-01

A numerical solution to the equations of motion for the ekpyrotic bulk brane scenario in the moduli space approximation is presented. The visible universe brane has positive tension, and we use a potential that goes to zero exponentially at large distance, and also goes to zero at small distance. In the case considered, no bulk brane, visible brane collision occurs in the solution. This property and the general behavior of the solution is qualitatively the same when the visible brane tension is negative, and for many different parameter choices

Numerical simulations and mathematical models of flows in complex geometries

DEFF Research Database (Denmark)

Hernandez Garcia, Anier

The research work of the present thesis was mainly aimed at exploiting one of the strengths of the Lattice Boltzmann methods, namely, the ability to handle complicated geometries to accurately simulate flows in complex geometries. In this thesis, we perform a very detailed theoretical analysis...... and through the Chapman-Enskog multi-scale expansion technique the dependence of the kinetic viscosity on each scheme is investigated. Seeking for optimal numerical schemes to eciently simulate a wide range of complex flows a variant of the finite element, off-lattice Boltzmann method [5], which uses...... the characteristic based integration is also implemented. Using the latter scheme, numerical simulations are conducted in flows of different complexities: flow in a (real) porous network and turbulent flows in ducts with wall irregularities. From the simulations of flows in porous media driven by pressure gradients...

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)

Modelling and numerical simulation of two-phase flows using the two-fluid two-pressure approach; Modelisation et simulation numerique des ecoulements diphasiques par une approche bifluide a deux pressions

Energy Technology Data Exchange (ETDEWEB)

Guillemaud, V

2007-03-15

This thesis is devoted to the modelling and numerical simulation of liquid-vapor flows. In order to describe these phase transition flows, a two-fluid two-pressure approach is considered. This description of the liquid-vapor mixing is associated to the seven-equation model introduced by Baer and Nunziato. This work investigates the properties of this model in order to simulate the phase transition flows occurring in nuclear engineering. First, a theoretical thermodynamic framework is constructed to describe the liquid-vapor mixing. Provided with this framework, various modelling choices are suggested for the interaction terms between the phases. These closure laws comply with an entropy inequality. The mathematical properties of this model are thereafter examined. The convective part is associated to a nonconservative hyperbolic system. First, we focus on the definition of its weak solutions. Several flow regimes for the two-phase mixing derive from this analysis. Such regimes for the two-phase flows are analogous to the torrential and fluvial regimes for the shallow-water equations. Furthermore, we establish the linear and nonlinear stabilities of the liquid-vapor equilibrium. Finally, the implementation of a turbulence model and the introduction of a reconstruction process for the interfacial area are investigated in order to refine the description of the interfacial transfers. Using a fractional step approach, a Finite Volume method is at last constructed to simulate this model. First, various nonconservative adaptations of standard Riemann solvers are developed to approach the convective part. Unlike the classic nonconservative framework, these schemes converge towards the same solution. Furthermore, a new relaxation scheme is proposed to approach the interfacial transfers. Provided with these schemes, the whole numerical method preserves the liquid-vapor equilibria. Using this numerical method, a careful comparison between the one- and two-pressure two

Visualization techniques in plasma numerical simulations

International Nuclear Information System (INIS)

Kulhanek, P.; Smetana, M.

2004-01-01

Numerical simulations of plasma processes usually yield a huge amount of raw numerical data. Information about electric and magnetic fields and particle positions and velocities can be typically obtained. There are two major ways of elaborating these data. First of them is called plasma diagnostics. We can calculate average values, variances, correlations of variables, etc. These results may be directly comparable with experiments and serve as the typical quantitative output of plasma simulations. The second possibility is the plasma visualization. The results are qualitative only, but serve as vivid display of phenomena in the plasma followed-up. An experience with visualizing electric and magnetic fields via Line Integral Convolution method is described in the first part of the paper. The LIC method serves for visualization of vector fields in two dimensional section of the three dimensional plasma. The field values can be known only in grid points of three-dimensional grid. The second part of the paper is devoted to the visualization techniques of the charged particle motion. The colour tint can be used for particle temperature representation. The motion can be visualized by a trace fading away with the distance from the particle. In this manner the impressive animations of the particle motion can be achieved. (author)

Numerical nodal simulation of the axial power distribution within nuclear reactors using a kinetics diffusion model. I

International Nuclear Information System (INIS)

Barros, R.C. de.

1992-05-01

Presented here is a new numerical nodal method for the simulation of the axial power distribution within nuclear reactors using the one-dimensional one speed kinetics diffusion model with one group of delayed neutron precursors. Our method is based on a spectral analysis of the nodal kinetics equations. These equations are obtained by integrating the original kinetics equations separately over a time step and over a spatial node, and then considering flat approximations for the forward difference terms. These flat approximations are the only approximations that are considered in the method. As a result, the spectral nodal method for space - time reactor kinetics generates numerical solutions for space independent problems or for time independent problems that are completely free from truncation errors. We show numerical results to illustrate the method's accuracy for coarse mesh calculations. (author)

Aggregation work at polydisperse micellization: ideal solution and "dressed micelle" models comparing to molecular dynamics simulations.

Science.gov (United States)

Burov, S V; Shchekin, A K

2010-12-28

General thermodynamic relations for the work of polydisperse micelle formation in the model of ideal solution of molecular aggregates in nonionic surfactant solution and the model of "dressed micelles" in ionic solution have been considered. In particular, the dependence of the aggregation work on the total concentration of nonionic surfactant has been analyzed. The analogous dependence for the work of formation of ionic aggregates has been examined with regard to existence of two variables of a state of an ionic aggregate, the aggregation numbers of surface active ions and counterions. To verify the thermodynamic models, the molecular dynamics simulations of micellization in nonionic and ionic surfactant solutions at two total surfactant concentrations have been performed. It was shown that for nonionic surfactants, even at relatively high total surfactant concentrations, the shape and behavior of the work of polydisperse micelle formation found within the model of the ideal solution at different total surfactant concentrations agrees fairly well with the numerical experiment. For ionic surfactant solutions, the numerical results indicate a strong screening of ionic aggregates by the bound counterions. This fact as well as independence of the coefficient in the law of mass action for ionic aggregates on total surfactant concentration and predictable behavior of the "waterfall" lines of surfaces of the aggregation work upholds the model of "dressed" ionic aggregates.

Numerical simulations for impact damage detection in composites using vibrothermography

International Nuclear Information System (INIS)

Pieczonka, L J; Uhl, T; Szwedo, M; Staszewski, W J; Aymerich, F

2010-01-01

Composite materials are widely used in many engineering applications due to their high strength-to-weight ratios. However, it is well known that composites are susceptible to impact damage. Detection of impact damage is an important issue in maintenance of composite structures. Various non-destructive image-based techniques have been developed for damage detection in composite materials. These include vibrothermography that detects surface temperature changes due to heating associated with frictional energy dissipation by damage. In the present paper numerical simulations are used to investigate heat generation in a composite plate with impact damage in order to support damage detection analysis with vibrothermography. Explicit finite elements are used to model ultrasonic wave propagation in the damaged plate. Simulated delamination and cracks induce frictional heating in the plate. Coupled thermo-mechanical simulations are performed in high frequencies using commercial LS-Dyna finite element code. Very good qualitative agreement between measurements and simulations has been obtained. The area of increased temperature corresponds very well with the damaged area in both experiments and simulations. Numerical model has to be further refined in order to quantitatively match the experiments. The main issues of concern are frictional and thermal properties of composites. The final goal of these research efforts is to predict damage detection sensitivity of vibrothermography in real engineering applications based on numerical models.

special algorithm for the numerical solution of system of initial value ...

African Journals Online (AJOL)

Nwokem et al.

Science World Journal Vol 12(No 4) 2017 ... Over the years, several researchers have considered the collocation method as a way of generating numerical solutions to ... study problems in mathematics, engineering, computer science and.

MHD turbulent dynamo in astrophysics: Theory and numerical simulation

Science.gov (United States)

Chou, Hongsong

2001-10-01

This thesis treats the physics of dynamo effects through theoretical modeling of magnetohydrodynamic (MHD) systems and direct numerical simulations of MHD turbulence. After a brief introduction to astrophysical dynamo research in Chapter 1, the following issues in developing dynamic models of dynamo theory are addressed: In Chapter 2, nonlinearity that arises from the back reaction of magnetic field on velocity field is considered in a new model for the dynamo α-effect. The dependence of α-coefficient on magnetic Reynolds number, kinetic Reynolds number, magnetic Prandtl number and statistical properties of MHD turbulence is studied. In Chapter 3, the time-dependence of magnetic helicity dynamics and its influence on dynamo effects are studied with a theoretical model and 3D direct numerical simulations. The applicability of and the connection between different dynamo models are also discussed. In Chapter 4, processes of magnetic field amplification by turbulence are numerically simulated with a 3D Fourier spectral method. The initial seed magnetic field can be a large-scale field, a small-scale magnetic impulse, and a combination of these two. Other issues, such as dynamo processes due to helical Alfvénic waves and the implication and validity of the Zeldovich relation, are also addressed in Appendix B and Chapters 4 & 5, respectively. Main conclusions and future work are presented in Chapter 5. Applications of these studies are intended for astrophysical magnetic field generation through turbulent dynamo processes, especially when nonlinearity plays central role. In studying the physics of MHD turbulent dynamo processes, the following tools are developed: (1)A double Fourier transform in both space and time for the linearized MHD equations (Chapter 2 and Appendices A & B). (2)A Fourier spectral numerical method for direct simulation of 3D incompressible MHD equations (Appendix C).

Mathematical models and numerical simulation in electromagnetism

CERN Document Server

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.

Simulation of effects of redox and precipitation on diffusion of uranium solution species in backfill

International Nuclear Information System (INIS)

Carnahan, C.L.

1987-12-01

This investigation addresses the problem of prediction of the rate of migration of redox-sensitive solution species within packing and backfill materials under conditions of variable oxidation potential. Effects of changes of oxidation potential and precipitation of stable uranium compounds during diffusion of uranium from a region of high oxidation potential into a region of low oxidation potential were simulated numerically. Questions of particular interest addressed in the investigation were the existence of a moving ''redox front'' and the influence of precipitation-dissolution processes on uranium migration. The simulations showed that no expanding redox fronts existed at any simulated time up to 3.2 x 10 5 years (10 13 s). In simulations where precipitation of stable solids was not allowed, variations of oxidation potential did not affect total uranium concentrations in solution. Concentration profiles could be predicted simply by diffusion of the (constant) source concentrations. In simulations where precipitation of stable solids was allowed, uraninite and calcium uranate accumulated at the source-transport domain interface, while coffinite penetrated further into the transport domain. Total uranium concentrations in regions of precipitation were determined by solubilities of the precipitated solids, and were six to seven orders of magnitude lower than those in the simulations without precipitation, throughout the domain of transport. 14 refs., 7 figs., 2 tabs

Numerical simulation for two-phase jet problem

International Nuclear Information System (INIS)

Lee, W.H.; Shah, V.L.

1981-01-01

A computer program TWOP was developed for obtaining the numerical solutions of three-dimensional, transient, two-phase flow system with nonequilibrium and nonhomogeneous conditions. TWOP employs two-fluid model and a set of the conservation equations formulated by Harlow and Amsden along with their Implicit Multi-Field (IMF) numerical technique that allows all degrees of couplings between the two fields. We have further extended the procedure of Harlow and Amsden by incorporating the implicit couplings of phase transition and interfacial heat transfer terms in the energy equations. Numerical results of two tested problems are presented to demonstrate the capabilities of the TWOP code. The first problem is the separation of vapor and liquid, showing that the code can handle the computational difficulties such as liquid packing and sharp interface phenomena. The second problem is the high pressure two-phase jet impinged on vertical plate, demonstrating the important role of the interfacial mass and momentum exchange

Numerical simulation and experimental validation of coiled adiabatic capillary tubes

Energy Technology Data Exchange (ETDEWEB)

Garcia-Valladares, O. [Centro de Investigacion en Energia, Universidad Nacional Autonoma de Mexico (UNAM), Apdo. Postal 34, 62580 Temixco, Morelos (Mexico)

2007-04-15

The objective of this study is to extend and validate the model developed and presented in previous works [O. Garcia-Valladares, C.D. Perez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: mathematical formulation and numerical model, Applied Thermal Engineering 22 (2) (2002) 173-182; O. Garcia-Valladares, C.D. Perez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part II: experimental validation and parametric studies, Applied Thermal Engineering 22 (4) (2002) 379-391] to coiled adiabatic capillary tube expansion devices working with pure and mixed refrigerants. The discretized governing equations are coupled using an implicit step by step method. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpies, temperatures, pressures, vapor qualities, velocities, heat fluxes, etc.) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretized. The numerical model allows analysis of aspects such as geometry, type of fluid (pure substances and mixtures), critical or non-critical flow conditions, metastable regions, and transient aspects. Comparison of the numerical simulation with a wide range of experimental data presented in the technical literature will be shown in the present article in order to validate the model developed. (author)

Tests of numerical simulation algorithms for the Kubo oscillator

International Nuclear Information System (INIS)

Fox, R.F.; Roy, R.; Yu, A.W.

1987-01-01

Numerical simulation algorithms for multiplicative noise (white or colored) are tested for accuracy against closed-form expressions for the Kubo oscillator. Direct white noise simulations lead to spurious decay of the modulus of the oscillator amplitude. A straightforward colored noise algorithm greatly reduces this decay and also provides highly accurate results in the white noise limit

The numerical simulation of accelerator components

International Nuclear Information System (INIS)

Herrmannsfeldt, W.B.; Hanerfeld, H.

1987-05-01

The techniques of the numerical simulation of plasmas can be readily applied to problems in accelerator physics. Because the problems usually involve a single component ''plasma,'' and times that are at most, a few plasma oscillation periods, it is frequently possible to make very good simulations with relatively modest computation resources. We will discuss the methods and illustrate them with several examples. One of the more powerful techniques of understanding the motion of charged particles is to view computer-generated motion pictures. We will show several little movie strips to illustrate the discussions. The examples will be drawn from the application areas of Heavy Ion Fusion, electron-positron linear colliders and injectors for free-electron lasers. 13 refs., 10 figs., 2 tabs

Numerical simulation of manual operation at MID stand control room

International Nuclear Information System (INIS)

Doca, C.; Dobre, A.; Predescu, D.; Mielcioiu, A.

2003-01-01

Since 2000 at INR Pitesti a package of software products devoted to numerical simulation of manual operations at fueling machine control room was developed. So far, specified, designed, worked out and implemented was the PUPITRU code. The following issues were solved: graphical aspects of specific computer - human operator interface; functional and graphical simulation of the whole associated equipment of the control desk components; implementation of the main notation as used in the automated schemes of the control desk in view of the fast identification of the switches, lamps, instrumentation, etc.; implementation within PUPITRU code of the entire data base used in the frame of MID tests; implementation of a number of about 1000 numerical simulation equations describing specific operational MID testing situations

Numerical simulation of thermal fracture in functionally graded

Indian Academy of Sciences (India)

Numerical simulation of thermal fracture in functionally graded materials using element-free ... Initially, the temperature distribution over the domain is obtained by solving the heat transfer problem. ... Department of Mechanical Engineering, National Institute of Technology, Hamirpur 177005, India ... Contact | Site index.

A Numerical Approach for Hybrid Simulation of Power System Dynamics Considering Extreme Icing Events

DEFF Research Database (Denmark)

Chen, Lizheng; Zhang, Hengxu; Wu, Qiuwei

2017-01-01

numerical simulation scheme integrating icing weather events with power system dynamics is proposed to extend power system numerical simulation. A technique is developed to efficiently simulate the interaction of slow dynamics of weather events and fast dynamics of power systems. An extended package for PSS...

Asymptotic study and numerical simulation of laser wave propagation in an inhomogeneous medium; Etude asymptotique et simulation numerique de la propagation laser en milieu inhomogene

Energy Technology Data Exchange (ETDEWEB)

Doumic, M

2005-05-15

To simulate the propagation of a monochromatic laser beam in a medium, we use the paraxial approximation of the Klein-Gordon (in the time-varying problem) and of the Maxwell (in the non time-depending case) equations. In a first part, we make an asymptotic analysis of the Klein-Gordon equation. We obtain approximated problems, either of Schroedinger or of transport-Schroedinger type. We prove the existence and uniqueness of a solution for these problems, and estimate the difference between it and the exact solution of the Klein-Gordon equation. In a second part, we study the boundary problem for the advection Schroedinger equation, and show what the boundary condition must be so that the problem on our domain should be the restriction of the problem in the whole space: such a condition is called a transparent or an absorbing boundary condition. In a third part, we use the preceding results to build a numerical resolution method, for which we prove stability and show some simulations. (author)

Reactor numerical simulation and hydraulic test research

International Nuclear Information System (INIS)

Yang, L. S.

2009-01-01

In recent years, the computer hardware was improved on the numerical simulation on flow field in the reactor. In our laboratory, we usually use the Pro/e or UG commercial software. After completed topology geometry, ICEM-CFD is used to get mesh for computation. Exact geometrical similarity is maintained between the main flow paths of the model and the prototype, with the exception of the core simulation design of the fuel assemblies. The drive line system is composed of drive mechanism, guide bush assembly, fuel assembly and control rod assembly, and fitted with the rod level indicator and drive mechanism power device

A mass conserving level set method for detailed numerical simulation of liquid atomization

Energy Technology Data Exchange (ETDEWEB)

Luo, Kun; Shao, Changxiao [State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027 (China); Yang, Yue [State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing 100871 (China); Fan, Jianren, E-mail: fanjr@zju.edu.cn [State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027 (China)

2015-10-01

An improved mass conserving level set method for detailed numerical simulations of liquid atomization is developed to address the issue of mass loss in the existing level set method. This method introduces a mass remedy procedure based on the local curvature at the interface, and in principle, can ensure the absolute mass conservation of the liquid phase in the computational domain. Three benchmark cases, including Zalesak's disk, a drop deforming in a vortex field, and the binary drop head-on collision, are simulated to validate the present method, and the excellent agreement with exact solutions or experimental results is achieved. It is shown that the present method is able to capture the complex interface with second-order accuracy and negligible additional computational cost. The present method is then applied to study more complex flows, such as a drop impacting on a liquid film and the swirling liquid sheet atomization, which again, demonstrates the advantages of mass conservation and the capability to represent the interface accurately.

A finite difference method for numerical solution of the Nernst-Planck equations when convective flux and electric current are involved

International Nuclear Information System (INIS)

Aguilera, V.M.; Garrido, J.; Mafe, S.; Pellicer, J.

1985-01-01

An algorithm for the solution of Nernst-Planck equations with simultaneous convective flux and electric current has been developed without using Poisson's equation. The numerical simulation which has been developed reproduces the behaviour of the system employing their experimental variables as parameters of the algorithm. However, other procedures are only capable of dealing with some of the experimental conditions described here. The agreement between the theoretically predicted values and the experimentally obtained is quite reasonable. (author)

Salt Effect on Osmotic Pressure of Polyelectrolyte Solutions: Simulation Study

Directory of Open Access Journals (Sweden)

Jan-Michael Y. Carrillo

2014-07-01

Full Text Available Abstract: We present results of the hybrid Monte Carlo/molecular dynamics simulations of the osmotic pressure of salt solutions of polyelectrolytes. In our simulations, we used a coarse-grained representation of polyelectrolyte chains, counterions and salt ions. During simulation runs, we alternate Monte Carlo and molecular dynamics simulation steps. Monte Carlo steps were used to perform small ion exchange between simulation box containing salt ions (salt reservoir and simulation box with polyelectrolyte chains, counterions and salt ions (polyelectrolyte solution. This allowed us to model Donnan equilibrium and partitioning of salt and counterions across membrane impermeable to polyelectrolyte chains. Our simulations have shown that the main contribution to the system osmotic pressure is due to salt ions and osmotically active counterions. The fraction of the condensed (osmotically inactive counterions first increases with decreases in the solution ionic strength then it saturates. The reduced value of the system osmotic coefficient is a universal function of the ratio of the concentration of osmotically active counterions and salt concentration in salt reservoir. Simulation results are in a very good agreement with osmotic pressure measurements in sodium polystyrene sulfonate, DNA, polyacrylic acid, sodium polyanetholesulfonic acid, polyvinylbenzoic acid, and polydiallyldimethylammonium chloride solutions.

Numerical solution of modified differential equations based on symmetry preservation.

Science.gov (United States)

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

Hybrid numerical methods for multiscale simulations of subsurface biogeochemical processes

International Nuclear Information System (INIS)

Scheibe, T D; Tartakovsky, A M; Tartakovsky, D M; Redden, G D; Meakin, P

2007-01-01

Many subsurface flow and transport problems of importance today involve coupled non-linear flow, transport, and reaction in media exhibiting complex heterogeneity. In particular, problems involving biological mediation of reactions fall into this class of problems. Recent experimental research has revealed important details about the physical, chemical, and biological mechanisms involved in these processes at a variety of scales ranging from molecular to laboratory scales. However, it has not been practical or possible to translate detailed knowledge at small scales into reliable predictions of field-scale phenomena important for environmental management applications. A large assortment of numerical simulation tools have been developed, each with its own characteristic scale. Important examples include 1. molecular simulations (e.g., molecular dynamics); 2. simulation of microbial processes at the cell level (e.g., cellular automata or particle individual-based models); 3. pore-scale simulations (e.g., lattice-Boltzmann, pore network models, and discrete particle methods such as smoothed particle hydrodynamics); and 4. macroscopic continuum-scale simulations (e.g., traditional partial differential equations solved by finite difference or finite element methods). While many problems can be effectively addressed by one of these models at a single scale, some problems may require explicit integration of models across multiple scales. We are developing a hybrid multi-scale subsurface reactive transport modeling framework that integrates models with diverse representations of physics, chemistry and biology at different scales (sub-pore, pore and continuum). The modeling framework is being designed to take advantage of advanced computational technologies including parallel code components using the Common Component Architecture, parallel solvers, gridding, data and workflow management, and visualization. This paper describes the specific methods/codes being used at each

Practical design of magnetostatic structure using numerical simulation

CERN Document Server

Wang, Qiuliang

2013-01-01

Covers the practical numerical method for the analysis and design of magnets Extensively covers the magnet design and computation aspects from theories to practical applications, emphasizing design methods of practical structures such as superconducting, electromagnetic and permanent magnet for use in various scientific instruments, industrial processing, biomedicine and special electrical equipments. The computations cover a wide range of numerical techniques and analytical derivation to efficiently provide solutions to complicated problems that are often encountered in practice, where simple analytical calculations are no longer adequate. Chapters include: Introduction of Magnet Technology, Magnetostatic Equation for the Magnet Structure, Finite Element Analysis for Magnetostatic Field, Integral Method for Magnetostatic Field, Numerical Method of Solenoid Coils Design, Series Analysis of Axially Symmetric Magnetic Field, Magnets with High Magnetic Field and High Homogeneity, Permanent Magnet and its App...

Mathematical modeling and numerical simulation of unilateral dynamic rupture propagation along very-long reverse faults

Science.gov (United States)

Hirano, S.

2017-12-01

For some great earthquakes, dynamic rupture propagates unilaterally along a horizontal direction of very-long reverse faults (e.g., the Mw9.1 Sumatra earthquake in 2004, the Mw8.0 Wenchuan earthquake in 2008, and the Mw8.8 Maule earthquake in 2010, etc.). It seems that barriers or creeping sections may not lay along the opposite region of the co-seismically ruptured direction. In fact, in the case of Sumatra, the Mw8.6 earthquake occurred in the opposite region only three months after the mainshock. Mechanism of unilateral mode-II rupture along a material interface has been investigated theoretically and numerically. For mode-II rupture propagating along a material interface, an analytical solution implies that co-seismic stress perturbation depends on the rupture direction (Weertman, 1980 JGR; Hirano & Yamashita, 2016 BSSA), and numerical modeling of plastic yielding contributes to simulating the unilateral rupture (DeDonteny et al., 2011 JGR). However, mode-III rupture may dominate for the very-long reverse faults, and it can be shown that stress perturbation due to mode-III rupture does not depend on the rupture direction. Hence, an effect of the material interface is insufficient to understand the mechanism of unilateral rupture along the very-long reverse faults. In this study, I consider a two-dimensional bimaterial system with interfacial dynamic mode-III rupture under an obliquely pre-stressed configuration (i.e., the maximum shear direction of the background stress is inclined from the interfacial fault). First, I derived an analytical solution of regularized elastic stress field around a steady-state interfacial slip pulse using the method of Rice et al. (2005 BSSA). Then I found that the total stress, which is the sum of the background stress and co-seismic stress perturbation, depends on the rupture direction even in the mode-III case. Second, I executed a finite difference numerical simulation with a plastic yielding model of Andrews (1978 JGR; 2005

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

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 Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions

Directory of Open Access Journals (Sweden)

Marina Popolizio

2018-01-01

Full Text Available Multiterm fractional differential equations (MTFDEs nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag–Leffler (ML functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.

Concept and numerical simulations of a reactive anti-fragment armour layer

Science.gov (United States)

Hušek, Martin; Kala, Jiří; Král, Petr; Hokeš, Filip

2017-07-01

The contribution describes the concept and numerical simulation of a ballistic protective layer which is able to actively resist projectiles or smaller colliding fragments flying at high speed. The principle of the layer was designed on the basis of the action/reaction system of reactive armour which is used for the protection of armoured vehicles. As the designed ballistic layer consists of steel plates simultaneously combined with explosive material - primary explosive and secondary explosive - the technique of coupling the Finite Element Method with Smoothed Particle Hydrodynamics was used for the simulations. Certain standard situations which the ballistic layer should resist were simulated. The contribution describes the principles for the successful execution of numerical simulations, their results, and an evaluation of the functionality of the ballistic layer.

Experimental and numerical simulation of thermomechanical phenomena during a TIG welding process

International Nuclear Information System (INIS)

Depradeux, L.; Julien, J.F.

2004-01-01

In this study, a parallel experimental and numerical simulation of phenomena that take place in the Heat Affected Zone (HAZ) during TIG welding on 316L stainless steel is presented. The aim of this study is to predict by numerical simulation residual stresses and distortions generated by the welding process. For the experiment, a very simple geometry with reduced dimensions is considered: the specimens are disks, made of 316L. The discs are heated in the central zone in order to reproduce thermo-mechanical cycles that take place in the HAZ during a TIG welding process. During and after thermal cycle, a large quantity of measurement is provided, and allows to compare the results of different numerical models used in the simulations. The comparative thermal and mechanical analysis allows to assess the general ability of the numerical models to describe the structural behavior. The importance of the heat input rate and material characteristics is also investigated. When a melted zone is created, the thermal simulation reproduce well the temperature field in the upper face of the disk, but the size of the weld pool is not correctly rated, as fluid flows are not taken into account. Despite this fact, the general structural behavior is well represented by simulation

Evaluation of the numerical solution of polymer flooding; Avaliacao da solucao numerica da injecao de polimeros em reservatorios de petroleo