A direct solver for the least-squares spectral collocation system on rectangular elements for the incompressible Navier-Stokes equations
type: Item
instance of: scholarly article
title: A direct solver for the least-squares spectral collocation system on rectangular elements for the incompressible Navier-Stokes equations
zbMATH Open document ID: 1193.76096
author: Wilhelm Heinrichs
author: Thorsten Kattelans
published in: Journal of Computational Physics
publication date: 2008-05-16T00:00:00Z
review text: The authors develop a least-square spectral collocation scheme for steady and unsteady Stokes equations and for incompressible Navier-Stokes equations where the original domain has been decomposed into quadrilateral subelements and on the element interfaces continuity of the functions is enforced. To avoid high condition numbers of normal equations, a direct solver (QR decomposition of the matrices) is used for the overdetermined systems. The numerical simulations confirm the high accuracy of the proposed scheme, and solving the overdetermined systems with QR decomposition yields better approximation results. The computational cost of QR decomposition is higher than using normal equations. At the same time, by using pseudoinverse Clenshaw-Curtis quadrature rule one gets the same results as by using QR decomposition, but with much higher computational costs. For unsteady Stokes equations, the presented scheme also demonstrates a good performance for different Reynolds numbers, for different time steps and for various numbers of elements. Finally, the scheme is successfully applied to the regularized lid-driven cavity problems where good results are achieved.
reviewed by: Titus Petrila
Mathematics Subject Classification ID: 76M22
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 5276048
zbMATH Keywords: condition numbers
zbMATH Keywords: improved stability
zbMATH Keywords: QR decomposition
MaRDI profile type: Publication
full work available at URL: j.jcp.2008.01.025
OpenAlex ID: W1966279710
cites work: DISCONTINUOUS/CONTINUOUS LEAST-SQUARES FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS
cites work: Discontinuous least-squares finite element method for the div-curl problem
cites work: Q3752987
cites work: On the solution of the Navier-Stokes equations using Chebyshev projection schemes with third-order accuracy in time
cites work: Benchmark spectral results on the lid-driven cavity flow
cites work: Q4039908
cites work: High-Order Methods for Incompressible Fluid Flow
cites work: A New Method of Stabilization for Singular Perturbation Problems with Spectral Methods
cites work: Q4199478
cites work: Analysis of a discontinuous least squares spectral element method
cites work: Splitting techniques with staggered grids for the Navier-Stokes equations in the 2D case
cites work: Splitting Techniques for the Pseudospectral Approximation of the Unsteady Stokes Equations
cites work: Least-squares spectral collocation for discontinuous and singular perturbation problems
cites work: Least-squares spectral collocation for the Navier-Stokes equations
cites work: Least-squares spectral collocation with the overlapping Schwarz method for the incompressible Navier-Stokes equations
cites work: An adaptive least-squares spectral collocation method with triangular elements for the incompressible Navier-Stokes equations
cites work: Least-squares finite elements for the Stokes problem
cites work: Least-squares finite element method for fluid dynamics
cites work: A least-squares finite element method for incompressible Navier-Stokes problems
cites work: On the least-squares method
cites work: Spectral methods for problems in complex geometries
cites work: Spectral methods for incompressible viscous flow
cites work: Spectral/\(hp\) least-squares finite element formulation for the Navier-Stokes equations.
cites work: Space-time coupled spectral/\(hp\) least-squares finite element formulation for the incompressible Navier-Stokes equations
cites work: Least-squares finite element formulations for viscous incompressible and compressible fluid flows
cites work: A least-squares spectral element formulation for the Stokes problem
cites work: Least-squares spectral elements applied to the Stokes problem
cites work: Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations
cites work: Q4890329
DOI: 10.1016/J.JCP.2008.01.025
description: scientific article; zbMATH DE number 5276048