Direct Discontinuous Galerkin methods for the reacting multi-component flow equations

Absillis, Gianni; Luo, Hong; Greene, Patrick; Nourgaliev, Robert; Goodson, M.

doi:10.1016/j.compfluid.2025.106774

Direct Discontinuous Galerkin methods for the reacting multi-component flow equations

Journal Article · Wed Aug 13 00:00:00 EDT 2025 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2025.106774· OSTI ID:3000352

^[1]; Luo, Hong ^[1]; Greene, Patrick ^[2]; Nourgaliev, Robert ^[2]; ^[3]

North Carolina State University, Raleigh, NC (United States)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Corvid Technologies, Mooresville, NC (United States)

The Direct Discontinuous Galerkin (DDG (Liu and Yan, 2008)) method and a counterpart with Interface Correction (DDGIC (Danis and Yan, 2022)) are extended to compute diffusion terms that arise when solving the compressible multi-component flow equations in thermochemical nonequilibrium. Thermodynamic properties, transport properties, chemical reaction rates, and energy exchange terms are computed using Mutation++ (Scoggins et al., 2020). The DG method is applied on unstructured grids, where the accuracy and convergence rates can be sensitive to the numerical method chosen for parabolic terms. A method for determining the homogeneity tensor of the flow equations required for DDGIC is shown. The convergence properties of the DDG methods are studied and compared to the Interior Penalty (IP) method. A number of numerical experiments are conducted to assess the accuracy and performance of the method. The numerical results and convergence studies indicate that DDG and DDGIC provide accurate solutions and perform well for general flows in thermochemical nonequilibrium.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: National Aeronautics and Space Administration (NASA); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 3000352

Report Number(s):: LLNL--JRNL-2003361

Journal Information:: Computers and Fluids, Journal Name: Computers and Fluids Vol. 301; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (37)

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics Nourgaliev, R.; Greene, P.; Weston, B. Shock Waves, Vol. 29, Issue 5 https://doi.org/10.1007/s00193-018-0871-8	journal	November 2018
Differencing of the diffusion equation in Lagrangian hydrodynamic codes Kershaw, David S. Journal of Computational Physics, Vol. 39, Issue 2 https://doi.org/10.1016/0021-9991(81)90158-3	journal	February 1981
A low-diffusion flux-splitting scheme for Navier-Stokes calculations Edwards, Jack R. Computers & Fluids, Vol. 26, Issue 6 https://doi.org/10.1016/S0045-7930(97)00014-5	journal	July 1997
A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods Kuzmin, Dmitri Journal of Computational and Applied Mathematics, Vol. 233, Issue 12 https://doi.org/10.1016/j.cam.2009.05.028	journal	April 2010
Finite element-based invariant-domain preserving approximation of hyperbolic systems: Beyond second-order accuracy in space Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan Computer Methods in Applied Mechanics and Engineering, Vol. 418 https://doi.org/10.1016/j.cma.2023.116470	journal	January 2024
Space–time discontinuous Galerkin method for the compressible Navier–Stokes equations Klaij, C. M.; van der Vegt, J. J. W.; van der Ven, H. Journal of Computational Physics, Vol. 217, Issue 2 https://doi.org/10.1016/j.jcp.2006.01.018	journal	September 2006
An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier–Stokes equations Hartmann, Ralf; Houston, Paul Journal of Computational Physics, Vol. 227, Issue 22 https://doi.org/10.1016/j.jcp.2008.07.015	journal	November 2008
Towards shock-stable and accurate hypersonic heating computations: A new pressure flux for AUSM-family schemes Kitamura, Keiichi; Shima, Eiji Journal of Computational Physics, Vol. 245 https://doi.org/10.1016/j.jcp.2013.02.046	journal	July 2013
A direct discontinuous Galerkin method for the compressible Navier–Stokes equations on arbitrary grids Cheng, Jian; Yang, Xiaoquan; Liu, Xiaodong Journal of Computational Physics, Vol. 327 https://doi.org/10.1016/j.jcp.2016.09.049	journal	December 2016
A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations Danis, Mustafa E.; Yan, Jue Journal of Computational Physics, Vol. 452 https://doi.org/10.1016/j.jcp.2021.110904	journal	March 2022
On the design of stable, consistent, and conservative high-order methods for multi-material hydrodynamics Pandare, Aditya K.; Waltz, Jacob; Li, Weizhao Journal of Computational Physics, Vol. 490 https://doi.org/10.1016/j.jcp.2023.112313	journal	October 2023
Mutation + + : MUlticomponent Thermodynamic And Transport properties for IONized gases in C++ Scoggins, James B.; Leroy, Vincent; Bellas-Chatzigeorgis, Georgios SoftwareX, Vol. 12 https://doi.org/10.1016/j.softx.2020.100575	journal	July 2020
Analytical and numerical studies of the structure of steady separated flows Burggraf, Odus R. Journal of Fluid Mechanics, Vol. 24, Issue 1 https://doi.org/10.1017/S0022112066000545	journal	January 1966
A Viscosity Equation for Gas Mixtures Wilke, C. R. The Journal of Chemical Physics, Vol. 18, Issue 4 https://doi.org/10.1063/1.1747673	journal	April 1950
Finite element methods for elliptic equations using nonconforming elements Baker, Garth A. Mathematics of Computation, Vol. 31, Issue 137 https://doi.org/10.1090/S0025-5718-1977-0431742-5	journal	January 1977
Total variation diminishing Runge-Kutta schemes Gottlieb, Sigal; Shu, Chi-Wang Mathematics of Computation of the American Mathematical Society, Vol. 67, Issue 221 https://doi.org/10.1090/S0025-5718-98-00913-2	journal	January 1998
Code Verification by the Method of Manufactured Solutions Roache, Patrick J. Journal of Fluids Engineering, Vol. 124, Issue 1 https://doi.org/10.1115/1.1436090	journal	November 2001
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems Peraire, J.; Persson, P. -O. SIAM Journal on Scientific Computing, Vol. 30, Issue 4 https://doi.org/10.1137/070685518	journal	January 2008
An Elliptic Collocation-Finite Element Method with Interior Penalties Wheeler, Mary Fanett SIAM Journal on Numerical Analysis, Vol. 15, Issue 1 https://doi.org/10.1137/0715010	journal	February 1978
An Interior Penalty Finite Element Method with Discontinuous Elements Arnold, Douglas N. SIAM Journal on Numerical Analysis, Vol. 19, Issue 4 https://doi.org/10.1137/0719052	journal	August 1982
The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems Liu, Hailiang; Yan, Jue SIAM Journal on Numerical Analysis, Vol. 47, Issue 1 https://doi.org/10.1137/080720255	journal	January 2009
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo SIAM Journal on Numerical Analysis, Vol. 39, Issue 5 https://doi.org/10.1137/S0036142901384162	journal	January 2002
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems Cockburn, Bernardo; Shu, Chi-Wang SIAM Journal on Numerical Analysis, Vol. 35, Issue 6 https://doi.org/10.1137/S0036142997316712	journal	December 1998
Self-Consistent Effective Binary Diffusion in Multicomponent Gas Mixtures Ramshaw, J. D. Journal of Non-Equilibrium Thermodynamics, Vol. 15, Issue 3 https://doi.org/10.1515/jnet.1990.15.3.295	journal	January 1990
Hydrodynamic Theory of Multicomponent Diffusion and Thermal Diffusion in Multitemperature Gas Mixtures Ramshaw, John D. Journal of Non-Equilibrium Thermodynamics, Vol. 18, Issue 2 https://doi.org/10.1515/jnet.1993.18.2.121	journal	January 1993
Evaluation of Euler Fluxes for Hypersonic Heating Computations Kitamura, Keiichi; Shima, Eiji; Nakamura, Yoshiaki AIAA Journal, Vol. 48, Issue 4 https://doi.org/10.2514/1.41605	journal	April 2010
Data-Parallel Line Relaxation Method for the Navier-Stokes Equations Wright, Michael J.; Candler, Graham V.; Bose, Deepak AIAA Journal, Vol. 36, Issue 9 https://doi.org/10.2514/2.586	journal	September 1998
Assessment of two-temperature kinetic model for ionizing air Park, Chul Journal of Thermophysics and Heat Transfer, Vol. 3, Issue 3 https://doi.org/10.2514/3.28771	journal	July 1989
Computation of nonequilibrium hypersonic flowfields around hemisphere cylinders Josyula, Eswar; Shang, Joseph S. Journal of Thermophysics and Heat Transfer, Vol. 7, Issue 4 https://doi.org/10.2514/3.476	journal	October 1993
Problems of rate chemistry in the flight regimes of aeroassisted orbital transfer vehicles Park, C. 19th Thermophysics Conference https://doi.org/10.2514/6.1984-1730	conference	June 1984
Multi-component diffusion with application to computational aerothermodynamics Sutton, Kenneth; Gnoffo, Peter 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference https://doi.org/10.2514/6.1998-2575	conference	February 2013
Sub-Cell Shock Capturing for Discontinuous Galerkin Methods Persson, Per-Olof; Peraire, Jaime 44th AIAA Aerospace Sciences Meeting and Exhibit https://doi.org/10.2514/6.2006-112	conference	June 2012
Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids Gnoffo, Peter 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition https://doi.org/10.2514/6.2010-1271	conference	January 2010
A Survey of the Isentropic Euler Vortex Problem using High-Order Methods Spiegel, Seth C.; Huynh, Ht; DeBonis, James R. 22nd AIAA Computational Fluid Dynamics Conference https://doi.org/10.2514/6.2015-2444	conference	June 2015
A Direct Discontinuous Galerkin Method with Interface Correction for the Compressible Navier-Stokes Equations on Unstructured Grids Cheng, Jian; Yue, Huiqiang; Yu, Shengjiao Advances in Applied Mathematics and Mechanics, Vol. 10, Issue 1 https://doi.org/10.4208/aamm.OA-2017-0060	journal	June 2018
The Direct Discontinuous Galerkin (DDG) Method for Diffusion with Interface Corrections Yan, Hailiang Liu and Jue Communications in Computational Physics, Vol. 8, Issue 3 https://doi.org/10.4208/cicp.010909.011209a	journal	June 2010
SymPy: symbolic computing in Python Meurer, Aaron; Smith, Christopher P.; Paprocki, Mateusz PeerJ Computer Science, Vol. 3 https://doi.org/10.7717/peerj-cs.103	journal	January 2017

Similar Records

Direct discontinuous Galerkin method and its variations for second order elliptic equations

Journal Article · Mon Aug 22 20:00:00 EDT 2016 · Journal of Scientific Computing · OSTI ID:1330547

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

Conference · Sun May 01 00:00:00 EDT 2011 · OSTI ID:1027880

A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

Journal Article · Thu Nov 01 00:00:00 EDT 2012 · Communications in Computational Physics · OSTI ID:1062197

Related Subjects

Diffusion
Direct discontinuous Galerkin
Discontinuous Galerkin
Interface correction
Multi-component
Reacting

Direct Discontinuous Galerkin methods for the reacting multi-component flow equations

Citation Formats

References (37)

Similar Records

Related Subjects