pyoomph.equations.kuramoto_sivashinsky module

class pyoomph.equations.kuramoto_sivashinsky.KuramotoSivashinskyBoundary(*args: Any, **kwargs: Any)[source]

Bases: Equations

Represents the Neumann boundary conditions for the Kuramoto-Sivashinsky equation, given by:

dot(grad(h),n) = 0

class pyoomph.equations.kuramoto_sivashinsky.KuramotoSivashinskyEquations(*, a1=-1, a2=-1, a3=1, b=0, c=0, space='C2', curvspace=None, swap_test_functions=False, fieldname='height', curvfieldname='curvature')[source]

Bases: Equations

Represents the Kuramoto-Sivashinsky equation, which is a fourth order partial differential equation given by:

dh/dt = b*h + c*h^2 + a1*curv - a2*laplace(curv) + a3*|grad(h)|^2 curv = laplacian(h)

where h is the height field, curv is the curvature, a1, a2, a3, b and c are constants, laplace is the Laplace operator and grad is the gradient of h.

Parameters:

  • a1 (ExpressionOrNum) – Coefficient of the (anti)-diffusive term.

  • a2 (ExpressionOrNum) – Coefficient of the fourth order term.

  • a3 (ExpressionOrNum) – Coefficient of the KS-nonlinearity.

  • b (ExpressionOrNum) – Coefficient of h.

  • c (ExpressionOrNum) – Coefficient of h^2.

  • space (FiniteElementSpaceEnum) – Finite element space.

  • curvspace (FiniteElementSpaceEnum) – Finite element space for the curvature.

  • swap_test_functions (bool) – Swap the test functions of height and curvature.