Riviere, Beatrice M.2013-09-162013-09-162013-09-162013-09-162013-052013-09-16May 2013Li, Jizhou. "Locally Mass-Conservative Method With Discontinuous Galerkin In Time For Solving Miscible Displacement Equations Under Low Regularity." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/71985">https://hdl.handle.net/1911/71985</a>.https://hdl.handle.net/1911/71985The miscible displacement equations provide the mathematical model for simulating the displacement of a mixture of oil and miscible fluid in underground reservoirs during the Enhance Oil Recovery(EOR) process. In this thesis, I propose a stable numerical scheme combining a mixed finite element method and space-time discontinuous Galerkin method for solving miscible displacement equations under low regularity assumption. Convergence of the discrete solution is investigated using a compactness theorem for functions that are discontinuous in space and time. Numerical experiments illustrate that the rate of convergence is improved by using a high order time stepping method. For petroleum engineers, it is essential to compute finely detailed fluid profiles in order to design efficient recovery procedure thereby increase production in the EOR process. The method I propose takes advantage of both high order time approximation and discontinuous Galerkin method in space and is capable of providing accurate numerical solutions to assist in increasing the production rate of the miscible displacement oil recovery process.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Discontinuous GalerkinMiscible displacementLow regularityHigh order time discretizationMixed finite element methodStabilityCompactnessThesis2013-09-16123456789/ETD-2013-05-539