David M. Williams
Publications

Journal Articles

D. M. Williams, "An Analysis of Discontinuous Galerkin Methods for the Compressible Euler Equations: Entropy and L2 Stability," Numerische Mathematik, (2019) https://doi.org/10.1007/s00211-019-01027-9

A. S. Wixom, G. S. Walters, S. L. Martinelli, and D. M. Williams, "Generalized Polynomial Chaos with Optimized Quadrature Applied to a Turbulent Boundary Layer Forced Plate," Journal of Computational and Nonlinear Dynamics, 14, (2019) 021010

D. M. Williams, "An Entropy Stable, Hybridized Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations," Mathematics of Computation, 87, (2018) 95-121

D. M. Williams, D. S. Kamenetskiy, and P. R. Spalart, "On Stagnation Pressure Increases in Calorically Perfect, Ideal Gases," International Journal of Heat and Fluid Flow, 58, (2016) 40-53

D. M. Williams, L. Shunn, and A. Jameson, "Symmetric Quadrature Rules for Simplexes Based on Sphere Close Packed Lattice Arrangements," Journal of Computational and Applied Mathematics, 266, (2014) 18-38

D. M. Williams and A. Jameson, "Energy Stable Flux Reconstruction Schemes for Advection-Diffusion Problems on Tetrahedra," Journal of Scientific Computing, 59, (2014) 721-759

D. M. Williams, P. Castonguay, P. E. Vincent, and A. Jameson, "Energy Stable Flux Reconstruction Schemes for Advection-Diffusion Problems on Triangles," Journal of Computational Physics, 250, (2013) 53-76

P. Castonguay, D. M. Williams, P. E. Vincent, and A. Jameson, "Energy Stable Flux Reconstruction Schemes for Advection-Diffusion Problems," Computer Methods in Applied Mechanics and Engineering, 267 (2013) 400-417

Conference Papers

D. M. Williams and A. Jameson, "Nodal Points and the Nonlinear Stability of High-Order Methods for Unsteady Flow Problems on Tetrahedral Meshes," AIAA Paper 2013-2830, 43rd AIAA Fluid Dynamics Conference, San Diego, CA, (2013)

D. M. Williams, P. Castonguay, P. E. Vincent, and A. Jameson, "An Extension of Energy Stable Flux Reconstruction to Unsteady, Non-linear, Viscous Problems on Mixed Grids," AIAA Paper 2011-3405, 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI, (2011)

P. Castonguay, D. M. Williams, P. E. Vincent, M. R. Lopez, and A. Jameson, "On the Development of a High-Order, Multi-GPU Enabled, Compressible Viscous Flow Solver for Mixed Grids," AIAA Paper 2011-3229, 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI, (2011)

Dissertation

D. M. Williams, "Energy Stable High-Order Methods for Simulating Unsteady, Viscous, Compressible Flows on Unstructured Grids," Stanford University, (2013)