Pressure less spectral methods
I'am working on a spectral method for the Navier Stokes equations in primitive variables. The idea is to cancell the pressure terms by using divergence free test functions for the inner product. Nice thing is that you dont need to worry about the pressure velocity coupling problem. The idea is based on a method by Leonard.
So far things are going OK, but we are having problems imposing the boundary conditions in spectral form.
Anybody out there working on similar ideas that may have an interest on this ?.
Re: Pressure less spectral methods
Since you are imposing boundary conditions, I guess you are using an expansion of non periodic polynomial like Legendre, Chebyshev, etc... and your domain is not periodic (at least in one of the dimensions).
Spectral Methods are high order accuracy methods and therfore the imposition of the boundary conditions on the primitive variables has to be done very carefully and mathematically as accurate as possible.
First you must not overimposed boundary conditions, which means that you impose on conditions only for each degree of spatial derivative (i.e. the density equation - 1 condition; the NS equations with the viscous diffusive terms - 2 conditions, one at each boundary).
Second you must use the method of Characteristics to solve for the incoming and outgoing flow variables and only after that, you can impose the condition on the primitive variables, using the values that you obtained throught the incoming and outgoing characteristics.
If you need references to that, let me know.
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