@Article{CiCP-10-3,
author = {},
title = {On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {3},
pages = {635--671},
abstract = {<p style="text-align: justify;">This paper is concerned with a new version of the Osher-Solomon Riemann
solver and is based on a numerical integration of the path-dependent dissipation matrix.
The resulting scheme is much simpler than the original one and is applicable to
general hyperbolic conservation laws, while retaining the attractive features of the original
solver: the method is entropy-satisfying, differentiable and complete in the sense
that it attributes a different numerical viscosity to each characteristic field, in particular
to the intermediate ones, since the full eigenstructure of the underlying hyperbolic system
is used. To illustrate the potential of the proposed scheme we show applications
to the following hyperbolic conservation laws: Euler equations of compressible gasdynamics
with ideal gas and real gas equation of state, classical and relativistic MHD
equations as well as the equations of nonlinear elasticity. To the knowledge of the authors,
apart from the Euler equations with ideal gas, an Osher-type scheme has never
been devised before for any of these complicated PDE systems. Since our new general
Riemann solver can be directly used as a building block of high order finite volume
and discontinuous Galerkin schemes we also show the extension to higher order of
accuracy and multiple space dimensions in the new framework of P<sub>N</sub>P<sub>M</sub> schemes on
unstructured meshes recently proposed in [9].</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.170610.021210a},
url = {https://global-sci.com/article/80934/on-universal-osher-type-schemes-for-general-nonlinear-hyperbolic-conservation-laws}
}