A weak Legendre collocation spectral method for the solution of the incompressible Navier-Stokes equations in unstructured quadrilateral subdomains

Kondaxakis, D; Tsangaris, S

dc.contributor.author	Kondaxakis, D	en
dc.contributor.author	Tsangaris, S	en
dc.date.accessioned	2014-03-01T01:18:34Z
dc.date.available	2014-03-01T01:18:34Z
dc.date.issued	2003	en
dc.identifier.issn	0021-9991	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15098
dc.subject	weak collocation legendre method	en
dc.subject	domain decomposition	en
dc.subject	influence matrix	en
dc.subject	axisymmetric simulation	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	MULTIDOMAIN METHOD	en
dc.subject.other	TURBULENT FLOWS	en
dc.subject.other	ELEMENT METHOD	en
dc.subject.other	NUMERICAL-SIMULATION	en
dc.subject.other	CHEBYSHEV	en
dc.subject.other	GEOMETRIES	en
dc.subject.other	FORMULATION	en
dc.subject.other	LAMINAR	en
dc.subject.other	DOMAIN	en
dc.subject.other	TIME	en
dc.title	A weak Legendre collocation spectral method for the solution of the incompressible Navier-Stokes equations in unstructured quadrilateral subdomains	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0021-9991(03)00350-4	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0021-9991(03)00350-4	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	A weak Legendre spectral method is developed for the solution of the primitive variable formulation of the unsteady incompressible Navier-Stokes equations, in general two-dimensional and axisymmetric geometries. A semi-implicit projection method is utilized for the temporal approximation and for decoupling the velocity field from the pressure field. A series of elliptic boundary value problems arises from the above procedure, each of which is spatially discretized by a weak collocation method in multiple nonoverlapping subdomains. In particular, a modified variational formulation of the partial differential equations is presented which leads, after discretization, to a weak multidomain approximation of the corresponding problems. A weak formalism for the influence matrix technique is also developed, which is consistent with the spatial discretization scheme and successfully separate the equations for the internal nodes from the ones governing the interface unknowns. A method of dealing with the singularity problem faced by the weak formulation at axisymmetric problems is proposed, while a combination of direct methods is studied for tackling effectively the linear algebraic systems resulting from the full discretization. Exponential convergence is demonstrated for a plethora of Stokes and Navier-Stokes simulations. (C) 2003 Elsevier B.V. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	JOURNAL OF COMPUTATIONAL PHYSICS	en
dc.identifier.doi	10.1016/S0021-9991(03)00350-4	en
dc.identifier.isi	ISI:000186710700007	en
dc.identifier.volume	192	en
dc.identifier.issue	1	en
dc.identifier.spage	124	en
dc.identifier.epage	156	en