arXiv subjects

Ryan F. Johnson

Publications and source records attributed to Ryan F. Johnson.

13 recordsLinked to original sources

arXiv2026

Tensor Train Representation of High-Dimensional Unsteady Flamelet Manifolds

This study, for the first time, investigates the use of tensor trains (TTs) to represent high-dimensional unsteady flamelet progress variable (UFPV) manifolds in chemically reacting computational fluid dynamics (CFD). The UFPV framework captures the thermochemical state of reacting flows using a reduced set of parameters and pre-computed manifolds, avoiding the need to transport all species or solve large stiff reaction systems. High-dimensional manifolds enhance accuracy by resolving coupled thermochemical effects critical in high-speed reacting flows but impose substantial memory demands. Here, a five-dimensional UFPV manifold is constructed and stored in the TT format to address this limitation. Several chemical mechanisms and table sizes are examined to evaluate TT compression performance and accuracy. The TT representation achieves significant memory reduction while preserving manifold fidelity and combustion behavior. A one-dimensional reacting-flow case using the discontinuous Galerkin (DG)-based JENRE Multiphysics Framework confirms that TT-compressed manifolds are interchangeable with standard UFPV tables. In addition to memory reduction, benchmark tests show that TT-based manifold sampling can achieve up to 2.4X speedup relative to dense tensor evaluation. Although demonstrated for UFPV combustion models, the proposed TT framework is broadly applicable to other tabulation-based combustion methodologies and provides a scalable alternative to machine learning (ML)-based approaches for representing high-dimensional combustion manifolds.

physics.comp-ph↗

arXiv2025

ChemGen: Code Generation for Multispecies Chemically Reacting Flow Simulations

This paper introduces ChemGen, a software package that uses code generation to integrate multispecies thermodynamics and chemical kinetics into C+-based computational physics codes. ChemGen aims to make chemical kinetics more accessible in existing simulation frameworks and help bridge the gap between combustion modeling and computational physics. The package employs the concept of decorators which enable flexible C++ code generation to target established software ecosystems. ChemGen generates code to evaluate thermodynamic properties, chemical source terms, and their analytical derivatives for Jacobian calculations. Also included are a variety of implicit time integration schemes, linear solvers, and preconditioners. The various components of Chemgen are verified by demonstrating agreement with Cantera and/or theoretical convergence rates. Finally, we integrate ChemGen into OpenFOAM and achieve a speedup over its native chemistry solver by approximately four times. ChemGen is an ongoing project released under the NRL Open License, a source-available license provided by the U.S. Naval Research Laboratory.

physics.comp-ph↗

arXiv2025

Simulation of Non-Premixed, Supersonic Combustion using the Discontinuous Galerkin Method on Fully Unstructured Grids

In this study, three-dimensional simulations of a reacting hydrogen jet in supersonic crossflow using a structure-preserving discontinuous Galerkin (DG) formulation are examined. The hydrogen jet, with a momentum flux ratio of five, is injected into a high enthalpy crossflow. The sensitivities of the solution to the grid element size and polynomial order are investigated to determine an accurate and computationally efficient approach to simulating high-speed airbreathing propulsion vehicles. The results demonstrate that DG(p = 2) solutions, which are nominally third-order accurate in smooth regions of the flow, show reasonable agreement with existing experimental results. The separation shock formation behind the jet is found to be heavily grid dependent and necessary for accurate simulations of the reacting jet in supersonic crossflow. It is determined that the highest resolution cell and polynomial order is required to capture the upstream separation shock and consequently the flame stabilization point. The mixing and combustion mode is also determined using the flame index and demonstrates the flow is heavily skewed towards a non-premixed diffusion mode which is consistent with previously run simulations of this case using traditional finite volume schemes and sub grid scale modeling approaches. Beyond this analysis, given the prevalent use of structured hexahedral meshes in the computation of realistic high-speed, chemically reacting flows, the novelty of this work lies in demonstrating accurate simulation of such a flow on a fully unstructured tetrahedral mesh. This highlights the potential of these methods to handle both complicated geometries and complex physics.

physics.flu-dyn↗

arXiv2025

Conservative, pressure-equilibrium-preserving discontinuous Galerkin method for compressible, multicomponent flows

This paper concerns preservation of velocity and pressure equilibria in smooth, compressible, multicomponent flows in the inviscid limit. First, we derive the velocity-equilibrium and pressure-equilibrium conditions of a standard discontinuous Galerkin method that discretizes the conservative form of the compressible, multicomponent Euler equations. We show that under certain constraints on the numerical flux, the scheme is velocity-equilibrium-preserving. However, standard discontinuous Galerkin schemes are not pressure-equilibrium-preserving. Therefore, we introduce a discontinuous Galerkin method that discretizes the pressure-evolution equation in place of the total-energy conservation equation. Semidiscrete conservation of total energy, which would otherwise be lost, is restored via the correction terms of [Abgrall, J. Comput. Phys., 372, 2018, pp. 640-666] and [Abgrall et al., J. Comput. Phys., 453, 2022, 110955]. Since the addition of the correction terms prevents exact preservation of pressure and velocity equilibria, we propose modifications that then lead to a velocity-equilibrium-preserving, pressure-equilibrium-preserving, and (semidiscretely) energy-conservative discontinuous Galerkin scheme, although there are certain tradeoffs. Additional extensions are also introduced. We apply the developed scheme to smooth, interfacial flows involving mixtures of thermally perfect gases initially in pressure and velocity equilibria to demonstrate its performance in one, two, and three spatial dimensions.

math.NA↗

arXiv2024

Conservative discontinuous Galerkin method for supercritical, real-fluid flows

This paper presents a conservative discontinuous Galerkin method for the simulation of supercritical and transcritical real-fluid flows without phase separation. A well-known issue associated with the use of fully conservative schemes is the generation of spurious pressure oscillations at contact interfaces, which are exacerbated when a cubic equation of state and thermodynamic relations appropriate for this high-pressure flow regime are considered. To reduce these pressure oscillations, which can otherwise lead to solver divergence in the absence of additional dissipation, an L2-projection of primitive variables is performed in the evaluation of the flux. We apply the discontinuous Galerkin formulation to a variety of test cases. The first case is the advection of a sinusoidal density wave, which is used to verify the convergence of the scheme. The next two involve one- and two-dimensional advection of a nitrogen/n-dodecane thermal bubble, in which the ability of the methodology to reduce pressure oscillations and maintain solution stability is assessed. The final test cases consist of two- and three-dimensional injection of an n-dodecane jet into a nitrogen chamber.

physics.flu-dyn↗

arXiv2024

Effect of ozone sensitization on the reflection patterns and stabilization of standing detonation waves induced by curved ramps

Standing detonation engines are a promising detonation-based propulsion technology. The most commonly studied standing detonation configuration involves a straight-sided wedge that induces an oblique detonation wave. A recently introduced standing-detonation-engine concept entails a curved ramp that leads to formation of a curved detonation wave. The continuous compression or expansion induced by the ramp curvature can have significant influence on the flow characteristics and wave patterns of the detonation wave, offering greater flexibility in engine design than conventional wedge geometries. This study aims to further explore this relatively new standing-detonation-engine concept by examining the effect of ignition promoters, namely ozone, on the flow characteristics and reflection patterns of curved detonation waves induced by convex or concave ramps inside a confined combustion chamber. Simulations are performed using a positivity-preserving and entropy-bounded discontinuous Galerkin method with curved elements to exactly represent the ramp geometries. In the context of wedge-induced oblique detonation waves, ozone addition has been found to decrease the initiation length and lead to a smoother shock-detonation transition. This can then attenuate the detonation and reduce stagnation-pressure losses, thus improving the potential propulsion performance. In the context of detonation waves induced by curved ramps, although ozone addition similarly shortens the initiation zone, the curvature of the ramp introduces additional effects that can amplify or counteract both the ozone-induced contraction of the initiation zone and the aforementioned detonation attenuation. Furthermore, specific examples are presented wherein ozone addition changes the type of reflection pattern (e.g., regular reflection, stationary Mach reflection, and non-stationary Mach reflection).

physics.flu-dyn↗

arXiv2024

Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Navier-Stokes equations

This article concerns the development of a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for the multicomponent, chemically reacting, compressible Navier-Stokes equations with complex thermodynamics. In particular, we extend to viscous flows the fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin method for the chemically reacting Euler equations that we previously introduced. An important component of the formulation is the positivity-preserving Lax-Friedrichs-type viscous flux function devised by Zhang [J. Comput. Phys., 328 (2017), pp. 301-343], which was adapted to multicomponent flows by Du and Yang [J. Comput. Phys., 469 (2022), pp. 111548] in a manner that treats the inviscid and viscous fluxes as a single flux. Here, we similarly extend the aforementioned flux function to multicomponent flows but separate the inviscid and viscous fluxes, resulting in a different dissipation coefficient. This separation of the fluxes allows for use of other inviscid flux functions, as well as enforcement of entropy boundedness on only the convective contribution to the evolved state, as motivated by physical and mathematical principles. We also detail how to account for boundary conditions and incorporate previously developed techniques to reduce spurious pressure oscillations into the positivity-preserving framework. Furthermore, potential issues associated with the Lax-Friedrichs-type viscous flux function in the case of zero species concentrations are discussed and addressed. The resulting formulation is compatible with curved, multidimensional elements and general quadrature rules with positive weights. A variety of multicomponent, viscous flows is computed, ranging from a one-dimensional shock tube problem to multidimensional detonation waves and shock/mixing-layer interaction.

math.NA↗

arXiv2024

Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part II: The multidimensional case

In this second part of our two-part paper, we extend to multiple spatial dimensions the one-dimensional, fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme developed in the first part for the chemically reacting Euler equations. Our primary objective is to enable robust and accurate solutions to complex reacting-flow problems using the high-order discontinuous Galerkin method without requiring extremely high resolution. Variable thermodynamics and detailed chemistry are considered. Our multidimensional framework can be regarded as a further generalization of similar positivity-preserving and/or entropy-bounded discontinuous Galerkin schemes in the literature. In particular, the proposed formulation is compatible with curved elements of arbitrary shape, a variety of numerical flux functions, general quadrature rules with positive weights, and mixtures of thermally perfect gases. Preservation of pressure equilibrium between adjacent elements, especially crucial in simulations of multicomponent flows, is discussed. Complex detonation waves in two and three dimensions are accurately computed using high-order polynomials. Enforcement of an entropy bound, as opposed to solely the positivity property, is found to significantly improve stability. Mass, total energy, and atomic elements are shown to be discretely conserved.

math.NA↗

arXiv2023

A note on reducing spurious pressure oscillations in fully conservative discontinuous Galerkin simulations of multicomponent flows

A well-known issue associated with the use of fully conservative schemes in multicomponent-flow simulations is the generation of spurious pressure oscillations at contact interfaces. These oscillations can rapidly lead to solver divergence even in the presence of smooth interfaces that are not fully resolved. In this note, we compare various strategies for reducing such oscillations that do not (a) introduce conservation error, (b) rely on artificial viscosity or limiting, or (c) degrade order of accuracy in smooth regions of the flow. The considered test case is one-dimensional advection of a high-pressure nitrogen/n-dodecane thermal bubble using the thermally perfect gas model. Several results are presented that contradict those corresponding to the more conventional hydrogen/oxygen thermal-bubble case.

physics.flu-dyn↗

arXiv2022

Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part I: The one-dimensional case

In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for simulating the chemically reacting, compressible Euler equations with complex thermodynamics. The proposed formulation is an extension of the conservative, high-order numerical method previously developed by Johnson and Kercher [J. Comput. Phys., 423 (2020), 109826] that maintains pressure equilibrium between adjacent elements. In this first part of our two-part paper, we focus on the one-dimensional case. Our methodology is rooted in the minimum entropy principle satisfied by entropy solutions to the multicomponent, compressible Euler equations, which was proved by Gouasmi et al. [ESAIM: Math. Model. Numer. Anal., 54 (2020), 373--389] for nonreacting flows. We first show that the minimum entropy principle holds in the reacting case as well. Next, we introduce the ingredients required for the solution to have nonnegative species concentrations, positive density, positive pressure, and bounded entropy. We also discuss how to retain the aforementioned ability to preserve pressure equilibrium between elements. Operator splitting is employed to handle stiff chemical reactions. To guarantee satisfaction of the minimum entropy principle in the reaction step, we develop an entropy-stable discontinuous Galerkin method based on diagonal-norm summation-by-parts operators for solving ordinary differential equations. The developed formulation is used to compute canonical one-dimensional test cases, namely thermal-bubble advection, multicomponent shock-tube flow, and a moving hydrogen-oxygen detonation wave with detailed chemistry. We find that the enforcement of an entropy bound can considerably reduce the large-scale nonlinear instabilities that emerge when only the positivity property is enforced, to an even greater extent than in the monocomponent, calorically perfect case.

math.NA↗

arXiv2020

Effect of Inflow Turbulence on Premixed Combustion in a Cavity Flameholder

A discontinuous Galerkin finite element method code, JENRE, was used to perform highly resolved simulations of ramjet-mode combustion in the University of Virginia Supersonic Combustion Facility cavity flameholder at a flight enthalpy of Mach 5. Prior experiments measured a freestream turbulence intensity at the inflow to the cavity ranging from 10 - 15%. A synthetic turbulence inflow generator was implemented for the simulations in this work to reproduce the turbulence at the inflow to the cavity. Velocity perturbations and turbulence intensity generated by the turbulent inflow boundary condition are shown to match those values measured in the facility using particle induced velocimetry. Simulations were performed both with and without inflow turbulence to study the effect of turbulence on flame stability and structure. In both cases, a cavity-stabilized flame was achieved. The inflow turbulence promoted more robust combustion, causing the flame to propagate further from the cavity into the core flow, broadening the flame angle with respect to the axial flow direction. The flame angle captured in the simulation agrees with experimental results and theoretical prediction. The cavity's vortex shedding frequency was identified. Flame strain rate and pressure fluctuations in the cavity shear layer were also measured and found to vary periodically at a frequency equal to that of the vortex shedding. High flow strain rate in the cavity shear layer, driven by the vortex shedding process, is identified as a cause of flame stretching and low OH concentrations as the flame traverses the cavity ramp. The effect of spatial resolution on the simulations is discussed through a comparison of cases using second-order and third-order accurate discontinuous Galerkin finite elements.

physics.flu-dyn↗

arXiv2020

A Conservative Discontinuous Galerkin Discretization for the Chemically Reacting Navier-Stokes Equations

We present a detailed description and verification of a discontinuous Galerkin finite element method (DG) for the multi-component chemically reacting compressible Navier-Stokes equations that retains the desirable properties of DG, namely discrete conservation and high-order accuracy in smooth regions of the flow. Pressure equilibrium between adjacent elements is maintained through the consistent evaluation of the thermodynamics model and the resulting weak form, as well as the proper choice of nodal basis. As such, the discretization does not generate unphysical pressure oscillations in smooth regions of the flow or at material interfaces where the temperature is continuous. Additionally, we present an hp-adaptive DG method for solving systems of ordinary differential equations, DGODE, which is used to resolve the temporal evolution of the species concentrations due to stiff chemical reactions. The coupled solver is applied to several challenging test problems including multi-component shocked flows as well as chemically reacting detonations, deflagrations, and shear flows with detailed kinetics. We demonstrate that the discretization does not produce unphysical pressure oscillations and, when applicable, we verify that it maintains discrete conservation. The solver is also shown to reproduce the expected temperature and species profiles throughout a detonation as well as the expected two-dimensional cellular detonation structure. We also demonstrate that the solver can produce accurate, high-order, approximations of temperature and species profiles without artificial stabilization for the case of a one-dimensional pre-mixed flame. Finally, high-order solutions of two- and three-dimensional multi-component chemically reacting shear flows, computed without any additional stabilization, are presented.

physics.comp-ph↗

arXiv2019

A Conservative Discontinuous Galerkin Discretization for the Total Energy Formulation of the Reacting Navier Stokes Equations

This paper describes the total energy formulation of the compressible reacting Navier-Stokes equations which is solved numerically using a fully conservative discontinuous Galerkin finite element method (DG). Previous applications of DG to the compressible reacting Navier-Stokes equations required nonconservative fluxes or stabilization methods in order to suppress unphysical oscillations in pressure that led to the failure of simple test cases. In this paper, we demonstrate that material interfaces with a temperature discontinuity result in numerical unphysical pressure oscillations if the species internal energy is nonlinear with respect to temperature. We demonstrate that a temperature discontinuity is the only type of material interface that results in unphysical pressure oscillations for a conservative discretization of the total energy formulation. Furthermore, we demonstrate that unphysical pressure oscillations will be generated at any material interface, including material interfaces with at which the temperature is continuous, if the thermodynamics are frozen during the temporal integration of the conserved state. Additionally, we demonstrate that the oscillations are amplified if the specific heat at constant pressure is incorrectly evaluated directly from the NASA polynomial expressions. Instead, the mean value, which we derive in this manuscript, should be used to compute the specific heat at constant pressure. This can reduce the amplitude of, but not prevent, unphysical oscillations where the species concentrations numerically mix. We then present solutions to several test cases using the total energy formulation and demonstrate spurious pressure oscillations were not generated for material interfaces if the temperature is continuous and that it is better behaved than frozen thermodynamic formulations if the temperature is discontinuous.

physics.comp-ph↗