Isogeometric Analysis of Navier-Stokes Flow Using Locally Refinable B-Splines

Abstract

Local refinement is crucial in all computer methods for flow problems, e.g., to resolve boundary layers. Locally Refinable (LR) B-splines are a recent approach to local refinement within isogeometric analysis based on piecewise polynomials. In this work we present numerical investigations of the use of LR B-splines in isogeometric analysis of flow problems. The problems considered are based on the steady-state, incompressible Navier-Stokes equations in two dimensions. We give a brief introduction to LR B-splines and to isogeometric analysis in fluid mechanics in general. We propose two families of LR B-spline discretizations of the pressure and velocity fields for solving the mixed formulation of the governing equations using isogeometric analysis. And through representative examples, we investigate the stability of the discretizations, we study their ability to reproduce an analytical solution, and we examine their performance on a standard benchmark problem.