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The plane-cube intersection problem has been around in literature since 1984and iterative solutions to it have been used as part of piecewise linearinterface construction (PLIC) in computational fluid dynamics simulation codesever since. In many cases, PLIC is the bottleneck of these simulationsregarding compute time, so a faster, analytic solution to the plane-cubeintersection would greatly reduce compute time for such simulations. We derivean analytic solution for all intersection cases and compare it to the oneprevious solution from Scardovelli and Zaleski (Ruben Scardovelli and StephaneZaleski. "Analytical relations connecting linear interfaces and volumefractions in rectangular grids". In: Journal of Computational Physics 164.1(2000), pp. 228-237.), which we further improve to include edge cases andmicro-optimize to reduce arithmetic operations and branching. We then extendour comparison regarding compute time and accuracy to include two differentiterative solutions as well. We find that the best choice depends on theemployed hardware platform: on the CPU, Newton-Raphson is fastest withvectorization while analytic solutions perform better without. The reason forthis is that vectorization instruction sets do not include trigonometricfunctions as used in the analytic solutions. On the GPU, the fastest method isour optimized version of the analytic SZ solution. We finally provide detailson one of the applications of PLIC: curvature calculation for theVolume-of-Fluid model used for free surface fluid simulations in combinationwith the lattice Boltzmann method.

computation

Analytic Solution to the Piecewise Linear Interface Construction Problem  and its Application in Curvature Calculation for Volume-of-Fluid Simulation  Codes