Abstract
A pseudospectral method for the solution of incompressible flow problems based on an iterative solver involving an implicit treatment of linearized convective terms is presented. The method is designed for moderately complex geometries by means of a multi-domain approach. Key components are a Chebyshev collocation discretization, a special pressure-correction scheme and a restarted GMRES method with a preconditioner derived from a fast direct solver. The performance of the method with respect to the multi-domain functionality is investigated and compared to finite-volume approaches.
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REFERENCES
Bramble, J. H., Pasciak, J. E., and Schatz, A. H. (1986). The construction of preconditioners for elliptic problems by substructuring I. Math. Comp. 47, 103–134.
da Cunha, R. D., and Hopkins, T. R. (1994). A parallel implementation of the restarted GMRES iterative method for nonsymmetric systems of linear equations. Adv. Comput. Math. 2(3), 261–277.
Dimitropoulos, C. D. (1997). An efficient and robust spectral solver for nonseparable elliptic equations. J. Comput. Phys. 133, 186–191.
Batchelor, G. K. (ed.), (1960). The Collected Work of G. I. Taylor, Vol. 2, Cambridge University Press, Cambridge.
Haldenwang, P., Labrosse, G., Abboudi, S., and Deville, M. (1984). Chebyshev 3d spectral and 2d pseudospectral solvers for the Helmholtz equation. J. Comput. Phys. 55, 115–128.
Hugues, S., and Randriamampianina, A. (1997). An improved projection scheme applied to pseudospectral methods for the incompressible Navier–Stokes equations. Internat. J. Numer. Methods Fluids.
Macaraeg, M., and Streett, C. L. (1986). Improvements in spectral collocation through a multiple domain technique. Appl. Numer. Math. 2, 95–108.
Raspo, I., Ouazzani, J., and Peyret, R. (1996). A spectral multidomain technique for the computation of the Czochralski melt configuration. Internat. J. Numer. Methods Heat Fluid Flow 6, 31–58.
Schäfer, M., and Turek, S. (1996). Benchmark computations of laminar flow around a cylinder. In Hirschel, E. H. (ed.), Flow Simulation with High-Performance Computers II, NNFM 52, pp. 547–566.
Tric, E., Betrouni, M., and Labrosse, G. (1998). Accurate solutions of natural convection flow of air in a differentially heated cubic cavity. In Computational Fluid Dynamics '98, ECCOMAS 98, pp. 979–982.
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Droll, P., Schäfer, M. A Pseudospectral Multi-Domain Method for the Incompressible Navier–Stokes Equations. Journal of Scientific Computing 17, 365–374 (2002). https://doi.org/10.1023/A:1015133521791
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DOI: https://doi.org/10.1023/A:1015133521791