The spatial discretization of unsteady incompressible Navier–Stokes 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 Runge–Kutta 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 Runge–Kutta 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.
CitacióMontlaur, A.; Fernandez, S.; Huerta, A. High-order implicit time integration for unsteady incompressible flows. "International journal for numerical methods in fluids", 30 Novembre 2011.