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A non-parametrized entropy correction for Roe’s approximate Riemann solver. (English) Zbl 0861.65073
The approximate Riemann solver of P. L. Roe [J. Comput. Phys. 43, 357-372 (1981; Zbl 0474.65066)] is improved. A new nonparameterized approach is proposed which is based on a nonlinear Hermite interpolation of an approximate flux function and the exact resolution of nonconvex scalar Riemann problems. Convergence and consistency with the entropy condition are proved for scalar convex conservation laws with arbitrarily large initial data. For strictly hyperbolic systems of conservation laws consistency of the resulting scheme with the entropy condition is also proved for initial data sufficiently close to a constant. A one-dimensional shock-tube and a two-dimensional supersonic forward facing step are considered as examples.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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