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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.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
76M22 Spectral methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage

Citations:

Zbl 0544.65071
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References:

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