Numerical methods for three-dimensional analysis of shock instability in supernova cores

We studied the standing accretion shock instability (SASI) for a core-collapse supernova explosion. SASI induces a nonspherically symmetric motion of a standing spherical shock wave. In order to investigate the growth of SASI, we solved the three-dimensional compressible Euler equations using ZEUS-MP/2 code based on the finite-difference method with a staggered mesh of spherical polar geometry. Although the von Neumann and Richtmyer artificial viscosity is used in ZEUS-MP/2 code to capture shock waves, we propose utilizing a tensor artificial viscosity in order to overcome the numerical instability regarded as the carbuncle phenomenon. This numerical instability emerges around the grid polar axis and precludes mode analysis of SASI.