Octree based DSMC - Python implementation

Table of Contents

1. Introduction
2. Requirements
3. Installation
4. Test Cases

1. Introduction

DSMC implementation using an octree as a variable mesh based on https://doi.org/10.1016/j.jcp.2008.04.038. Implementation in done in python 3.10.

2. Requirements

• python 3.10.
• pip3
• numpy
• llvmlite
• scipy
• numba

3. Installation

The module can be installed using pip3 from the repository root as

pip3 install .

4. Test Cases

All test cases were performed using Argon. The gas properties are as follows:

gas	$\sigma_T / m^2$	$m / kg$
Ar	3.631681e-19	6.6422e-26

4.1 Heat Bath

Simulation of temperature relaxation of Argon in closed domain. The simulation domain is cube with a side length of $2 \cdot 10^{-3} m$. The simulation properties are as follows

$\Delta t / s$	$w$	$T / K$	$n / m^{-3}$	$u / (m/s)$
1e-5	0.5e-8	300	1e+20	1000.0

where $\Delta t$ is the time step, $w$ is the particle weight, $T$ the temperature, $n$ the number density and $u$ the velocity in x direction. The simulation results can be seen below.

4.2 Hypersonic flow around cube

Hypersonic flow around a cuboid. The parameters are as follows

$\Delta t / s$	$w$	$T / K$	$n / m^{-3}$	$v_{x, z} / (m s^{-1})$	$v_y / (m s^{-1})$
1e-6	0.25e+15	273.0	2.6e+19	0	-3043.0

4.3 Shock Tube

This test case is Sod's shock tube problem. Initial conditions for the left hand side $C_L$ and the right hand side $C_R$ are found below

$$ C_L = \begin{pmatrix} n_L \\ u_L \\ T_L \\ \end{pmatrix} = \begin{pmatrix} 2.41432e22 \\ 0 \\ 300 \\ \end{pmatrix} $$

$$ C_R = \begin{pmatrix} n_R \\ u_R \\ p_L \\ \end{pmatrix}= \begin{pmatrix} 2.41432e21 \\ 0 \\ 300 \\ \end{pmatrix} $$

The simulation parameters

$\Delta t / s$	$w$
1e-7	1e-8

The simulation domain is a rectangular tube with a square cross section with the side length $2 \cdot 10^{-4} m$ and a length of $0.1 m$. Results can be seen below.