Admissible states and bound-preserving schemes for relativistic magnetohydrodynamics
摘要： In the numerical simulation of relativistic magnetohydrodynamics (RMHD), a well-known major cause of problems is when the numerical solutions violate the physical bound constraints, i.e., the positivity of the density and pressure as well as the subluminal constraint on the fluid velocity. Design of provably bound-preserving (BP) schemes for RMHD is highly desired but challenging. The difficulties mainly come from the intrinsic complexity of the RMHD equations as well as the indeterminate relation between the BP property and the divergence-free condition on the magnetic field. In this talk, I am going to introduce our recent effort on the design and analysis of the BP schemes for RMHD, which are based on deeply studying several mathematical properties of the admissible state set. It will be shown that a discrete divergence-free condition is crucial for achieving the BP property. Several numerical examples will be provided to further demonstrate the theoretical findings.
20171228Kailiang Wu Admissible states and bound-preserving schemes for relativistic magnetohydrodynamics