The modified method of characteristics with adjusted advection and an accelerated domain decomposition procedure
Abstract
The MMOC procedure for approximating the solutions of transport-dominated diffusion problems does not automatically preserve integral conservation laws, leading to (mass) balance errors in many kinds of flow problems. The variant, called the MMOCAA, discussed herein preserves the conservation law at a minor additional computational cost. It is shown that its solution, in either Galerkin or finite difference form, converges at the same rates as were proved earlier by Douglas and Russell for the standard MMOC procedure. Also, the application of the MMOCAA to a problem in two-phase, immiscible flow in porous media is discussed. A domain decomposition procedure based on Robin transmission conditions applicable to elliptic boundary problems was first introduced by P. L. Lions and later discussed by a number of authors. In all of these discussions, the weighting of the flux and the trace of the solution were independent of the iterative step number. For some model problems I introduce a cycle of weights and prove that an acceleration of the convergence rate similar to that occurring for alternating-direction iteration using a cycle of pseudo-time steps results. I also describe an analogous procedure for a mixed finite element approximation for a model Neumann problem and to consider an overlapping subdomain of the iteration, while retaining the variable parameter cycle.
Degree
Ph.D.
Advisors
Douglas, Purdue University.
Subject Area
Mathematics
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