Method and system for solving finite element models using multiphase physics

摘要

"METHOD AND SYSTEM FOR SOLVING FINITE MIND MODELS USING MULTIPHASE PHASES". These are systems and methods for solving finite element models, where the matrix that governs the solution is modified by adjusting the weight of the matrix coefficients such that the elements on the diagonal of the matrix are nonnegative and the off-diagonal elements are non-positive. In one embodiment, a system is discretized into a finite element mesh with the contribution of each node to the discretization being weighted based on the direction of fluid flow through each element. Nodes upstream of the other nodes of the respective elements are weighted more heavily to make the resulting matrix substantially diagonal. This matrix is solved using traditional techniques.