Level-by-level artificial viscosity and visualization for MHD simulation with adaptive mesh refinement

Abstract

We propose a numerical method to determine the artificial viscosity in magnetohydrodynamics (MHD) simulations with adaptive mesh refinement (AMR) method, where the artificial viscosity is adaptively changed due to the resolution level of the AMR hierarchy. Although the suitable value of the artificial viscosity depends on the governing equations and the model of target problem, it can be determined by von Neumann stability analysis. By means of the new method, "level-by-level artificial viscosity method," MHD simulations of Rayleigh-Taylor instability (RTI) are carried out with the AMR method. The validity of the level-by-level artificial viscosity method is confirmed by the comparison of the linear growth rates of RTI between the AMR simulations and the simple simulations with uniform grid and uniform artificial viscosity whose resolution is the same as that in the highest level of the AMR simulation. Moreover, in the nonlinear phase of RTI, the secondary instability is clearly observed where the hierarchical data structure of AMR calculation is visualized as high resolution region floats up like terraced fields.

Research Plan of Complex Global Simulation Unit

“…Another notable attempt of increasing numerical resolution is the use of the adaptive mesh refinement (AMR) method [75]. The AMR method has also been developed for simulating the Rayleigh-Taylor instability of MHD in plasma [76]. Despite these endeavors, traditional numerical techniques have not been sufficiently improved to overcome the limitations associated with a demand for high computational resources.…”

Perspective of Meta-Hierarchy Dynamics

“…Their resolution is a key issue in order to treat the large scale gap. One of the solutions in simulation studies is the Adaptive Mesh Refinement technique [20,21] which can dynamically and locally change the resolution and can efficiently calculate scale differences of more than three orders of magnitude in massively parallel computers. Furthermore, as the next challenge, we have to consider the situation that a large difference of scale exceeds the scale range where the validity of the governing equations is guaranteed.…”