A Lagrangian GRP Algorithm for Axisymmetric Problems of Compressible Fluids

Abstract

We devise a Lagrangian Generalized Riemann Problem (GRP) algorithm for axisymmetric hydrodynamics, which pays attention to high-resolution boundary treatment at the symmetric axis. The numerical boundary condition here is first formulated the same as the scheme on interior cells. Then we uniformly obtain the requisite interface values in constructing numerical fluxes and sources through the newly-tailored GRP solver and its one-sided variant. There also exist some innovations in the other two critical procedures: the derivation of vertex velocities and the compliance with the geometry conservation law (GCL). Several challenging numerical examples are utilized to demonstrate the performance of our algorithm in resolving discontinuities, maintaining symmetry, alleviating overheating phenomena, and dealing with complex fluids.