Spectral approximation to advection-diffusion problems by the fictitious interface method
type: Item
instance of: scholarly article
title: Spectral approximation to advection-diffusion problems by the fictitious interface method
zbMATH Open document ID: 0809.65109
author: A. Frati
author: Franco Pasquarelli
author: Alfio Quarteroni
published in: Journal of Computational Physics
publication date: 1993-10-13T00:00:00Z
review text: This work originates from numerical matching techniques for problems involving boundary layers. In particular, a spatial region \(\Omega\) is considered that can be partitioned into two regions, \(\Omega_ 1\) and \(\Omega_ 2\), such that an advection-diffusion equation \(-\epsilon\Delta u \text{div }(bu) b_ 0 u= f\), is satisfied in \(\Omega_ 1\), and an advection equation (obtained by dropping the viscous term), \(\text{div}(bu) b_ 0 u= f\), is satisfied in \(\Omega_ 2\). Here, \(b_ 0\) and \(f\) are given scalar functions, and \(b\) is the given advection vector. The difficulty in such formulations lies in the specification and numerical treatment of the boundary conditions at the interface of \(\Omega_ 1\) and \(\Omega_ 2\). The authors describe discretization of these equations in a 2D rectangular region, and in particular, the boundary conditions at the interface. These discretizations arise from spectral approximations to the equations based upon Gauss-Lobatto-Legendre knots. The resulting system of equations is sparse, and numerical examples are presented showing the results of preconditioned GMRES solution techniques. Reference is made to applications involving time-dependent and nonlinear advection-diffusion systems.
reviewed by: J.A.Crow
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 428546
zbMATH Keywords: fictitious interface method
zbMATH Keywords: spectral methods
zbMATH Keywords: boundary layers
zbMATH Keywords: advection-diffusion equation
zbMATH Keywords: spectral approximations
zbMATH Keywords: numerical examples
zbMATH Keywords: preconditioned GMRES solution techniques
Wikidata QID: Q56996653
MaRDI profile type: Publication
full work available at URL: jcph.1993.1137
OpenAlex ID: W2093889206
DOI: 10.1006/JCPH.1993.1137
description: scientific article; zbMATH DE number 428546