The difficulties in solving the incompressible Navier-Stokes problem are well-known. In particular, the nonlinear, saddle-point nature of the problem leads to difficulties in preconditioning and solving the linear systems. Schemes based on algebraic splitting have long been successfully applied to the time-dependent version of the problem; however their extension to the steady-state case remained elusive for many years. In new works published in Mathematics of Computation and Numerical Methods for Partial Differential Equations, we have successfully demonstrated how one may apply these methods to steady-state problems, greatly reducing the computational difficulties of this problem. This problem is very relevant to the application of computational fluid dynamics in blood flow problems, as flow in smaller and midsized vessels (for example in coronary or cerebral arteries) is frequently modeled as a steady incompressible flow.
January 28th, 2019