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Update README.md
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pkufzh committed Jan 20, 2022
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Expand Up @@ -37,20 +37,23 @@ All the developed *MATLAB* codes are saved under the ***Codes*** folder.

- <font color = 'blue'>**Flux_Vect_Split_Common.m**</font>
- **Flux Vector Splitting (FVS)** with different methods *(Optional)*
- **Steger-Warming (S-W)**
- **Steger-Warming (S-W)**
- **Lax-Friedrichs (L-F)**
- **van Leer**
- **Liou-Steffen (Advection Upstream Splitting Method, AUSM)**

- <font color = 'blue'>**Flux_Diff_Split_Common.m**</font>

- **Flux Difference Splitting (FDS)** with different methods *(Optional)*
- ***Roe*** Scheme
- ***Roe*** Scheme

- <font color = 'blue'>**Diff_Cons_Common.m**</font>

- 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 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}^{-} $.

- 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 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
Expand All @@ -63,8 +66,8 @@ All the developed *MATLAB* codes are saved under the ***Codes*** folder.
- ***Note:*** All the **upwind schemes** used in this program had been converted into the conservative form.

- <font color = 'blue'>**Cal_Minmod.m**</font>
- **Cal. minmod(a, b)**
- *Sign Definition*
- **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)
Expand Down Expand Up @@ -138,4 +141,4 @@ Bilibili Space: https://space.bilibili.com/167343763

------

<font size = 2.5>This project is protected by the MIT license. Please obey the open source rules.</font>
<font size = 2.5>*This project is protected by the MIT license. Please obey the open source rules.*</font>

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