Title data
Lehmann, Moritz ; Gekle, Stephan:
Analytic Solution to the Piecewise Linear Interface Construction Problem and Its Application in Curvature Calculation for VolumeofFluid Simulation Codes.
In: Computation.
Vol. 10
(2022)
Issue 2
.
 No. 21.
ISSN 20793197
DOI: https://doi.org/10.3390/computation10020021
Project information
Project title: 



Project financing: 
Andere Universität Bayreuth 
Abstract in another language
The plane–cube intersection problem has been discussed in the literature since 1984 and iterative solutions to it have been used as part of piecewise linear interface construction (PLIC) in computational fluid dynamics simulation codes ever since. In many cases, PLIC is the bottleneck of these simulations regarding computing time, so a faster analytic solution to the plane–cube intersection would greatly reduce the computing time for such simulations. We derive an analytic solution for all intersection cases and compare it to the previous solution from Scardovelli and Zaleski (Scardovelli, R.; Zaleski, S. Analytical relations connecting linear interfaces and volume fractions in rectangular grids. J. Comput. Phys. 2000, 164, 228–237), which we further improve to include edge cases and microoptimize to reduce arithmetic operations and branching. We then extend our comparison regarding computing time and accuracy to include two different iterative solutions as well. We find that the best choice depends on the employed hardware platform: on the CPU, Newton–Raphson is fastest with compiler optimization enabled, while analytic solutions perform better than iterative solutions without. On the GPU, the fastest method is our optimized version of the analytic SZ solution. We finally provide details on one of the applications of PLIC—curvature calculation for the VolumeofFluid model used for free surface fluid simulations in combination with the lattice Boltzmann method.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Professor Theoretical Physics VI  Simulation and Modelling of Biofluids > Professor Theoretical Physics VI  Simulation and Modelling of Biofluids  Univ.Prof. Dr. Stephan Gekle Research Institutions > Collaborative Research Centers, Research Unit > SFB 1357  MIKROPLASTIK 
Result of work at the UBT:  Yes 
DDC Subjects:  000 Computer Science, information, general works 000 Computer Science, information, general works > 004 Computer science 500 Science > 500 Natural sciences 500 Science > 510 Mathematics 500 Science > 530 Physics 
Date Deposited:  10 Feb 2022 07:43 
Last Modified:  10 Feb 2022 07:43 
URI:  https://eref.unibayreuth.de/id/eprint/68654 