Fekete-Gauss spectral elements with application to Navier-Stokes flows
March 6, 2012
3:00 p.m.
Richard Pasquetti
Abstract
Spectral element methods on simplicial meshes (TSEM) show both the advantages of spectral and finite element methods, i.e. spectral accuracy and geometry flexibility. We first summarize works previously done for elliptic problems and then present a TSEM solver of the incompressible Navier-Stokes equations. In time it uses a projection method and in space the basis functions are polynomial of arbitrary degree. The so-called Fekete-Gauss TSEM is employed, i.e. Fekete (resp. Gauss) points of the triangle are used as interpolation (resp. quadrature) points. For the sake of consistency, isoparametric elements are used to approximate curved geometries. The resolution algorithm is based on an efficient Schur complement method, so that one only solves for the element boundary nodes.
Moreover, the algebraic system is never assembled so that the number of degree of freedom is not limiting. Examples of results are provided for classical benchmarks: the driven cavity flow, the flow between eccentric cylinders and the wake of a cylinder.