Fekete-Gauss Spectral Elements for Incompressible Navier-Stokes Flows: The Two-Dimensional Case (Communications in Computational Physics, 2013)
Spectral element methods on simplicial meshes, say TSEM, show both theadvantages of spectral and finite element methods, i.e., spectral accuracy and geometrical flexibility. We present a TSEM solver of the two-dimensional (2D) incompressibleNavier-Stokes equations, with possible extension to the 3D case. It uses a projectionmethod in time and piecewise polynomial basis functions of arbitrary degree in space.The so-called Fekete-Gauss TSEM is employed, i.e., Fekete (resp. Gauss) points of thetriangle 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 solvesfor the element boundary nodes. Moreover, the algebraic system is never assembled,therefore the number of degrees of freedom is not limiting. An accuracy study is carried out and results are provided for classical benchmarks: the driven cavity flow, theflow between eccentric cylinders and the flow past a cylinder.