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Least-Squares Spectral Element Methods in Computational Fluid Dynamics

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Advanced Computational Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 71))

Abstract

The least-squares spectral elementmethod (LSQSEM) is a relatively novel technique for the numerical approximation of the solution of partial differential equations. The method combines the weak formulation based on the minimization of a residual norm, the least-squares formulation, with the higher-order spectral element discretization. A well-posed least-squares formulation leads to a symmetric, positive-definite system of algebraic equations which are highly amenable to wellestablished solvers such as the preconditioned conjugate gradient method. Furthermore, the formulation is very robust in the sense that no stabilization operators are required to acquire convergent solutions. The spectral element discretization renders high order accuracy to the scheme. This new numerical scheme is applied to incompressible, compressible and non-Newtonian flow problems.

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Authors and Affiliations

  1. Dept. of Aerospace Engineering, TU Delft, Kluyverweg 1, 2629 HS, Delft, The Netherlands

    Marc Gerritsma

  2. Flemish Institute for Technological Research, Boeretang 200, BE-2400, Mol, Belgium

    Bart De Maerschalck

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  1. Marc Gerritsma
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  2. Bart De Maerschalck
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Correspondence to Marc Gerritsma .

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Editors and Affiliations

  1. Scientific Computing &, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098 XG, Netherlands

    Barry Koren

  2. Inst. Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, Netherlands

    Kees Vuik

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Gerritsma, M., De Maerschalck, B. (2009). Least-Squares Spectral Element Methods in Computational Fluid Dynamics. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_7

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