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A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations

Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 120)

Abstract

One possibility to solve stiff ODEs like the example of Prothero and Robinson [21] or differential algebraic equations are Runge-Kutta methods (RK methods) [9, 31]. Explicit RK methods may not be a good choice since for getting a stable numerical solution a stepsize restriction should be accepted, i.e. the problem should be solved with very small timesteps. Therefore it might be better to use implicit or linear implicit RK methods, so-called Rosenbrock–Wanner methods. Fully implicit RK methods may be ineffective for solving high dimensional ODEs since they need a high computational effort to solve the huge nonlinear system. Therefore we consider in this note diagonally implicit RK methods (DIRK methods).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of Scientific ComputingTU BraunschweigBraunschweigGermany

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