Phurbas: An Adaptive, Lagrangian, Meshless, Magnetohydrodynamics Code. I. Algorithm

TL;DR

Phurbas is a novel meshless, Lagrangian magnetohydrodynamics code that employs adaptive particles, high-order interpolation, and dynamic resolution to efficiently simulate complex fluid flows without the limitations of fixed grids.

Contribution

The paper introduces a new adaptive, meshless MHD algorithm using moving least squares interpolation and dynamic particle management for improved simulation flexibility.

Findings

Robust modeling of fluid flows with adaptive particles.

Efficient handling of complex geometries and flow features.

Enhanced stability through artificial viscosity fields.

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. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which 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. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. This paper derives and documents the Phurbas algorithm as implemented in Phurbas version 1.1. A following paper presents the implementation and test problem results.