Search NASA⌕ Search

Engineering topics

Fisher, Travis C.

Publications and source records attributed to Fisher, Travis C..

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Entropy Stable Discretization of Compressible Flows in Thermochemical Nonequilibrium

Entropy stable numerical methods for compressible flow have been demonstrated to exhibit better robustness than purely linearly stable methods and need less overall artificial dissipation for long simulations in subsonic and transonic flows. In this work we seek to extend these benefits to multicomponent, multitemperature flows in thermochemical nonequilibrium such as combustion and hypersonic flight. We first derive entropy functions that symmetrize the governing equations and allow stability proofs for such systems. The impact of diffusion model selection on provable entropy stability is considered in detail, including both rigorous models of irreversible thermodynamics and simplified models of greater practical interest. Based on the proven entropy functions we develop affordable, entropy conservative two-point flux functions for solution in conservation form. We derive entropy conservative fluxes for calorically and thermally perfect mixtures, with heat capacities described by either polynomials of the temperature or formulas from statistical thermodynamics.

42 ENGINEERING↗
NASA NTRS2016

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.

Carpenter, Mark H.↗