Adaptive Mesh Refinement and Relativistic Mhd

Compact objects combine a wide array of fascinating physics, and gravitational waves may open new ways to probe these objects. We are interested in systems where gravitational and magnetic fields are dynamically important. One challenge in simulating astrophysical compact objects is that these systems require a range of important length and time scales. Adaptive mesh refinement (AMR) thus becomes an increasingly important tool for large scale computations. Furthermore, large computational problems on today’s computers must be able to effectively utilize a large number of distributed processors. To address some of the challenges in studying compact objects with numerical relativity, we have developed a code to solve the general relativistic magnetohydrodynamics (GRMHD) equations with AMR. We use the had infrastructure, a modular code for solving hyperbolic and elliptic differential equations with distributed parallel AMR. had uses Berger–Oliger style AMR with sub-cycling in time. Refinement criteria may be problem specific, or a shadow hierarchy allows one to easily estimate the truncation error dynamically for use in specifying refinement criteria. The equations to be solved for a specific problem are isolated in equation modules, which may be used independently or combined with other modules. For example, the MHD and GR equations are in separate modules, which may be used independently or combined for the GRMHD code. The MHD equations are solved using the Convex Essentially Non-Oscillatory (CENO) method, a third order scheme for smooth fluid flow. Although our AMR driver can accommodate both finite difference and finite volume discretization methods, we choose a finite difference high-resolution shock-capturing method for the fluid equations to simplify the combined GRMHD code. We use hyperbolic divergence cleaning to control the ∇·B = 0 constraint for the magnetic field. Communi-