A non-parametrized entropy correction for Roe's approximate Riemann solver
The approximate Riemann solver of \textit{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.
scientific article; zbMATH DE number 932037