MADNESS
0.10.1
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The source is here.
where the force and the viscocity and are given in the code.
Step 1. Calculate the pressure at time explicitly.
Everything in the RHS is either given or known; thus can be obtained by applying a Coulomb operator.
Step 2. Calculate the velocity at time n+1.
Again, is calculated by applying the BSH operator to the RHS.
The resulting method is a first order in time scheme and can be extended by Spectral/Krylov deferred corrections to construct higher order methods. Particularly, the construction of a second order scheme under this frame is easy and similar to the Crank-Nicolson technique, which is also demonstrated by the example.