Studies of mortar finite volume element methods and fractional flow formulation for two-phase flow in porous media
7/19/07, 5:00 p.m. – 6:30 p.m.
Yufei Cao Institut für Angewandte Analysis und Numerische Simulation
With the rapid development of computational mathematics, discretization methods using domain decomposition concept are becoming powerful tools to handle real-life problems with complicated domains or complex processes, and have the capabilities of high performance computation to large-scale problems. Mortar finite element method is one of the domain decomposition methods which allows the coupling of different physical models, numerical schemes and non-matching grids along interior interfaces of the computational domain. Therefore, there has been growing interest in the mortar finite element method due to its flexibility and great potential for large-scale parallel computation.On the other hand, the finite volume element methods are popular in computational fluid mechanics since they can keep the properties of original problems, i.e., satisfy discrete local mass conservation which is the most desirable feature of the numerical methods for many applications.Combining the above two methods, mortar finite volume element(MFVE) method is formed. Due to the advantagescombination of flexibility and local conservation, it's attractive to solve porous media flow problems using MFVE method.Therefore, MFVE methods for simple models including stationary elliptic problems and time-dependent parabolic problems are first studied in the presentation. Furthermore, in order to implement MFVE methods into multi-phase flow problems in porous media, the fractional flow formulation for two-phase flow is then carefully studied in comparison with the fully coupled formulation including numerical solutions, adaptive possibilities and other application: time-of-flight simulation.