High-order implicit time integration for unsteady incompressible flows

The spatial discretization of unsteady incompressible NavierStokes equations is stated as a system of differential algebraic equations, corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Asymptotic stability of RungeKutta and Rosenbrock methods applied to the solution of the resulting index-2 differential algebraic equations system is analyzed. A critical comparison of Rosenbrock, semi-implicit, and fully implicit RungeKutta methods is performed in terms of order of convergence and stability. Numerical examples, considering a discontinuous Galerkin formulation with piecewise solenoidal approximation, demonstrate the applicability of the approaches and compare their performance with classical methods for incompressible flows. Copyright (c) 2011 John Wiley & Sons, Ltd.