A Parallel Multiscale Mixed Finite-Element Method for the Matlab Reservoir Simulation Toolbox

Abstract

We start by giving a brief introduction to reservoirs and reservoir modelling at different scales. We introduce a mathematical model for the two-phase flow, before we look at numerical discretizations. In particular we look at the Multiscale Mixed Finite-Element (MsMFE) Method from the Matlab Reservoir Simulation Toolbox (MRST), developed by SINTEF. Next we introduce a mimetic method, (with the inverse ip_simple inner product, wich is used for solving the local flow problems required to construct the basis functions used in the MsMFE method. After we have given a short introduction to parallel computing, and some common terms, we introduce a parallel MsMFE method. The method makes use of the Matlab Parallel Computing Toolbox, and it lets us calculate the inner products, as well as construct the basis functions of the MsMFE Method, in parallel. The new method makes use of a structure for storing the inner products that proves to be facillitate faster construction of the required basis functions than the regular structure used in MRST. We conclude that the new functions performs quite well, and consequently that the MsMFE method is well-suited for parallelization; additinally we conclude that the Parallel Computing Toolbox works well for this task. We note that, for larger problems, the parallel MsMFE method displays a near linear speedup for up to twelve Matlab workers. The new parallel functions are released as a module for MRST under the GNU General Public License (GPL). They can be downloaded from http://master.andershoff.net.