Stabilized formulations and Smagorinsky turbulence model for incompressible flows

Abstract

We investigate the stabilization parameters used in the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations for flow problems. We present a comparative study of the stabi-lization parameters defined in different ways. The stabilization parameters are closely related to the locallength scales ("element length"). Our comparisons include parameters defined based on the element-levelmatrices and vectors, some earlier definitions of element lengths, extensions of these to higher-order ele-ments, and calculations for quadrilateral and triangular elements with different shapes. We also comparethe numerical viscosities generated by these stabilized formulations with the eddy viscosity associatedwith a Smagorinsky turbulence model that is based on element length scales.