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Source Terms (source + term)

Distribution by Scientific Domains

Engineering	75%
Mathematics and Statistics	11%
Chemistry	8%
Earth and Environmental Science	4%

Selected Abstracts

Numerical simulation of model scramjet combustor flowfield

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2007
Yuan-Guang Wang
Abstract A new concept has been raised and adopted in this paper to enlarge the scope of the two-dimensional model particularly for the purpose of dealing with three-dimensional normal injection cases. Meanwhile, the method has a very good performance for its short cyclic period. The new idea was realized through special resolution with continuity equations; i.e., mass flow was directly added in the source term of the continuity equation. To prove the robustness of this illuminating method, comparisons using calculations were carried out, and the results are satisfactory. A model scramjet combustor tested on the free-jet scramjet test facility was illustrated and underwent numerical calculations with the two-dimensional program, adopting the above simplified injecting method. To simulate the chemical reaction process in the scramjet tunnel, a five-species, single-step reaction model was introduced in the calculation process. This research presents the major aerodynamic parameters and components of mass fraction distribution within the model combustor channel, which made it easy to observe and analyze the flowfield. Finally, wall pressure comparisons between the numerical and experimental results were carried out to verify the accuracy of the calculation model. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(5): 295, 302, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20159 [source]

Simulation of fluid,structure interaction with the interface artificial compressibility method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3-4 2010
Joris Degroote
Abstract Partitioned fluid,structure interaction simulations of the arterial system are difficult due to the incompressibility of the fluid and the shape of the domain. The interface artificial compressibility (IAC) method mitigates the incompressibility constraint by adding a source term to the continuity equation in the fluid domain adjacent to the fluid,structure interface. This source term imitates the effect of the structure's displacement as a result of the fluid pressure and disappears when the coupling iterations have converged. The IAC method requires a small modification of the flow solver but not of the black-box structural solver and it outperforms a partitioned quasi-Newton coupling of the two black-box solvers in a simulation of a carotid bifurcation. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Radial basis functions for solving near singular Poisson problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2003
C. S. Chen
Abstract In this paper, we investigate the use of radial basis functions for solving Poisson problems with a near-singular inhomogeneous source term. The solution of the Poisson problem is first split into two parts: near-singular solution and smooth solution. A method for evaluating the near-singular particular solution is examined. The smooth solution is further split into a particular solution and a homogeneous solution. The MPS-DRM approach is adopted to evaluate the smooth solution. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Explicit calculation of smoothed sensitivity coefficients for linear problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
R. A. Bia, ecki
Abstract A technique of explicit calculation of sensitivity coefficients based on the approximation of the retrieved function by a linear combination of trial functions of compact support is presented. The method is applicable to steady state and transient linear inverse problems where unknown distributions of boundary fluxes, temperatures, initial conditions or source terms are retrieved. The sensitivity coefficients are obtained by solving a sequence of boundary value problems with boundary conditions and source term being homogeneous except for one term. This inhomogeneous term is taken as subsequent trial functions. Depending on the type of the retrieved function, it may appear on boundary conditions (Dirichlet or Neumann), initial conditions or the source term. Commercial software and analytic techniques can be used to solve this sequence of boundary value problems producing the required sensitivity coefficients. The choice of the approximating functions guarantees a filtration of the high frequency errors. Several numerical examples are included where the sensitivity coefficients are used to retrieve the unknown values of boundary fluxes in transient state and volumetric sources. Analytic, boundary-element and finite-element techniques are employed in the study. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Unstructured finite volume discretization of two-dimensional depth-averaged shallow water equations with porosity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010
L. Cea
Abstract This paper deals with the numerical discretization of two-dimensional depth-averaged models with porosity. The equations solved by these models are similar to the classic shallow water equations, but include additional terms to account for the effect of small-scale impervious obstructions which are not resolved by the numerical mesh because their size is smaller or similar to the average mesh size. These small-scale obstructions diminish the available storage volume on a given region, reduce the effective cross section for the water to flow, and increase the head losses due to additional drag forces and turbulence. In shallow water models with porosity these effects are modelled introducing an effective porosity parameter in the mass and momentum conservation equations, and including an additional drag source term in the momentum equations. This paper presents and compares two different numerical discretizations for the two-dimensional shallow water equations with porosity, both of them are high-order schemes. The numerical schemes proposed are well-balanced, in the sense that they preserve naturally the exact hydrostatic solution without the need of high-order corrections in the source terms. At the same time they are able to deal accurately with regions of zero porosity, where the water cannot flow. Several numerical test cases are used in order to verify the properties of the discretization schemes proposed. Copyright © 2009 John Wiley & Sons, Ltd. [source]

An Euler system source term that develops prototype Z-pinch implosions intended for the evaluation of shock-hydro methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2009
J. W. Banks
Abstract In this paper, a phenomenological model for a magnetic drive source term for the momentum and total energy equations of the Euler system is described. This body force term is designed to produce a Z-pinch like implosion that can be used in the development and evaluation of shock-hydrodynamics algorithms that are intended to be used in Z-pinch simulations. The model uses a J × B Lorentz force, motivated by a 0-D analysis of a thin shell (or liner implosion), as a source term in the equations and allows for arbitrary current drives to be simulated. An extension that would include the multi-physics aspects of a proposed combined radiation hydrodynamics (rad-hydro) capability is also discussed. The specific class of prototype problems that are developed is intended to illustrate aspects of liner implosions into a near vacuum and with idealized pre-fill plasma effects. In this work, a high-resolution flux-corrected-transport method implemented on structured overlapping meshes is used to demonstrate the application of such a model to these idealized shock-hydrodynamic studies. The presented results include an asymptotic solution based on a limiting-case thin-shell analytical approximation in both (x, y) and (r, z). Additionally, a set of more realistic implosion problems that include density profiles approximating plasma pre-fill and a set of perturbed liner geometries that excite a hydro-magnetic like Rayleigh,Taylor instability in the implosion dynamics are demonstrated. Finally, as a demonstration of including and evaluating multiphysics effects in the Euler system, a simple radiation model is included and self-convergence results for two types of (r, z) implosions are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Composite high resolution localized relaxation scheme based on upwinding for hyperbolic conservation laws

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2009
Ritesh Kumar Dubey
Abstract In this work we present an upwind-based high resolution scheme using flux limiters. Based on the direction of flow we choose the smoothness parameter in such a way that it leads to a truly upwind scheme without losing total variation diminishing (TVD) property for hyperbolic linear systems where characteristic values can be of either sign. Here we present and justify the choice of smoothness parameters. The numerical flux function of a high resolution scheme is constructed using wave speed splitting so that it results into a scheme that truly respects the physical hyperbolicity property. Bounds are given for limiter functions to satisfy TVD property. The proposed scheme is extended for non-linear problems by using the framework of relaxation system that converts a non-linear conservation law into a system of linear convection equations with a non-linear source term. The characteristic speed of relaxation system is chosen locally on three point stencil of grid. This obtained relaxation system is solved using composite scheme technique, i.e. using a combination of proposed scheme with the conservative non-standard finite difference scheme. Presented numerical results show higher resolution near discontinuity without introducing spurious oscillations. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008
Alireza Zia
Abstract An explicit Godunov-type solution algorithm called SEA (simple efficient algorithm) has been introduced for the shallow water equations. The algorithm is based on finite volume conservative discretisation method. It can deal with wet/dry and irregular beds. Second-order accuracy, in both time and space, is achieved using prediction and correction steps. A very simple and efficient flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purposes. In order to make sure about the balance between the flux gradient and the bed slope, treatment of the source term has been done using a new procedure inspired mainly by the physical rather than mathematical consideration. SEA has been applied to one-dimensional problems, although it can equally be applied to multi-dimensional problems. In order to assess the capability of proposed algorithm in dealing with practical applications, several test cases have been examined. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Numerical aspects of improvement of the unsteady pipe flow equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007
Romuald Szymkiewicz
Abstract The paper presents an analysis of some recently proposed improvements of the water hammer equations, which concern the friction term in the momentum equation. A comparison of the experimental data and numerical results shows that the required damping and smoothing of the pressure wave cannot be obtained by modification of the friction factor only. In order to evaluate the significance of the introduced improvements into the momentum equation, the accuracy of the numerical solution has been analysed using the modified equation approach. The analysis shows why the physical dissipation process observed in the water hammer phenomenon cannot be reproduced with the commonly used source term in Darcy,Weisbach form, representing friction force in the momentum equation. Therefore, regardless of the proposed form of the friction factor for unsteady flow, the model of water hammer improved in such a way keeps its hyperbolic character. Consequently, it cannot ensure the expected effects of damping and smoothing of the calculation head oscillations. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Simulation of shallow flows over variable topographies using unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006
A. Mohammadian
Abstract Simulation of shallow flows over variable topographies is a challenging case for most available shock-capturing schemes. This problem arises because the source terms and flux gradients are not balanced in the numerical computations. Treatments for this problem generally work well on structured grids, but they are usually too expensive, and most of them are not directly applicable to unstructured grids. In this paper we propose two efficient methods to treat the source terms without upwinding and to satisfy the compatibility condition on unstructured grids. In the first method, the calculation of the bed slope source term is performed by employing a compatible approximation of water depth at the cell interfaces. In the second one, different components of the bed slope term are considered separately and a compatible discretization of the components is proposed. The present treatments are applicable for most schemes including the Roe's method without changing the performance of the original scheme for smooth topographies. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006
Vincent Guinot
Abstract Two-dimensional shallow water models with porosity appear as an interesting path for the large-scale modelling of floodplains with urbanized areas. The porosity accounts for the reduction in storage and in the exchange sections due to the presence of buildings and other structures in the floodplain. The introduction of a porosity into the two-dimensional shallow water equations leads to modified expressions for the fluxes and source terms. An extra source term appears in the momentum equation. This paper presents a discretization of the modified fluxes using a modified HLL Riemann solver on unstructured grids. The source term arising from the gradients in the topography and in the porosity is treated in an upwind fashion so as to enhance the stability of the solution. The Riemann solver is tested against new analytical solutions with variable porosity. A new formulation is proposed for the macroscopic head loss in urban areas. An application example is presented, where the large scale model with porosity is compared to a refined flow model containing obstacles that represent a schematic urban area. The quality of the results illustrates the potential usefulness of porosity-based shallow water models for large scale floodplain simulations. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Improved non-staggered central NT schemes for balance laws with geometrical source terms

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2004
rnjari
Abstract In this paper we extend the non-staggered version of the central NT (Nessyahu,Tadmor) scheme to the balance laws with geometrical source term. This extension is based on the source term evaluation that includes balancing between the flux gradient and the source term with an additional reformulation that depends on the source term discretization. The main property of the scheme obtained by the proposed reformulation is preservation of the particular set of the steady-state solutions. We verify the improved scheme on two types of balance laws with geometrical source term: the shallow water equations and the non-homogeneous Burger's equation. The presented results show good behaviour of the considered scheme when compared with the analytical or numerical results obtained by using other numerical schemes. Furthermore, comparison with the numerical results obtained by the classical central NT scheme where the source term is simply pointwise evaluated shows that the proposed reformulations are essential. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Chebyshev super spectral viscosity solution of a two-dimensional fluidized-bed model

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003
Scott A. SarraArticle first published online: 13 MAY 200
Abstract The numerical solution of a model describing a two-dimensional fluidized bed by a Chebyshev super spectral viscosity (SSV) method is considered. The model is in the form of a hyperbolic system of conservation laws with a source term, coupled with an elliptic equation for determining a stream function. The coupled elliptic equation is solved by a finite-difference method. The mixed SSV/finite-difference method produces physically shaped bubbles, on a very coarse grid. Fine scale details, which were not present in previous finite-difference solutions, are present in the solution. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Relaxation schemes for the shallow water equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003
A. I. Delis
Abstract We present a class of first and second order in space and time relaxation schemes for the shallow water (SW) equations. A new approach of incorporating the geometrical source term in the relaxation model is also presented. The schemes are based on classical relaxation models combined with Runge,Kutta time stepping mechanisms. Numerical results are presented for several benchmark test problems with or without the source term present. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A finite volume solver for 1D shallow-water equations applied to an actual river

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2002
N. Gouta
Abstract This paper describes the numerical solution of the 1D shallow-water equations by a finite volume scheme based on the Roe solver. In the first part, the 1D shallow-water equations are presented. These equations model the free-surface flows in a river. This set of equations is widely used for applications: dam-break waves, reservoir emptying, flooding, etc. The main feature of these equations is the presence of a non-conservative term in the momentum equation in the case of an actual river. In order to apply schemes well adapted to conservative equations, this term is split in two terms: a conservative one which is kept on the left-hand side of the equation of momentum and the non-conservative part is introduced as a source term on the right-hand side. In the second section, we describe the scheme based on a Roe Solver for the homogeneous problem. Next, the numerical treatment of the source term which is the essential point of the numerical modelisation is described. The source term is split in two components: one is upwinded and the other is treated according to a centred discretization. By using this method for the discretization of the source term, one gets the right behaviour for steady flow. Finally, in the last part, the problem of validation is tackled. Most of the numerical tests have been defined for a working group about dam-break wave simulation. A real dam-break wave simulation will be shown. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Darcy's law-based model for wicking in paper-like swelling porous media

AICHE JOURNAL, Issue 9 2010
Reza Masoodi
Abstract The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source]

Effect of sample size on microwave power absorption within dielectric materials: 2D numerical results vs. closed-form expressions

AICHE JOURNAL, Issue 6 2009
S. Curet
Abstract This study deals with the analytical and numerical solutions of the heat source term because of microwave heating for high and low dielectric materials in 1D and 2D configurations. The authors compare closed-form expressions dedicated to microwave power calculation to numerical simulations. A comprehensive and accurate analysis of the microwave power reflected from the surface of the sample is also carried out during microwave heating. The influence of sample length is studied using an original numerical procedure. The study highlights that 1D closed-form expressions can be extended to 2D configurations in the case of sufficiently high dielectric properties. Examples of heating rate during 2D microwave heating in TE10 mode are finally presented. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

Finite energy solutions of self-adjoint elliptic mixed boundary value problems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2010
Giles Auchmuty
Abstract This paper describes existence, uniqueness and special eigenfunction representations of H1 -solutions of second order, self-adjoint, elliptic equations with both interior and boundary source terms. The equations are posed on bounded regions with Dirichlet conditions on part of the boundary and Neumann conditions on the complement. The system is decomposed into separate problems defined on orthogonal subspaces of H1(,). One problem involves the equation with the interior source term and the Neumann data. The other problem just involves the homogeneous equation with Dirichlet data. Spectral representations of the solution operators for each of these problems are found. The solutions are described using bases that are, respectively, eigenfunctions of the differential operator with mixed null boundary conditions, and certain mixed Steklov eigenfunctions. These series converge strongly in H1(,). Necessary and sufficient conditions for the Dirichlet part of the boundary data to have a finite energy extension are described. The solutions for a problem that models a cylindrical capacitor is found explicitly. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Blowup of solutions for a class of non-linear evolution equations with non-linear damping and source terms

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2002
Yang Zhijian
We consider the blowup of solutions of the initial boundary value problem for a class of non-linear evolution equations with non-linear damping and source terms. By using the energy compensation method, we prove that when p>max{m, ,}, where m, , and p are non-negative real numbers and m+1, ,+1, p+1 are, respectively, the growth orders of the non-linear strain terms, damping term and source term, under the appropriate conditions, any weak solution of the above-mentioned problem blows up in finite time. Comparison of the results with the previous ones shows that there exist some clear condition boundaries similar to thresholds among the growth orders of the non-linear terms, the states of the initial energy and the existence and non-existence of global weak solutions. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Probability Density Function (PDF) Simulation of Turbulent Reactive Gas-Solid Flow in a Riser

CHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 3 2009
S. N. P. Vegendla
Abstract A hybrid Lagrangian-Eulerian methodology is developed for the numerical simulation of turbulent reactive gas-solid flow. The SO2 -NOx Adsorption Process (SNAP) in a riser reactor with dilute gas-solid flow is taken as a test case. A three-dimensional time-dependent simulation is performed. By using the transported composition PDF method [1], modeling of the mean chemical source term and mass transfer terms in the gas-solid flow model equations is no longer needed. A notional particle-based Monte-Carlo algorithm is used to solve the transported composition PDF equations. A Finite-Volume technique is used to calculate the hydrodynamic fields from the Reynolds Averaged Navier Stokes (RANS) equations combined with the k -, turbulence model for the gas phase and the Kinetic Theory of Granular Flow (KTGF) for the solid phase [2]. The newly developed hybrid solution technique is tested with the SNAP chemistry that has a total of 13 scalars (i.e., 5 gas phase components and 8 solid phase species) for which the composition fields of the reactive species are calculated. A good agreement between simulated and experimental gas-outlet composition of a demonstration unit is obtained. [source]

Numerical simulation of the inception of channel meandering

EARTH SURFACE PROCESSES AND LANDFORMS, Issue 9 2005
Jennifer G. Duan
Abstract The inception of channel meandering is the result of the complex interaction between flow, bed sediment, and bank material. A depth-averaged two-dimensional hydrodynamic model is developed to simulate the inception and development of channel meandering processes. The sediment transport model calculates both bedload and suspended load assuming equilibrium sediment transport. Bank erosion consists of two interactive processes: basal erosion and bank failure. Basal erosion is calculated from a newly derived equation for the entrainment of sediment particles by hydrodynamic forces. The mass conservation equation, where basal erosion and bank failure are considered source terms, was solved to obtain the rate of bank erosion. The parallel bank failure model was tested with the laboratory experiments of Friedkin on the initiation and evolution processes of non-cohesive meandering channels. The model replicates the downstream translation and lateral extension of meandering loops reasonably well. Plots of meandering planforms illustrate the evolution of sand bars and redistribution of flow momentum in meandering channels. This numerical modelling study demonstrates the potential of depth-integrated two-dimensional models for the simulation of meandering processes. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Collocation methods based on radial basis functions for solving stochastic Poisson problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2007
Somchart ChantasiriwanArticle first published online: 19 JUN 200
Abstract Collocation methods based on radial basis functions can be used to provide accurate solutions to deterministic problems. For stochastic problems, accurate solutions may not be desirable if they are too sensitive to random inputs. In this paper, four methods are used to solve stochastic Poisson problems by expressing solutions in terms of source terms and boundary conditions. Comparison among the methods reveals that the method based on fundamental solutions performs better than other methods. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Accelerating iterative solution methods using reduced-order models as solution predictors

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006
R. Markovinovi
Abstract We propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess for the iterative process based on information in the solution vectors from previous time steps. The algorithm basically consists of two projection steps: (1) projecting the governing equations onto a subspace spanned by a low number of global empirical basis functions extracted from previous time step solutions, and (2) solving the governing equations in this reduced space and projecting the solution back on the original, high dimensional one. We applied the algorithm to numerical models for simulation of two-phase flow through heterogeneous porous media. In particular we considered implicit-pressure explicit-saturation (IMPES) schemes and investigated the scope to accelerate the iterative solution of the pressure equation, which is by far the most time-consuming part of any IMPES scheme. We achieved a substantial reduction in the number of iterations and an associated acceleration of the solution. Our largest test problem involved 93 500 variables, in which case we obtained a maximum reduction in computing time of 67%. The method is particularly attractive for problems with time-varying parameters or source terms. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Explicit calculation of smoothed sensitivity coefficients for linear problems

Shoreline tracking and implicit source terms for a well balanced inundation model

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010
Giovanni FranchelloArticle first published online: 31 JUL 200
Abstract The HyFlux2 model has been developed to simulate severe inundation scenario due to dam break, flash flood and tsunami-wave run-up. The model solves the conservative form of the two-dimensional shallow water equations using the finite volume method. The interface flux is computed by a Flux Vector Splitting method for shallow water equations based on a Godunov-type approach. A second-order scheme is applied to the water surface level and velocity, providing results with high accuracy and assuring the balance between fluxes and sources also for complex bathymetry and topography. Physical models are included to deal with bottom steps and shorelines. The second-order scheme together with the shoreline-tracking method and the implicit source term treatment makes the model well balanced in respect to mass and momentum conservation laws, providing reliable and robust results. The developed model is validated in this paper with a 2D numerical test case and with the Okushiri tsunami run up problem. It is shown that the HyFlux2 model is able to model inundation problems, with a satisfactory prediction of the major flow characteristics such as water depth, water velocity, flood extent, and flood-wave arrival time. The results provided by the model are of great importance for the risk assessment and management. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Unstructured finite volume discretization of two-dimensional depth-averaged shallow water equations with porosity

An approximate-state Riemann solver for the two-dimensional shallow water equations with porosity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010
P. Finaud-Guyot
Abstract PorAS, a new approximate-state Riemann solver, is proposed for hyperbolic systems of conservation laws with source terms and porosity. The use of porosity enables a simple representation of urban floodplains by taking into account the global reduction in the exchange sections and storage. The introduction of the porosity coefficient induces modified expressions for the fluxes and source terms in the continuity and momentum equations. The solution is considered to be made of rarefaction waves and is determined using the Riemann invariants. To allow a direct computation of the flux through the computational cells interfaces, the Riemann invariants are expressed as functions of the flux vector. The application of the PorAS solver to the shallow water equations is presented and several computational examples are given for a comparison with the HLLC solver. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Nonreflecting boundary conditions based on nonlinear multidimensional characteristics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2010
Qianlong Liu
Abstract Nonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2- and 3-D compressible Navier,Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1-D characteristics-based nonreflecting boundary conditions for complex multidimensional flows. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Momentum/continuity coupling with large non-isotropic momentum source terms

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2009
J. D. Franklin
Abstract Pressure-based methods such as the SIMPLE algorithm are frequently used to determine a coupled solution between the component momentum equations and the continuity equation. This paper presents a colocated variable pressure correction algorithm for control volumes of polyhedral/polygonal cell topologies. The correction method is presented independent of spatial approximation. The presence of non-isotropic momentum source terms is included in the proposed algorithm to ensure its applicability to multi-physics applications such as gas and particulate flows. Two classic validation test cases are included along with a newly proposed test case specific to multiphase flows. The classic validation test cases demonstrate the application of the proposed algorithm on truly arbitrary polygonal/polyhedral cell meshes. A comparison between the current algorithm and commercially available software is made to demonstrate that the proposed algorithm is competitively efficient. The newly proposed test case demonstrates the benefits of the current algorithm when applied to a multiphase flow situation. The numerical results from this case show that the proposed algorithm is more robust than other methods previously proposed. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Some results on the accuracy of an edge-based finite volume formulation for the solution of elliptic problems in non-homogeneous and non-isotropic media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009
Darlan Karlo Elisiário de Carvalho
Abstract The numerical simulation of elliptic type problems in strongly heterogeneous and anisotropic media represents a great challenge from mathematical and numerical point of views. The simulation of flows in non-homogeneous and non-isotropic porous media with full tensor diffusion coefficients, which is a common situation associated with the miscible displacement of contaminants in aquifers and the immiscible and incompressible two-phase flow of oil and water in petroleum reservoirs, involves the numerical solution of an elliptic type equation in which the diffusion coefficient can be discontinuous, varying orders of magnitude within short distances. In the present work, we present a vertex-centered edge-based finite volume method (EBFV) with median dual control volumes built over a primal mesh. This formulation is capable of handling the heterogeneous and anisotropic media using structured or unstructured, triangular or quadrilateral meshes. In the EBFV method, the discretization of the diffusion term is performed using a node-centered discretization implemented in two loops over the edges of the primary mesh. This formulation guarantees local conservation for problems with discontinuous coefficients, keeping second-order accuracy for smooth solutions on general triangular and orthogonal quadrilateral meshes. In order to show the convergence behavior of the proposed EBFV procedure, we solve three benchmark problems including full tensor, material heterogeneity and distributed source terms. For these three examples, numerical results compare favorably with others found in literature. A fourth problem, with highly non-smooth solution, has been included showing that the EBFV needs further improvement to formally guarantee monotonic solutions in such cases. Copyright © 2008 John Wiley & Sons, Ltd. [source]