Riemann problem for the 2D scalar conservation law involving linear fluxes with discontinuous coefficients

2020 ◽  
Vol 61 (11) ◽  
pp. 111504
Author(s):  
Hongjun Cheng ◽  
Hanchun Yang
Keyword(s):  
Riemann Problem ◽  
Conservation Law ◽  
Discontinuous Coefficients ◽  
Scalar Conservation Law ◽  
Scalar Conservation

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.

The Riemann problem for a scalar conservation law

1999 ◽  
pp. 72-94
Author(s):  
María Cristina Bustos ◽  
Fernando Concha ◽  
Raimund Bürger ◽  
Elmer M. Tory
Keyword(s):  
Riemann Problem ◽  
Conservation Law ◽  
Scalar Conservation Law ◽  
Scalar Conservation
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