A direct solver for the least-squares spectral collocation system on rectangular elements for the incompressible Navier-Stokes equations

Authors:
Wilhelm Heinrichs;Thorsten Kattelans
Affiliations:
University of Duisburg-Essen, Engineering Mathematics, Universitaetsstr. 3, D-45117 Essen, Germany;University of Duisburg-Essen, Engineering Mathematics, Universitaetsstr. 3, D-45117 Essen, Germany
Venue:
Journal of Computational Physics
Year:
2008

Citing 12
Cited 2

Least-square finite elements for Stokes problem

Computer Methods in Applied Mechanics and Engineering
Least-squares finite element method for fluid dynamics

Computer Methods in Applied Mechanics and Engineering
A new method of stabilization for singular perturbation problems with spectral methods

SIAM Journal on Numerical Analysis
Splitting techniques for the pseudospectral approximation of the unsteady Stokes equations

SIAM Journal on Numerical Analysis
Splitting techniques with staggered grids for the Navier—Stokes equations in the 2D case

Journal of Computational Physics
Least-squares spectral elements applied to the Stokes problem

Journal of Computational Physics
A Least-Squares Spectral Element Formulation for the Stokes Problem

Journal of Scientific Computing
Analysis of a Discontinuous Least Squares Spectral Element Method

Journal of Scientific Computing
Least-squares spectral collocation for discontinuous and singular perturbation problems

Journal of Computational and Applied Mathematics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

Journal of Computational Physics
Least-Squares Spectral Collocation for the Navier–Stokes Equations

Journal of Scientific Computing
Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

Journal of Computational Physics

Conservation of mass and momentum of the least-squares spectral collocation scheme for the Stokes problem

Journal of Computational Physics
Mass and momentum conservation of the least-squares spectral collocation method for the Navier-Stokes equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	31.45

Visualization

Abstract

A least-squares spectral collocation scheme for the Stokes and incompressible Navier-Stokes equations is proposed. The original domain is decomposed into quadrilateral subelements and on the element interfaces continuity of the functions is enforced in the least-squares sense. The collocation conditions and the interface conditions lead to overdetermined systems. These systems are directly solved by QR decomposition of the underlying matrices. By numerical simulations it is shown that the direct method leads to better results than the approach with normal equations. Furthermore, it is shown that the condition numbers can be reduced by introducing the Clenshaw-Curtis quadrature rule for imposing the average pressure to be zero. Finally, our scheme is successfully applied to the regularized and lid-driven cavity flow problems.