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Godunov Scheme (godunov + scheme)

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Engineering50%

Selected Abstracts

A hybrid FVM,LBM method for single and multi-fluid compressible flow problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010
Himanshu Joshi
Abstract The lattice Boltzmann method (LBM) has established itself as an alternative approach to solve the fluid flow equations. In this work we combine LBM with the conventional finite volume method (FVM), and propose a non-iterative hybrid method for the simulation of compressible flows. LBM is used to calculate the inter-cell face fluxes and FVM is used to calculate the node parameters. The hybrid method is benchmarked for several one-dimensional and two-dimensional test cases. The results obtained by the hybrid method show a steeper and more accurate shock profile as compared with the results obtained by the widely used Godunov scheme or by a representative flux vector splitting scheme. Additional features of the proposed scheme are that it can be implemented on a non-uniform grid, study of multi-fluid problems is possible, and it is easily extendable to multi-dimensions. These features have been demonstrated in this work. The proposed method is therefore robust and can possibly be applied to a variety of compressible flow situations. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Stability and accuracy of a semi-implicit Godunov scheme for mass transport

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004
Scott F. Bradford
Abstract Semi-implicit, Godunov-type models are adapted for solving the two-dimensional, time-dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor,corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second-order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax-Wendroff, Warming-Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank,Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi-discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi-implicit schemes. Some linear, two-dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A CFL-like constraint for the fast marching method in inhomogeneous chemical kinetics

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2008
Ramón Escobedo
Abstract Level sets and fast marching methods are a widely used technique for problems with moving interfaces. Chemical kinetics has been recently added to this family, for the description of reaction paths and chemical waves in homogeneous media, in which the velocity of the interface is described by a given field. A more general framework must consider variable velocities due to inhomogeneities induced by chemical changes. In this case, a constraint must be satisfied for the correct use of fast marching method. We deduce an analytical expression of this constraint when the Godunov scheme is used to solve the Eikonal equation, and we present numerical simulations of a case which must be enforced to obey the constraint. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source]

Weak formulation of boundary conditions for scalar conservation laws: an application to highway traffic modelling

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2006
Issam S. Strub
Abstract This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of the boundary conditions is needed for the problem to be well posed. The existence of the solution results from the convergence of the Godunov scheme. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for highway traffic). The numerical scheme is then applied to a highway scenario with data from highway Interstate-80 obtained from the Berkeley Highway Laboratory. Finally, the existence of a minimiser of travel time is obtained, with the corresponding optimal boundary control. Copyright © 2006 John Wiley & Sons, Ltd. [source]

An instability of the Godunov scheme

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2006
Alberto Bressan
We construct a solution to a 2 × 2 strictly hyperbolic system of conservation laws, showing that the Godunov scheme [13] can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing-viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or L1 -stability estimates can in general be valid for finite difference schemes. © 2006 Wiley Periodicals, Inc. [source]