conatus.walls

conatus.walls(a, b, *more, basis='chebyshev')

Bounded axis [a, b] (walls at a and b); walls(a, c, ..., b): a compound interval.

basis="chebyshev" (default): Chebyshev T, any wall conditions (tau method). basis="sincos": sine/cosine series sin(n pi (z-a)/L), cos(n pi (z-a)/L), n < N; each unknown is a pure sine or cosine series, its parity read off its homogeneous wall conditions (f = 0: sine; dz(f) = 0: cosine; free-slip velocity: cosine tangential, sine normal), no tau. Realised as the reflection subspace of RealFourier(2N) on the doubled period [a, 2b - a).

walls(a, c1, ..., b): a compound interval, one Chebyshev T series per piece [a, c1], [c1, c2], …, [ck, b] (resolution: one size per piece, N_z = (N_1, …, N_k+1)); at each interface the value and the derivatives up to the order of each equation minus one are continuous: those conditions and their taus are written automatically and listed by explain(). Use it to refine a thin interior layer or a region near one wall.

Parameters:

• a (float)

• b (float)

• more (float)

• basis (str)

Return type:

Walls