Data Structure and Algorithms for Adaptive Mesh Refinement

Fluid flow in an oil and gas reservoir is governed by a system of nonlinear partial-differential equations with different types of boundary conditions. To compute an approximate solution to this evolving problem, the integration domain (geometry of the reservoir) is discretized. Given the large size of this three-dimensional geometry (several kilometers in areal extent and sometimes up to 100 meters thick), and the cost of fluid flow simulation depending on the number of unknowns for each grid block, the time spans evolved (several years of production) and the features of current computers, the mesh used for solving these partial-differential equations is not refined enough.