Title: An accurate and robust genuinely multidimensional Riemann solver for Euler equations based on TV flux splitting,
Abstract: A simple robust genuinely multidimensional convective pressure split (CPS) ,
contact preserving, shock stable Riemann solver (GM-K-CUSP-X) for Euler
equations of gas dynamics is developed. The convective and pressure components
of the Euler system are separated following the Toro-Vazquez type PDE flux
splitting [Toro et al, 2012]. Upwind discretization of these components are
achieved using the framework of Mandal et al [Mandal et al, 2015]. The
robustness of the scheme is studied on a few two dimensional test problems. The
results demonstrate the efficacy of the scheme over the corresponding
conventional two state version of the solver. Results from two classic strong
shock test cases associated with the infamous Carbuncle phenomenon, indicate
that the present solver is completely free of any such numerical instabilities
albeit possessing contact resolution abilities.Such a finding emphasizes the
pre-existing notion about the positive effects that multidimensional flow
modelling may have towards curing of shock instabilities.