A New Residual Distribution Hydrodynamics Solver for Astrophysical Simulations

TL;DR

This paper introduces a new residual distribution hydrodynamics solver optimized for astrophysical simulations, capable of accurately modeling complex fluid structures with high efficiency at low resolutions in 2D and 3D.

Contribution

The paper presents a novel implementation of the residual distribution method with a variable time stepping routine, improving computational efficiency and accuracy in astrophysical fluid simulations.

Findings

Able to resolve complex fluid structures with as few as 3-5 resolution elements.

Demonstrates accuracy in Kelvin-Helmholtz and Sedov blast tests.

Competitive performance compared to state-of-the-art solvers, especially at low resolution.

Abstract

Many astrophysical systems can only be accurately modelled when the behaviour of their baryonic gas components is well understood. The residual distribution (RD) family of partial differential equation (PDE) solvers produce approximate solutions to the corresponding fluid equations. We present a new implementation of the RD method. The solver efficiently calculates the evolution of the fluid, with up to second order accuracy in both time and space, across an unstructured triangulation, in both 2D and 3D. We implement a novel variable time stepping routine, which applies a drifting mechanism to greatly improve the computational efficiency of the method. We conduct extensive testing of the new implementation, demonstrating its innate ability to resolve complex fluid structures, even at very low resolution. We can resolve complex structures with as few as 3-5 resolution elements, demonstrated by Kelvin-Helmholtz and Sedov blast tests. We also note that we find cold cloud destruction time scales consistent with those predicted by a typical PPE solver, albeit the exact evolution shows small differences. The code includes three residual calculation modes, the LDA, N and blended schemes, tailored for scenarios from smooth flows (LDA), to extreme shocks (N), and both (blended). We compare our RD solver results to state-of-the-art solvers used in other astrophysical codes, demonstrating the competitiveness of the new approach, particularly at low resolution. This is of particular interest in large scale astrophysical simulations, where important structures, such as star forming gas clouds, are often resolved by small numbers of fluid elements.