jejjohnson / jejjohnson/spectraldiffx
Kuramoto-Sivashinsky (KS) Model (1D Chaos)
- Dominant language
- Python
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Description
### Formulation
1D Kuramoto-Sivashinsky equation, chaotic PDE for benchmarking:
#### Governing Equation:
$$
u \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + \frac{\partial^2 u}{\partial x^2} + \frac{\partial^4 u}{\partial x^4} = 0$$
#### Forcing
- None, deterministic initial conditions
#### Starter code
```python
# Grid
N = 64
L = 2 * math.pi
grid = FourierGrid1D.from_N_L(N=N, L=L)
u = ... # initial condition
for t in timeline:
dudt = -u * d_dx(u) - d2_dx2(u) - d4_dx4(u)
```
#### Dependencies
- None; all operators exist
#### Reference: Kuramoto (1984), Sivashinsky (1977)
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