zbMATH — the first resource for mathematics

Spectral multigrid techniques for the Navier-Stokes equations. (English) Zbl 0783.76071
We consider the vorticity-streamfunction formulation. Discretization in time is performed by a second order semi-implicit scheme where the diffusive term is treated in an implicit manner while the convective term is evaluated explicitly. For the discretization of the resulting Stokes- type problem, we introduce a new spectral collocation method. We propose an efficient finite difference preconditioner.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
[1] Canuto, C.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A., Spectral methods in fluid dynamics, (1988), Springer New York · Zbl 0658.76001
[2] Ehrenstein, U.; Peyret, R., A Chebyshev collocation method for the Navier-Stokes equations with applications to double-diffusive convection, Internat. J. numer. methods fluids, 9, 427-452, (1989) · Zbl 0665.76107
[3] Vanel, J.M.; Peyret, R.; Bontoux, P., A pseudo-spectral solution of vorticity-streamfunction equations using influence matrix technique, (), 463-475 · Zbl 0606.76030
[4] Heinrichs, W., A stabilized treatment of the biharmonic operator with spectral methods, SIAM J. sci. statist. comput., 12, 1162-1172, (1991) · Zbl 0729.65088
[5] Brandt, A.; Fulton, S.R.; Taylor, G.D., Improved spectral multigrid methods for periodic elliptic problems, J. comput. phys., 58, 96-112, (1985) · Zbl 0569.65084
[6] Heinrichs, W., Line relaxation for spectral multigrid methods, J. comput. phys., 77, 166-182, (1988) · Zbl 0649.65055
[7] Heinrichs, W., Multigrid methods for combined finite difference and Fourier problems, J. comput. phys., 78, 424-436, (1988) · Zbl 0657.65118
[8] Quazzani, J.; Peyret, R.; Zakaria, A., Stability of collocation-Chebyshev schemes with application to the Navier-Stokes equations, (), 287-294
[9] Heinrichs, W., Spectral multigrid techniques for the Stokes problem in streamfunction formulation, J. comput. phys., 102, 310-318, (1992) · Zbl 0759.76059
[10] Canuto, C.; Pietra, P., Boundary and interface conditions within a finite element preconditioner for spectral methods, J. comput. phys., 91, 310-343, (1990) · Zbl 0717.65091
[11] Deville, M.; Mund, E., Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning, J. comput. phys., 60, 517-533, (1985) · Zbl 0585.65073
[12] W. Heinrichs, Finite element preconditioning for spectral multigrid methods, Appl. Math. Comput. in press. · Zbl 0795.65078
[13] Brandt, A., Guide to multigrid development, () · Zbl 0505.65037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.