Métodos Runge-Kutta implícitos de alto orden para flujos incompresibles

Abstract

The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Asymptotic stability of Runge-Kutta methods applied to the solution of the resulting index-2DAE system in analyzed, allowing a critical comparison of semi-implicit and fully implicit Runge-Kutta methods, in terms of order of convergence and stability. Numerical examples, considering a Discontinuous Galerkin formulation with piecewise solenoidal approximation, demonstrate the applicability of the approach, and compare its performance with classical methods for incompressible flows.

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