ABSTRACT
The solution of hyperbolic conservation laws is characterized by the finite speed of propagation and the development of discontinuities. Stable and robust numerical schemes, e.g. finite volume schemes, are based on upwind techniques in order to handle shocks and contact discontinuities. In general, schemes of this type are very expensive. In 1993, Harten derived a concept to reduce the computational costs. It is based on a multiscale decomposition such that regions with singularities can be located. Near discontinuities, an expensive upwind scheme is applied; otherwise a much cheaper finite difference scheme of high order is used. Harten's multiscale decomposition is based on the primitive function of the solution. This approach is inherently restricted to structured grids. In this paper we present an alternative multiscale decomposition using general reconstruction methods. Here, we consider the one-dimensional case and verify that our concept coincides with those of Harten's decomposition method. Furthermore, we apply our algorithm to dimensionally reduced hypersonic stagnation point flows around spheres. All these techniques can be extended to multidimensional problems even for unstructured grids (see [7]).
