rubenohana commited on
Commit
00b432a
1 Parent(s): 99ea5d9

Update README.md

Browse files
Files changed (1) hide show
  1. README.md +2 -2
README.md CHANGED
@@ -47,7 +47,7 @@ for batch in dataloader:
47
 
48
  **Equation**:
49
 
50
- ```math
51
  \begin{align}
52
  Re(\partial_t \mathbf{u^*} + (\mathbf{u^*}\cdot\nabla)\mathbf{u^*} ) + \nabla p^* &= \beta \Delta \mathbf{u^*} + (1-\beta)\nabla\cdot \mathbf{T}(\mathbf{C^*}),\\
53
  \partial_t \mathbf{C^*} + (\mathbf{u^*}\cdot\nabla)\mathbf{C^*} +\mathbf{T}(\mathbf{C^*}) &= \mathbf{C^*}\cdot\nabla \mathbf{u^*} + (\nabla \mathbf{u^*})^T \cdot \mathbf{C^*} + \epsilon \Delta \mathbf{C^*}, \\
@@ -55,7 +55,7 @@ Re(\partial_t \mathbf{u^*} + (\mathbf{u^*}\cdot\nabla)\mathbf{u^*} ) + \nabla p^
55
  \textrm{with} \quad \mathbf{T}(\mathbf{C^*}) &= \frac{1}{\text{Wi}}(f(\textrm{tr}(\mathbf{C^*}))\mathbf{C^*} - \mathbf{I}),\\
56
  \textrm{and} \quad f(s) &:= \left(1- \frac{s-3}{L^2_{max}}\right)^{-1}.
57
  \end{align}
58
- ```
59
 
60
  where \\(\mathbf{u^*} = (u^*,v^*)\\) is the streamwise and wall-normal velocity components, \\(p^*\\) is the pressure, \\(\mathbf{C^*}\\) is the positive definite conformation tensor which represents the ensemble average of the produce of the end-to-end vector of the polymer molecules. In 2D, 4 components of the tensor are solved: \\(c_{xx}^{*}, c^{*}_{yy}, c^{*}_{zz}, c^{*}_{xy}\\). \\(\mathbf{T}(\mathbf{C^{*}})\\) is the polymer stress tensor given by the FENE-P model.
61
 
 
47
 
48
  **Equation**:
49
 
50
+ $$
51
  \begin{align}
52
  Re(\partial_t \mathbf{u^*} + (\mathbf{u^*}\cdot\nabla)\mathbf{u^*} ) + \nabla p^* &= \beta \Delta \mathbf{u^*} + (1-\beta)\nabla\cdot \mathbf{T}(\mathbf{C^*}),\\
53
  \partial_t \mathbf{C^*} + (\mathbf{u^*}\cdot\nabla)\mathbf{C^*} +\mathbf{T}(\mathbf{C^*}) &= \mathbf{C^*}\cdot\nabla \mathbf{u^*} + (\nabla \mathbf{u^*})^T \cdot \mathbf{C^*} + \epsilon \Delta \mathbf{C^*}, \\
 
55
  \textrm{with} \quad \mathbf{T}(\mathbf{C^*}) &= \frac{1}{\text{Wi}}(f(\textrm{tr}(\mathbf{C^*}))\mathbf{C^*} - \mathbf{I}),\\
56
  \textrm{and} \quad f(s) &:= \left(1- \frac{s-3}{L^2_{max}}\right)^{-1}.
57
  \end{align}
58
+ $$
59
 
60
  where \\(\mathbf{u^*} = (u^*,v^*)\\) is the streamwise and wall-normal velocity components, \\(p^*\\) is the pressure, \\(\mathbf{C^*}\\) is the positive definite conformation tensor which represents the ensemble average of the produce of the end-to-end vector of the polymer molecules. In 2D, 4 components of the tensor are solved: \\(c_{xx}^{*}, c^{*}_{yy}, c^{*}_{zz}, c^{*}_{xy}\\). \\(\mathbf{T}(\mathbf{C^{*}})\\) is the polymer stress tensor given by the FENE-P model.
61