Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients. (English) Zbl 1078.35011
The authors study a model of conservative nonlinear conservation laws with a discontinuous flux function. More precisely, the following equation is being studied \(u_t + (k(x)u(1-u))_x = 0.\) The authors find a particular entropy condition which has to be fullfiled on the line of discontinuity of the coefficient \(k\), which guarantees the uniqueness of the entropy solution. Two new finite volume schemes are proposed to simulate the conservation laws with discontinuous coefficients. A comparison with commercial finite volume codes is done. It is shown that a loss of accuaracy of the commercial codes has been detected. A modified MUSCL method for stationary states is introduced as well.
Reviewer: Mária Lukáčová (Hamburg)
MSC:
| 35A35 | Theoretical approximation in context of PDEs |
| 35L65 | Hyperbolic conservation laws |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
conservation laws; discontinuous coefficient; finite volume schemes; resonance; new finite volume schemes; modified MUSCL methodReferences:
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