Chan, Jesse2020-09-232020-09-232020-122020-09-23December 2Lin, Yimin. "Entropy Stable Discontinuous Galerkin-Fourier Methods." (2020) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/109372">https://hdl.handle.net/1911/109372</a>.https://hdl.handle.net/1911/109372Entropy stable discontinuous Galerkin methods for nonlinear conservation laws replicate an entropy inequality at semi-discrete level. The construction of such methods depends on summation-by-parts (SBP) operators and flux differencing using entropy conservative finite volume fluxes. In this work, we propose a discontinuous Galerkin-Fourier method for systems of nonlinear conservation laws, which is suitable for simulating flows with spanwise homogeneous geometries. The resulting method is semi-discretely entropy conservative or entropy stable. Computational efficiency is achieved by GPU acceleration using a two-kernel splitting. Numerical experiments in 3D confirm the stability and accuracy of the proposed 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.Numerical PDEsHigh order methodsDiscontinuous Galerkin methodsHigh performance computingThesis2020-09-23