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Simulation numérique d'écoulements multi-fluides sur grille de calcul

Abstract : This thesis is about numerical methods for incompressible multi-fluid flows simulations on computational grids, in the framework of the MecaGrid project.A performance study of the grid MecaGrid shows that it has a highly heterogeneous architecture that differs from usual super-calculators. In order to improve the performances, several optimization techniques are presented like, for example, adjusting the computations and communications partitioning within the grid, and privileging the processors duty versus the very slow network communications.We chose numerical methods based on unstructured meshes composed of tetrahedrons in order to perform direct simulations of multi-fluid flows with interface capture. A unified approach, which recalls the Multiscale's, consists of condensing a pyramidal Bubble function as a universal stabilization technique.The incompressible flow is computed by using the Navier-Stokes equations, solved with a mixed finite element method with a P1+/P1 space interpolation. An implicit Euler time scheme is applied, as well as a Newton's algorithm in order to linearize the problem.The interfaces are captured by means of a Level-Set technique with a continued P1 space interpolation. It consists of solving a transport equation stabilized by a condensed Bubble (Residual-Free Bubbles), coupled with a Hamilton-Jacobi equation used to re-initialize the Level-Set function throughout its transportation. A comparison with a discontinued Galerkin method close to the Volume Of Fluid technique shows that the Level-Set stands out for its simplicity and the absence of numerical diffusion.Finally, some numerical simulations are validated by well-known test cases.
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Submitted on : Friday, April 17, 2009 - 4:03:10 PM
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  • HAL Id : tel-00376484, version 1


Olivier Basset. Simulation numérique d'écoulements multi-fluides sur grille de calcul. Mécanique []. École Nationale Supérieure des Mines de Paris, 2006. Français. ⟨tel-00376484⟩



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