Computational Fluid Dynamics with the Coupled Discrete Unified Gas Kinetic Scheme (CDUGKS)

TL;DR

This paper presents an open-source implementation of the CDUGKS, a versatile phase space scheme capable of simulating a wide range of flow regimes in computational fluid dynamics, demonstrating accuracy and flexibility across various test problems.

Contribution

The paper introduces a publicly available, second-order accurate implementation of CDUGKS that handles multiple flow regimes with independent time stepping, enhancing simulation capabilities in fluid dynamics.

Findings

Successfully simulates flows from Eulerian to free-streaming regimes

Accurately captures shocks and diffusive processes

Demonstrates flexibility with different Prandtl numbers

Abstract

In this paper, we introduce our open source implementation of the Coupled Discrete Unified Gas Kinetic Scheme (CDUGKS) of https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.053310, a phase space scheme capable of handling a wide range of flow regimes. We demonstrate its performance on several problems including a number of well known test problems from the astrophysical fluid dynamics literature such as the 1D Sod shock tube, 2D Kelvin-Helmholtz instability, 1D thermoacoustic wave, a triangular Gresho vortex, a sine wave velocity perturbation. For these problems, we show that the code can simulate flows ranging from the inviscid/Eulerian regime to the free-streaming regime, capturing shocks and emergent diffusive processes in the appropriate regimes. We also use a variety of Prandtl numbers to demonstrate the scheme's ability to simulate different thermal conductivities at fixed viscosity. The scheme is second-order accurate in space and time and, unlike many solvers, uses a time step that is independent of the mean free path of the gas. Our code (MP-CDUGKS) is public under a CC0 1.0 Universal license and is available on https://github.com/alvarozamora/CDUGKS