Discretizations in isogeometric analysis of Navier–Stokes flow

Abstract

This paper deals with isogeometric analysis of 2-dimensional, steady state, incompressible Navier–Stokes flow subjected to Dirichlet boundary conditions. We present a detailed description of the numerical method used to solve the boundary value problem. Numerical inf–sup stability tests for the simplified Stokes problem confirm the existence of many stable discretizations of the velocity and pressure spaces, and in particular show that stability may be achieved by means of knot refinement of the velocity space. Error convergence studies for the full Navier–Stokes problem show optimal convergence rates for this type of discretizations. Finally, a comparison of the results of the method to data from the literature for the lid-driven square cavity for Reynolds numbers up to 10,000 serves as benchmarking of the discretizations and confirms the robustness of the method.