Datasets:
rubenohana
commited on
Commit
•
00b432a
1
Parent(s):
99ea5d9
Update README.md
Browse files
README.md
CHANGED
@@ -47,7 +47,7 @@ for batch in dataloader:
|
|
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^*}, \\
|
@@ -55,7 +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 |
|