A combined variational and multi-grid approach for fluid dynamics simulation

D. Ophir, A. Yahalom, G. A. Pinhasi, M. Kopylenko

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


A new approach for solving Partial Differential Equations problems related to fluid dynamics problems is being proposed. The method merges two existing methods: Using the variational techniques of finding the Action Minimum and using the Multi-Grid techniques of solving the equation on a coarse grid, interpolating it to finer grids, performing reduced computer work on finest grid, receiving the same accuracy. The proposed method simplifies the Multi-level adaptive techniques (MLAT) ideas. The experiments has shown that solving the variation problem on a grid with n2 is much less expensive (more than factor 4) than that on a grid with (2n)2 grid-points. The method solves a problem on a coarse grid, interpolates it to the finer grid and uses the interpolated values as initial values - better guess values for the problem on the finer grid. The finer grid has changed its role in the second step, to a coarse grid. This process improves the solution duration. The interpolation computer-work maybe performed efficiently once and therefore may be neglected compared to the time invested in the variation solution itself. In this work we improve on our previous results17 and also investigate further aspects of our method including the effects of introducing a better initial configuration ("guess")7, using the relaxation technique and the effect of the required accuracy on computation time. We also compare the resources needed for interior and boundary points by our algorithm.

Original languageEnglish
Title of host publicationCollection of Technical Papers - 44th AIAA Aerospace Sciences Meeting
Number of pages13
StatePublished - 2006
Event44th AIAA Aerospace Sciences Meeting 2006 - Reno, NV, United States
Duration: 9 Jan 200612 Jan 2006

Publication series

NameCollection of Technical Papers - 44th AIAA Aerospace Sciences Meeting


Conference44th AIAA Aerospace Sciences Meeting 2006
Country/TerritoryUnited States
CityReno, NV


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