2D adaptivity for 3D problems: Parallel SPE10 reservoir simulation on dynamically adaptive prism grids

Abstract

We present an approach for parallel adaptive mesh refinement for 3D applications on triangular prism grids. Subsurface, oceanic or atmospheric flow problems in geosciences often have small vertical extent or anisotropic input data. Key solution features, such as shock waves, mostly emerge in horizontal directions and require little vertical capturing, such that 2D adaptivity is an attractive option. We extended sam(oa)2, a 2D code with fully dynamically adaptive refinement based on Sierpinski space-filling curves, by adding support for 2.5D grids: retaining fully adaptive horizontal refinement and load balancing, but introducing uniformly refined columns of vertical grid layers. We evaluate the potential of this approach on the SPE10 benchmark, a particularly hard two-phase flow problem in reservoir simulation. SPE10 investigates oil exploration by water injection in heterogeneous porous media. Performance of sam(oa)2 is memory-bound for this scenario with up to 70% throughput of the STREAM benchmark and parallel efficiency of approx. 91% for weak scaling on up to 8192 cores.