conatus.problems.plane_couette¶
- conatus.problems.plane_couette(*, Nx, Ny, Nz, Lx, Lz, Re, dealias)[source]¶
3D plane Couette flow, incompressible Navier–Stokes, as an IVP.
Equations (half-gap h = 1, walls at y = -1, +1 moving at u = -e_x and +e_x):
dt(u) - lap(u)/Re + grad(p) = -u.grad(u), div(u) = 0, u = -e_x at y = -1, u = +e_x at y = +1.
Units: length h, velocity U_w = wall speed, Re = U_w h / nu. Laminar solution U = y e_x. Same generalized-tau pressure treatment as
channel(); no pressure gradient.Validation reference: plane Couette flow is linearly stable at every Re (Romanov 1973, Funct. Anal. Appl. 7, 137). No tabulated eigenvalue is reproduced here: the check (
plane_couette_evp(), tests/problems/test_problems_shear.py) is Im c < 0 for the whole converged spectrum up to Re = 1e5, the centre-symmetry c -> -conj(c) of the spectrum, and convergence in N of the least-stable mode.- Parameters:
Nx (int)
Ny (int)
Nz (int)
Lx (float)
Lz (float)
Re (float)
dealias (float)
- Return type: