We describe some new preconditioning strategies for handling the algebraic systems of equations that arise from discretization of the incompressible Navier-Stokes equations. We demonstrate how these methods adapt in a straightforward manner to decisions on implicit or explicit time discretization, explore their use on a collection of benchmark problems, and show how they relate to classical tec...

We prove that the solution of a system of random ordinary di erential equations dX(t) dt = V(t;X(t)) with di usive scaling, X"(t) = "X( t " ), converges weakly to a Brownian Motion when " # 0. We assume that V(t;x), t 2 R, x 2 R is a d-dimensional, random, incompressible, stationary Gaussian eld which has mean zero and decorrelates in nite time.

This chapter illustrates the use of algebraic flux correction in the context of finite element methods for the incompressible Navier-Stokes equations and related models. In the convection-dominated flow regime, nonlinear stability is enforced using algebraic flux correction. The numerical treatment of the incompressibility constraint is based on the ‘Multilevel Pressure Schur Complement’ (MPSC)...

The aim of this lecture is to give an overview on modern numerical methods for the computation of incompressible flows. We start with a short introduction to fluid mechanics, including the derivation and discussion of the most important models and equations. The numerical methods discussed in the subsequent part are ordered due to the model they solve, i.e., we start with the stationary Stokes ...

−ν∇u+ u.∇u+∇p = f ∇ · u = 0 which are taken to hold in some domain Ω ⊂ IR together with appropriate boundary conditions. We concentrate on the steady state equations; timedependent problems are essentially easier in the context of iterative methods. We will make some comment on this later. The numerical results we present here come from mixed finite element approximation though the techniques a...