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Add README.md for HasegawWakatani example
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Yuuichi Asahi committed Feb 26, 2025
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# Solving 2D Hasegawa-Wakatani turbulence with Fourier spectral method

For turbulence simulations, we sometimes consider periodic boundaries by assuming that a system is homogeneous and isotropic. Under the periodic bondary conditions, we can solve the system of equations with Fourier spectral method. Here, we consider a typical 2D turbulence plasma turbulence model, called Hasegawa-Wakatani equation `[Wakatani, 1984](#Wakatani1984)`. With kokkos and kokkos-fft, we can easily implement the code like python while getting a big acceleration.
For turbulence simulations, we sometimes consider periodic boundaries by assuming that a system is homogeneous and isotropic. Under the periodic bondary conditions, we can solve the system of equations with Fourier spectral method. Here, we consider a typical 2D turbulence plasma turbulence model, called Hasegawa-Wakatani equation `[Wakatani, 1984](#Wakatani1984)`. With kokkos and kokkos-fft, we can easily implement the code just like python while getting a significant acceleration.

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"bondary" should be "boundary".

## Numerical description

In Fourier space, 2D Hasegawa-Wakatani model can be described as

![Continuity eq](https://latex.codecogs.com/svg.latex?\frac{\partial\hat{u}_k}{\partial{t}}+\\{\tilde{\phi},\tilde{u}\\}_k=-C_{k}\left(\hat{\phi}_k-\hat{n}_k\right)-\nu{k}^4{k}^2\hat{\phi}_k)
![Continuity eq](https://latex.codecogs.com/svg.latex?\frac{\partial\hat{u}_k}{\partial{t}}+\\{\tilde{\phi},\tilde{u}\\}_k=-C_{k}\left(\hat{\phi}_k-\hat{n}_k\right)-\nu{k}^4\hat{u}_k)

![Vorticity eq](https://latex.codecogs.com/svg.latex?\frac{\partial\hat{n}_k}{\partial{t}}+\\{\tilde{\phi},\tilde{n}\\}_k=-i\kappa{k_{y}}\hat{\phi}_k+C_{k}\left(\hat{\phi}_k-\hat{n}_k\right)-\nu{k}^4\hat{n}_k)

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