Richard Nyberg: Turbulence on GPUs: A modular 3D finite-difference approach

Turbulence is an omnipresent phenomenon in our environment. This does not  translate into an easily simulated occurrence though. For higher Reynolds numbers fine spatial resolution and small time steps are required, which in turn makes big  demands on memory capacity and computing performance. The pencil-code is a much used framework for high-order finite difference computations on compressible magnetohydrodynamic flows. It has local  developers and is written in a modular fashion. While pencil-code supports large problems with MPI on clusters, the computations on each node are sequential. Using CUDA we implement modular differential operators for GPUs. These can be incorporated into pencil-code for GPU parallelized computations. The  derivatives are computed with sixth order, central finite-differences. We put much effort into making the operators as efficient as possible. The operators can be used in simulations, based on finite-differences, to accelerate the computations and reduce the simulation run time in a simple way. To test  the performance gain we run a simulation of a simplified version of the MHD  equations using our operators and compare the simulation time to regular pencil-code. Computing turbulence in computers has a long history with the last major  progress made in the earth simulator. Perhaps the GPU enabled pencil-code code will be able to take the next jump.