Methods for compressible fluid simulation on GPUs using high-order finite differences

Johannes Pekkilä, Miikka S. Väisälä*, Maarit J. Käpylä, Petri J. Käpylä, Omer Anjum

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)


We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3.6× speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

Original languageEnglish
Pages (from-to)11-22
JournalComputer Physics Communications
Publication statusPublished - Aug 2017
MoE publication typeA1 Journal article-refereed


  • Astrophysical applications
  • Computational techniques
  • Computer science and technology
  • Finite difference methods in fluid dynamics
  • Fluid dynamics
  • Hydrodynamics


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