jejjohnson / jejjohnson/spectraldiffx

Kuramoto-Sivashinsky (KS) Model (1D Chaos)

Open
#14 1 comment 0 reactions 1 assignee Claimed by @jejjohnson View on GitHub
Dominant language
Python
Stars
1
Forks
0
PR merge metrics
No merged PRs in 30d

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)

Contributor guide

No contributing guide indexed for this repository

Assessment

This issue has not been assessed yet.

Get new issues in your inbox

A short digest of beginner-friendly GitHub issues.