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Numerical Simulation of 1-D Sod Shock Tube

Numerical Simulation of 1-D Sod Shock Tube

The MATLAB codes for the realization of the numerical simulation of 1-D Sod Shock Tube (v1.0)

Information

Author: pkufzh (Small Shrimp)

Course: Fundamentals of Computational Fluid Dynamics (CFD)

Submit: 2021/12/28

Version: v1.0

Description

All the developed MATLAB codes are saved under the Codes folder.

Main Program

Program_Sod_Shock_Tube_Main
- Main Program: Numerical simulation of 1-D compressible flow (Sod Shock Tube)

Attached Function Modules

Important Note: Please ensure the following files are placed in the same folder with the main program!

Flux_Vect_Split_Common.m
- Flux Vector Splitting (FVS) with different methods (Optional)
- Steger-Warming (S-W)
- Lax-Friedrichs (L-F)
- van Leer
- Liou-Steffen (Advection Upstream Splitting Method, AUSM)
Flux_Diff_Split_Common.m
- Flux Difference Splitting (FDS) with different methods (Optional)
- Roe Scheme
Diff_Cons_Common.m
Calculate the flux difference $\frac{\partial \mathbf{F}}{\partial x}$ from positive flux $\frac{\partial \mathbf{F}^{+}}{\partial x}$ and negative flux $\frac{\partial \mathbf{F}^{-}}{\partial x}$ with the conservation form through FVS or FDS, i.e.

$$ \mathbf{F}{j + \frac{1}{2}} = \mathbf{F}{j + \frac{1}{2} L}^{+} + \mathbf{F}_{j + \frac{1}{2} R}^{-} $$

Shock Capturing Methods (Optional)
- (TVD) Total Variation Diminishing Scheme with van Leer Limiter
- (NND, H. X. Zhang) Non-oscillatory, Non-free-parameters Dissipative Difference Scheme
- (Original WENO, 5 order, Jiang & Shu) Weighted Essentially Non-oscillatory Scheme Scheme
First Level Upwind Schemes (Optional)
- 1 order (2 points)
- 2 order (3 points)
- 3 order (4 points with bias)
- 5 order (6 points with bias)
Note: All the upwind schemes used in this program had been converted into the conservative form.

Cal_Minmod.m
- Calculate minmod(a, b)
- Sign Definition
$$ \operatorname{minmod}(a,b) = \frac{1}{2}\left[\operatorname{sgn}(a) + \operatorname{sgn}(b)\right]\cdot\operatorname{min}\left(\left|a\right|, \left|b\right|\right) $$

where $a$, $b$ is 1-Dimensional array with same length.

Plot_Props.m
- Plot the properties of fluid with preset and uniform axis coordinates

Exact Riemann Solution: Referred Functions by Gogol (2021)

Reference: Gogol (2021). Sod Shock Tube Problem Solver Click to the Website, From MATLAB Central File Exchange. Retrieved December 28, 2021. The main codes were developed by the original author.

analytic_sod.m
- Solve Sod's Shock Tube problem using exact Riemann solution
- Reference Page
sod_func.m
- Define functions to be used in analytic_sod.m
- Initial conditions
sod_demo.m
- A demo script file to show the use of analytic_sod.m

Note:

The above MATLAB codes were tested and passed on MATLAB R2021b, Windows 64-bit system.
For the vector images saved in the Paper.pdf are large, loading may be slow. Thanks for your patient waiting!!!

Reference

Gogol (2021). Sod Shock Tube Problem Solver (Click to the Website), MATLAB Central File Exchange. Retrieved December 28, 2021.
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