Publications

2021

C. V. Frontin, G. S. Walters, F. D. Witherden, C. W. Lee, D. M. Williams, and D. L. Darmofal, “Foundations of space-time finite element methods: polytopes, interpolation, and integration,” Applied Numerical Mathematics, 166, (2021) 92-113

K. Ganeshan and D. M. Williams, “An implicit discontinuous Galerkin finite element discrete Boltzmann method for high Knudsen number flows,” Physics of Fluids, 33, 032019, (2021)

2020

D. M. Williams and G. S. Walters, “Integration bounds for the regular simplex in n-dimensional space,” International Journal of Mathematical Education in Science and Technology, 1, (2020) 1-16

E. A. Miller, D. M. Williams, M. J. Cave, and K. Thayalakhandan, “A comparison of unsteady RANS and DES for simulating an axial compressor stage,” ASME Turbo Expo: Turbomachinery Technical Conference and Exposition, (2020)

X. Chen and D. M. Williams, “Versatile mixed methods for the incompressible Navier-Stokes equations,” Computers & Mathematics with Applications, 80, 6, (2020) 1555-1577

D. M. Williams, C. V. Frontin, E. A. Miller, and D. L. Darmofal, “A family of symmetric, optimized quadrature rules for pentatopes,” Computers & Mathematics with Applications, 80, 5, (2020) 1405-1420

2019

D. M. Williams, “An analysis of discontinuous Galerkin methods for the compressible Euler equations: Entropy and L2 stability,” Numerische Mathematik, 141, 4, (2019) 1079-1120

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, 2, (2019) 021010

2018

D. M. Williams, “An entropy stable, hybridizable discontinuous Galerkin method for the compressible Navier-Stokes equations,” Mathematics of Computation, 87, 309, (2018) 95-121

2016

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

2014

M. R. Lopez-Morales, J. Bull, J. Crabill, T. D. Economon, D. Manosalvas, J. Romero, A. Sheshadri, J. E. Watkins, D. Williams, F. Palacios, and A. Jameson, “Verification and validation of HiFiLES: a high-order LES unstructured solver on multi-GPU platforms,” AIAA Paper 2014-3168, 32nd AIAA Applied Aerodynamics Conference, Atlanta, GA, (2014)

D. M. Williams, L. Shunn, and A. Jameson, “Symmetric quadrature rules for simplexes based on Sphere Close Packed lattice arrangements,” Journal of Computational & 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

2013

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

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)

2011

P. Castonguay, D. Williams, P. E. Vincent, M. 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, June, (2011)

D. M. Williams, P. Castonguay, P. E. Vincent, and A. Jameson, “An extension of energy stable Flux Reconstruction to unsteady, nonlinear, viscous problems on mixed grids,” AIAA Paper 2011-3405, 20th AIAA Computational Fluid Dynamics Conference, Honolulu, June, (2011)