The Geometric Conservation Law - A link between finite-difference and finite-volume methods of flow computation on moving grids

1978 ◽  
Author(s):  
P. THOMAS ◽  
C. LOMBARD
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Conservation Law ◽  
Finite Volume Methods ◽  
Flow Computation ◽  
Moving Grids ◽  
Geometric Conservation Law

scholarly journals ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS

2003 ◽  
Vol 13 (02) ◽  
pp. 221-257 ◽  
Author(s):  
NICOLAS SEGUIN ◽  
JULIEN VOVELLE
Keyword(s):  
Finite Volume ◽  
Conservation Law ◽  
Discontinuous Coefficients ◽  
Finite Volume Methods ◽  
Finite Volume Schemes ◽  
Flux Function ◽  
Scalar Conservation Law ◽  
Line Of Discontinuity ◽  
Scalar Conservation ◽  
Industrial Context

We study here a model of conservative nonlinear conservation law with a flux function with discontinuous coefficients, namely the equation ut + (k(x)u(1 - u))x = 0. It is a particular entropy condition on the line of discontinuity of the coefficient k which ensures the uniqueness of the entropy solution. This condition is discussed and justified. On the other hand, we perform a numerical analysis of the problem. Two finite volume schemes, the Godunov scheme and the VFRoe-ncv scheme, are proposed to simulate the conservation law. They are compared with two finite volume methods classically used in an industrial context. Several tests confirm the good behavior of both new schemes, especially through the discontinuity of permeability k (whereas a loss of accuracy may be detected when industrial methods are performed). Moreover, a modified MUSCL method which accounts for stationary states is introduced.

COMPARISON OF FINITE VOLUME AND FINITE DIFFERENCE METHODS AND APPLICATION

2006 ◽  
Vol 04 (02) ◽  
pp. 163-208 ◽  
Author(s):  
S. FAURE ◽  
D. PHAM ◽  
R. TEMAM
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Finite Volume ◽  
Finite Difference Methods ◽  
Finite Volume Methods ◽  
Uniform Grid ◽  
Parabolic Boundary ◽  
Convergence Results ◽  
Difference Methods ◽  
Parabolic Boundary Value Problems

In this article, we consider finite volume methods based on a non-uniform grid. Finite volume methods are compared to finite difference methods based on a related grid. As an application, various convergence results are proved for the finite volume function spaces and for some model elliptic and parabolic boundary value problems using these discretization spaces.

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