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More minor README changes
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arsh-k committed Jan 13, 2024
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Expand Up @@ -59,15 +59,15 @@ We correct the velocity using the following update:

$$\frac{\mathbf{V}^{n+1}-\mathbf{V}^*}{\Delta t}=-\frac{1}{\rho} \nabla p^{n+1}$$

But for this we require the knowledge of pressure $p$ at $(n+1)$. Here, we exploit the fact that the next iterate of velocity obtained via our update has to be divergence-free as it should satisfy the continuity equation.
But for this we require the knowledge of pressure $p$ at $(n+1)$. Here, we exploit the fact that the next iterate of velocity obtained via our update has to be divergence-free as it should satisfy the continuity equation. Hence, we obtain an equation for the pressure at the $(n+1)$ iteration:

$$\nabla^2 p^{n+1}=\frac{\rho}{\Delta t} \nabla \cdot \mathbf{V}^*$$

We then proceed to evaluate the pressure using a pseudo-transient solver. The pseudo-transient solver has been implemented in the `update_dPrdτ!` and `update_Pr!` functions.

## Results

The simulations have been performed to study the flow around a sphere in a three dimensional domain for a Reynolds number $Re=1e6$. The results for two simulations are presented within the folder `docs`. One simulation has been run on a single GPU and the other on 8 GPU nodes.
The simulations have been performed to study the flow around a sphere in a three dimensional domain for a Reynolds number `Re=1e6`. The results for two simulations are presented within the folder `docs`. One simulation has been run on a single GPU and the other on 8 GPU nodes.

### Single GPU simulation
The lowest resolution has been performed on a single GPU with a grid size of `127*127*255` grid points and `nt=2000` time steps.
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