Phurbas: An Adaptive, Lagrangian, Meshless, Magnetohydrodynamics Code. II. Implementation and Tests

TL;DR

This paper introduces Phurbas, an adaptive, meshless magnetohydrodynamics simulation code that uses particles moving with the fluid, allowing for flexible, high-resolution modeling of MHD phenomena without traditional grid constraints.

Contribution

It presents a novel, fully adaptive, Lagrangian MHD algorithm with parallelization, capable of accurately simulating complex MHD systems and instabilities.

Findings

Successfully simulated linear MHD waves and shock tubes.

Demonstrated accurate growth rates for magnetorotational instability.

Validated the algorithm against analytical solutions.

Abstract

We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required to ensure the particles fill the computational volume, and gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. We have parallelized the code by adapting the framework provided by GADGET-2. A set of standard test problems, including 1e-6 amplitude linear MHD waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is presented. Finally we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. This paper documents the Phurbas algorithm as implemented in Phurbas version 1.1.