Multidimensional upwind hydrodynamics on unstructured meshes using graphics processing units - I. Two-dimensional uniform meshes

作者：Paardekooper S J^*

来源：Monthly Notices of the Royal Astronomical Society, 2017, 469(4): 4306-4340.

DOI：10.1093/mnras/stx1083

• hydrodynamics
• instabilities
• methods: numerical

We present a new method for numerical hydrodynamics which uses a multidimensional generalization of the Roe solver and operates on an unstructured triangular mesh. The main advantage over traditional methods based on Riemann solvers, which commonly use one-dimensional flux estimates as building blocks for a multidimensional integration, is its inherently multidimensional nature, and as a consequence its ability to recognize multidimensional stationary states that are not hydrostatic. A second novelty is the focus on graphics processing units (GPUs). By tailoring the algorithms specifically to GPUs, we are able to get speedups of 100-250 compared to a desktop machine. We compare the multidimensional upwind scheme to a traditional, dimensionally split implementation of the Roe solver on several test problems, and we find that the new method significantly outperforms the Roe solver in almost all cases. This comes with increased computational costs per time-step, which makes the new method approximately a factor of 2 slower than a dimensionally split scheme acting on a structured grid.

• 出版日期2017-8