Simulation of Field-Aligned Ideal MHD Flows Around Perfectly Conducting Cylinders Using an Artificial Compressibility Approach

Abstract

Ideal magnetohydrodynamics (MHD) simulations are known to have problems in satisfying the solenoidal constraint (del.13 = 0) and diverge unless appropriate numerical techniques are used to enforce this constraint. In this chapter, a technique inspired by the artificial compressibility concept is developed. This technique is thought to be a cure for the drawbacks of the families of solenoidal constraint-satisfying techniques presented in the literature so far: incorrect shock capturing and poor performance of the convective stabilization mechanism in regions of stagnant flow for Powell's source term method, exceedingly complex implementation for staggered-grid approaches, computationally expensive nature due to the necessity of a Poisson solver combined with hyperbolic and elliptic numerical methods for classical projection schemes. The new technique is in principle equivalent to the hyperbolic divergence cleaning technique advocated by other authors. However, the underlying derivation and justification are quite different. We apply our approach to a test case relevant to space weather predictions, a field-aligned (i.e., free-stream flow velocity and magnetic field are aligned) superfast-mode plasma around a quarter of a perfectly conducting cylinder, in which a complex dimpled bow shock topology occurs. The performance of our approach is demonstrated in terms of accuracy, robustness, and convergence speed.