TY - JOUR
T1 - A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows
AU - Blom, David S.
AU - Birken, Philipp
AU - Bijl, Hester
AU - Kessels, Fleur
AU - Meister, Andreas
AU - van Zuijlen, Alexander H.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
KW - ESDIRK
KW - Jacobian-free Newton-Krylov
KW - Navier-Stokes equations
KW - Rosenbrock methods
KW - Time adaptivity
KW - Unsteady flows
UR - http://resolver.tudelft.nl/uuid:8d8e6670-0502-4866-a49b-711e64518da9
UR - http://www.scopus.com/inward/record.url?scp=84978032472&partnerID=8YFLogxK
U2 - 10.1007/s10444-016-9468-x
DO - 10.1007/s10444-016-9468-x
M3 - Article
AN - SCOPUS:84978032472
SN - 1019-7168
VL - 42
SP - 1401
EP - 1426
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
IS - 6
ER -