科研之友
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摘要
The parareal algorithm is used to obtain temporal parallelization added to the parallelism obtained from the conventional spatial domain decomposition techniques for hydrodynamic problems. Parareal solution becomes unstable at high Reynolds numbers where the non-linear convection term in the Navier-Stokes equations becomes much larger than the diffusion term. A new framework that allows using parareal for unsteady high Reynolds number hydrodynamic problems is proposed where parareal coarse and fine time integration operators are incorporated with coarse and fine spatial grids respectively and RANS or DES turbulence models are employed with a blended filter that can be tuned for the stability of the method. This framework is composed of three solution stages where parareal serves as a transitional stage that bridges a coarse grid solution to a fine grid one. While in lower Reynolds number problems parareal solution can serve as a final solution, in higher Reynolds number problems with high degree of non-linearity parareal provides a shorter path to the final solution. Anticipating a parareal stage in a transitional sense allows a looser convergence requirement which leads to high speedup gains in that stage. On the other hand improved initial values at the beginning of the last stage yields a shorter final fine stage solution. A windowing technique is employed in this methodology to further control the parareal instabilities by keeping the parareal corrections smaller while still being able to cover an arbitrary simulation time with given computational resources. Application of this methodology has been illustrated with a fully turbulent vortex shedding from a cylinder and a flow from the Grand Passage tidal zone in the Bay of Fundy. It is concluded that a tuned turbulence model may sufficiently stabilize the parareal methodology for many practical problems such that it becomes applicable in the initialization process if not accurate enough as a final solution. MPI and OpenMP programming paradigms are used for temporal parallelism introduced by parareal and data parallelism obtained via spatial domain decomposition methods respectively. Also all computational tasks are accelerated using CUDA compatible GPGPUs.
- 出版日期2017-3
