A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flowsReport as inadecuate




A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows - Download this document for free, or read online. Document in PDF available to download.

Advances in Computational Mathematics

, Volume 42, Issue 6, pp 1401–1426

First Online: 06 July 2016Received: 05 June 2015Accepted: 23 June 2016

Abstract

In this article, we endeavour to find a fast solver for finite volume discretizations for compressible unsteady viscous flows. Thereby, we concentrate on comparing the efficiency of important classes of time integration schemes, namely time adaptive Rosenbrock, singly diagonally implicit SDIRK and explicit first stage singly diagonally implicit Runge-Kutta ESDIRK methods. To make the comparison fair, efficient equation system solvers need to be chosen and a smart choice of tolerances is needed. This is determined from the tolerance TOL that steers time adaptivity. For implicit Runge-Kutta methods, the solver is given by preconditioned inexact Jacobian-free Newton-Krylov JFNK and for Rosenbrock, it is preconditioned Jacobian-free GMRES. To specify the tolerances in there, we suggest a simple strategy of using TOL-100 that is a good compromise between stability and computational effort. Numerical experiments for different test cases show that the fourth order Rosenbrock method RODASP and the fourth order ESDIRK method ESDIRK4 are best for fine tolerances, with RODASP being the most robust scheme.

KeywordsRosenbrock methods Navier-Stokes equations ESDIRK Jacobian-free Newton-Krylov Unsteady flows Time adaptivity Communicated by: Silas Alben

Mathematics Subject Classification 201076N99  Download to read the full article text



Author: David S. Blom - Philipp Birken - Hester Bijl - Fleur Kessels - Andreas Meister - Alexander H. van Zuijlen

Source: https://link.springer.com/







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