|Time:||12/14/04, 4:00 p.m. – 5:30 p.m.|
|Lecturer:||Hong Wang, Department of Mathematics, University of South Carolina, U.S.A.|
|Venue:||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Eulerian-Lagrangian methods symmetrize the transport equations andgenerate accurate numerical solutions even if very large time steps andcoarse spatial grids are used. They have shown great performance in thenumerical simulations of single-phase flow and immiscible two phase flow.However, there exist serious mathematical and numerical difficultiesthat hinder the development of such methods for multiphase multicomponentcompositional flows in multiple space dimensions: (1) Eulerian-Lagrangianmethods require the governing equations to have a well-defined transportvelocity in terms of their primary unknowns. The molar mass balanceequations in compositional flows are expressed as a weighted sum of molefractions and phase velocities in different phases. (2) Although theexcessive numerical diffusion present in upwind methods severely smearsthe moving steep fronts and introduces grid orientation effect, itfirmly subdues and hides various numerical difficulties. Eulerian-Lagrangianmethods minimize numerical diffusion in upwind methods, leading tosignificantly improved accuracy. However, the numerical difficultiessubdued by the excessive numerical diffusion in upwind methods reoccur.Moreover, the use of Lagrangian coordinates in Eulerian-Lagrangian methodsintroduces extra difficulties. All these numerical difficulties are inaddition to the mathematical and numerical difficulties of compositionalmodeling.In this talk, we present a novel Eulerian-Lagrangian formulation formultiphase and multicomponent compositional flow. Our preliminarynumerical experiments show that the resulting numerical scheme generatesstable and physically reasonable numerical solutions even if extremelylarge time steps (of more than 0.1 pore volume injected) is used. Thisshows that the strong potential of the proposed mathematical formulation.