Funding: This project is supported by the Swiss National Science Foundation by contract #200021_147052.
Modern solvers for the Navier-Stokes equations are optimized for massively-parallel computing platforms and can easily use many thousands of processing units by decomposing the spatial flow domain into small sub-domains. This allows nowadays the solution of complex unsteady flow problems at high Reynolds numbers with billions of grid points.
The continued increase in theoretical computational power should allow us to simulate ever larger flow problems as long as we are able to decompose the flow domain into sufficiently many sub-domains. The excellent weak scaling performance of modern solvers suggests that we should be able to scale the simulations without any limit in sight. However, this optimistic extrapolation does not factor in the increasing number of time steps which typically comes along with larger flow domains. This problem is aggravated for a common class of flow problems which are concerned with the spatial evolution of time-harmonic perturbations, e.g., a vibrating ribbon perturbing a boundary layer flow. The numerical simulation of such problems with classical time marching methods requires long transient periods at the beginning of each simulation. These transient periods are of no particular physical interest. The relevant flow field is only established when a periodic (or at least statistically steady) solution has been reached. In terms of dynamical systems, this can be understood as the asymptotic approach to a limit cycle of a given system.
For such problems with periodic forcing, the spatial decomposition of the computational domain might not yield sufficient parallelism for the efficient usage of modern massively-parallel supercomputers. Only a parallelization of the time integration could ease this potential scaling limit for flow problems of this type.
In the present project, we shall investigate whether the periodicity of the forcing and the existence of a limit cycle solution can be exploited by replacing the classical time marching scheme by a direct discretization of the limit cycle solution by a truncated Fourier series. This process leads to a very large nonlinear system of equations which has the set of all flow fields at every resolved time step (or temporal Fourier mode) as its unknowns. The efficient solution of such a large system of equations is major obstacle toward the simulation of complex flow problems (e.g. full airplane wings).
We aim at developing a solver for such a global problem which distributes the solution of the different Fourier modes to different processing units. Therefore, the time axis is parallelized such that the number of parallel threads scales with the number of resolved Fourier modes.
Prof. Dr. Peter Arbenz ETH Zurich
Computer Science Department
Universitätsstrasse 6, CAB F51.1
CH-8092 Zürich Tel.: +41 44 632 74 32 Email: firstname.lastname@example.org
Prof. Dr. D. Obrist, University of Bern
ARTORG Center for Biomedical Engineering Research, Cardiovascular Engineering
CH-3008 Bern Tel.: +41 31 632 7576 Email: email@example.com