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An unconditionally stable, explicit Godunov scheme for systems of conservation laws
Author(s) -
Guinot Vincent
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.235
Subject(s) - conservation law , mathematics , godunov's scheme , scalar (mathematics) , linear system , riemann problem , system of linear equations , constraint (computer aided design) , courant–friedrichs–lewy condition , shallow water equations , nonlinear system , riemann hypothesis , mathematical analysis , numerical analysis , geometry , discretization , physics , quantum mechanics
Common explicit, Godunov‐type schemes are subject to a stability constraint. The time‐line interpolation technique allows this constraint to be eliminated without having to make the scheme implicit or to linearize the equations. For 2×2 systems of conservation laws, a system of non‐linear equations has to be solved in the general case to determine the left and right states of the Riemann problems at the cell interfaces. However, if one cell in the domain is wide enough for the Courant number to be locally lower than unity, it is not necessary to solve a system anymore and the values at the next time step can be computed directly. The method is detailed for linear and non‐linear scalar advection, as well as for 2×2 systems of hyperbolic conservation laws. It is illustrated by an application to a simplified model for two‐phase flow in pipes, which is described using a 2×2 system of non‐linear hyperbolic equations. Copyright © 2002 John Wiley & Sons, Ltd.