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Chebyshev collocation for a convective problem in primitive variable formulation. (English) Zbl 1032.76653

Summary: A Chebyshev collocation method is applied to the study of a thermal convection problem in the primitive variable formulation. This method has been succesfully applied to cylindrical coordinates and now it is extended to cartesian coordinates. The main challenge is to find appropriate boundary conditions for pressure. They are fixed mainly by projections of the Navier-Stokes equations at the boundaries. This scheme permits a collocation design which avoids spurious modes for pressure.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)
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