added fvm

Author: scaomath

README.md

@@ -42,6 +42,7 @@ Data generation instructions are available in the [SFNO folder](./fno).
 ## Examples
 - Demos of different simulation setups:
   - [2D simulation with a pseudo-spectral solver](./examples/Kolmogrov2d_rk4_cn_forced_turbulence.ipynb)
+  - [2D simulation with a finite volume solver](./examples/Kolmogrov2d_rk4_fvm_forced_turbulence.ipynb)
 - Demos of Spatiotemporal FNO's training and evaluation using the neural operator-assisted fluid simulation pipelines
   - [Training of SFNO for only 15 epochs for the isotropic turbulence example](./examples/ex2_SFNO_train.ipynb)
   - [Training of SFNO for only ***10*** epochs with 1k samples and reach `1e-2` level of relative error](./examples/ex2_SFNO_train_fnodata.ipynb) using the data in the FNO paper, which to our best knowledge no operator learner can do this in <100 epochs in the small data regime.
@@ -56,6 +57,7 @@ The Apache 2.0 License in the root folder applies to the `torch-cfd` folder of t
 ## Contributions
 PR welcome. Currently, the port of `torch-cfd` currently includes:
 - The pseudospectral method for vorticity uses anti-aliasing filtering techniques for nonlinear terms to maintain stability.
+- The finite volume method on a MAC grid for velocity, and using the projection scheme to impose the divergence free condition.
 - Temporal discretization: Currently only RK4 temporal discretization uses explicit time-stepping for advection and either implicit or explicit time-stepping for diffusion.
 - Boundary conditions: only periodic boundary conditions.
 

examples/Kolmogrov2d_rk4_fvm_forced_turbulence.ipynb

@@ -1,22 +1,28 @@
 ## TODO
 
-- [ ] add native PyTorch implementation for applying `torch.linalg` and `torch.fft` function directly on `GridArray`.
+- [x] add native PyTorch implementation for applying `torch.linalg` and `torch.fft` function directly on `GridArray`.
 - [x] add discrete Helmholtz decomposition in both spatial and spectral domains.
 - [x] adjust the function to act on `(batch, time, *spatial)` tensor, currently only `(*spatial)` is supported.
 - [x] add native vorticity computation, instead of taking FDM for pseudo-spectral.
 
 ## Changelog
 
 ### 0.1.0
-- Added a native PyTorch implementation of `scipy.linalg.circulant`: for a 1d array `column`
-  ```python
-  # scipy version
-  mat = scipy.linalg.circulant(column)
-
-  # torch version
-  idx = (n - torch.arange(n)[None].T + torch.arange(n)[None]) % n
-  mat = torch.gather(column[None, ...].expand(n, -1), 1, idx)
-  ```
+- Implemented the FVM method on a staggered MAC grid (pressure on cell centers).
+- Added native PyTorch implementation for applying `torch.linalg` and `torch.fft` functions directly on `GridArray` and `GridVariable`.
+- Added native implementation of arithmetic manipulation directly on `GridVariableVector`.
+- Added several helper functions `consistent_grid` to replace `consistent_grid_arrays`.
+- Removed dependence of `from torch.utils._pytree import register_pytree_node`
+- Minor notes:
+  - Added native PyTorch dense implementation of `scipy.linalg.circulant`: for a 1d array `column`
+    ```python
+    # scipy version
+    mat = scipy.linalg.circulant(column)
+
+    # torch version
+    idx = (n - torch.arange(n)[None].T + torch.arange(n)[None]) % n
+    mat = torch.gather(column[None, ...].expand(n, -1), 1, idx)
+    ```
 
 
 ### 0.0.8