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A spectral collocation method to solve Helmholtz problems with boundary conditions involving mixed tangential and normal derivatives. (English) Zbl 1055.65134
Summary: The performing spectral method, developed by P. Haldenwang, G. Labrasse, S. Abboudi, and M. Deville [J. Comput. Phys. 55, 115–128 (1984; Zbl 0544.65071)], to solve multi-dimensional Helmholtz equations, associated to mixed boundary conditions with constant coefficients, is extended to boundary conditions mixing a first order normal derivative with a second order tangential derivative. The accuracy of the proposed algorithm is evaluated on two test cases for which analytical solutions exist: an academic problem and a physical configuration including an interface with shear viscosity. The procedure is also applied to the research of the Rayleigh–Bénard instability thresholds in closed cavities with thin diffusive walls.
65N35Spectral, collocation and related methods (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
76M22Spectral methods (fluid mechanics)
76S05Flows in porous media; filtration; seepage