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

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Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((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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Rang, J. (2013). A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_18

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  • DOI: https://doi.org/10.1007/978-3-642-33221-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33220-3

  • Online ISBN: 978-3-642-33221-0

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