Riviere, Beatrice M.2016-01-252016-01-252015-052015-04-20May 2015Li, Jizhou. "High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity." (2015) Diss., Rice University. <a href="https://hdl.handle.net/1911/88087">https://hdl.handle.net/1911/88087</a>.https://hdl.handle.net/1911/88087In my thesis, I formulate, analyze and implement high order discontinuous Galerkin methods for simulating miscible displacement in porous media. The analysis concerning the stability and convergence under the minimal regularity assumption is established to provide theoretical foundations for using discontinuous Galerkin discretization to solve miscible displacement problems. The numerical experiments demonstrate the robustness and accuracy of the proposed methods. The performance study for large scale simulations with highly heterogeneous porous media suggests strong scalability which indicates the efficiency of the numerical algorithm. The simulations performed using the algorithms for physically unstable flow show that higher order methods proposed in thesis are more suitable for simulating such phenomenon than the commonly used cell-center finite volume method.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 Galerkin methodsmiscible displacementreservoir simulationshigh performance computinghigh order methodsviscous fingeringalgebraic multigriddomain decompositionThesis2016-01-25