conatus.problems.kuramoto_sivashinsky¶
- conatus.problems.kuramoto_sivashinsky(*, N, L, dealias)[source]¶
Kuramoto–Sivashinsky equation on the periodic line (0, L), IVP:
dt(u) + u_xx + u_xxxx = -u u_x.
Linear terms implicit (LHS), the quadratic term explicit (RHS). RealFourier(x, N, (0, L)). The size L is the only parameter (L = 22: the standard chaotic case).
Validation reference: the linear growth rate of exp(i k x) about u = 0 is exactly sigma = k^2 - k^4 (tests/problems/test_problems_patterns.py, every k = 2 pi j / L). L = 22: equilibria E1, E2 of energy 0.2609, 0.4382 and travelling wave TW1 of speed 0.73699 (Cvitanovic, Davidchack & Siminos 2010, SIAM J. Appl. Dyn. Syst. 9, 1, Tables 5.1-5.2; tutorial t05 reproduces them from this equation).
- Parameters:
N (int)
L (float)
dealias (float)
- Return type: