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Hybrid spectral-element-low-order methods for incompressible flows

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In this article we present a new formulation for coupling spectral element discretizations to finite difference and finite element discretizations addressing flow problems in very complicated geometries. A general iterative relaxation procedure (Zanolli patching) is employed that enforcesC 1 continuity along the patching interface between the two differently discretized subdomains. In fluid flow simulations of transitional and turbulent flows the high-order discretization (spectral element) is used in the outer part of the domain where the Reynolds number is effectively very high. Near “rough” wall boundaries (where the flow is effectively very viscous) the use of low-order discretizations provides sufficient accuracy and allows for efficient treatment of the complex geometry. An analysis of the patching procedure is presented for elliptic problems, and extensions to incompressible Navier-Stokes equations are implemented using an efficient high-order splitting scheme. Several examples are given for elliptic and flow model problems and performance is measured on both serial and parallel processors.

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Henderson, R., Karniadakis, G.E. Hybrid spectral-element-low-order methods for incompressible flows. J Sci Comput 6, 79–100 (1991).

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