High-order numerical scheme for compressible multi-component real gas flows using an extension of the Roe approximate Riemann solver and specific Monotonicity-Preserving constraints

•Generalization of the Roe approximate Riemann solver to Multicomponent Real Gas Flow.•High-order accuracy with One Step Monotonicity Preserving scheme.•Additional OSMP scheme on a combination of characteristic variables.•Accurate R22 bubble/shock interaction test case with detailed thermodynamic mo...

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Published in:	Journal of computational physics Vol. 450; p. 110821
Main Authors:	Lecointre, Luc, Vicquelin, Ronan, Kudriakov, Sergey, Studer, Etienne, Tenaud, Christian
Format:	Journal Article
Language:	English
Published:	Cambridge Elsevier Inc 01.02.2022 Elsevier Science Ltd Elsevier
Subjects:	Approximation Compressibility Computational physics Discontinuity Flow distribution Fluid mechanics Gas flow Gas mixtures Gases High temperature High-order numerical scheme Ideal gas Local thermodynamic equilibrium Mechanics Monotonicity-Preserving constraints Multi-component real gas flow Numerical analysis Numerical methods Physics Real gases Refrigerants Riemann solver Roe approximate Riemann solver Shock waves Sound Thermodynamic properties Thermodynamics Multi-component real gas flow Monotonicity-Preserving constraints Roe approximate Riemann solver High-order numerical scheme Multi-component Real Gas Flow
ISSN:	0021-9991, 1090-2716
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Abstract	•Generalization of the Roe approximate Riemann solver to Multicomponent Real Gas Flow.•High-order accuracy with One Step Monotonicity Preserving scheme.•Additional OSMP scheme on a combination of characteristic variables.•Accurate R22 bubble/shock interaction test case with detailed thermodynamic model. The purpose of this paper is to develop a high-order shock-capturing scheme capable of predicting flows where shock waves with high-temperature jumps interact with multi-component real gas mixtures, assuming a local thermodynamic equilibrium. We first propose a generalization of the Roe solver for distinct species with non-ideal thermodynamic properties that relies on the original method proposed by Vinokur & Montagné [1]. This method uses an approximation of compressibility factors to estimate a coherent value of the speed of sound at the Roe averaged state. This Roe averaged state is introduced in the One-Step Monotonicity-Preserving (OSMP) scheme, originally developed by Daru and Tenaud [2], to obtain an extension to the high-order with Lax-Wendroff procedure adequate for dealing with non-ideal gas flows. To avoid thermodynamic inconsistencies in the evolution of the Roe average state over a large stencil, we propose to reformulate the discrete total energy flux of the initial solver. This new formulation uses a combination of Riemann invariants related to the species mass fractions and avoids the influence of the independent values of the compressibility factors in the total energy flux computation. An additional M-P constraint on this new combination allows dealing with discontinuities. Based on the averaged speed of sound estimated by our proposed extension of the Vinokur & Montagné method, we demonstrate that this new formulation is equivalent to selecting a new combination of compressibility factors that completely fulfill the jump relationships of the Riemann problem. To properly capture discontinuities while optimizing the number of numerical cells, the new high-order OSMP scheme is combined with an Adaptive Multiresolution [3] procedure to automatically refine grid in regions where steep gradients occur and coarsen grid elsewhere. The order of the numerical method is evaluated on the convection of density and mass fraction waves. Its capability of capturing discontinuities is validated on a 1-D shock tube problem with a mixture of Nitrogen, Oxygen and dense refrigerant R22 gases. We show that smooth solutions, as well as discontinuities, are recovered with high accuracy. The 2-D interaction between a shock wave in Air with a cylindrical bubble initially filled with dense refrigerant R22 gas is also considered. Present results compare very well with both a recent fully resolved numerical solution of ideal gases and experimental results obtained with real gases. Compared to ideal gas solutions corresponding to calorically perfect gas, drastic changes are recorded on the predicted temperature and the bubble flow patterns that fully justify the use of relevant thermodynamics and the proposed numerical method to account for real gas properties.
AbstractList	The purpose of this paper is to develop a high-order shock-capturing scheme capable of predicting flows where shock waves with high-temperature jumps interact with multi-component real gas mixtures, assuming a local thermodynamic equilibrium. We first propose a generalization of the Roe solver for distinct species with non-ideal thermodynamic properties that relies on the original method proposed by Vinokur & Montagné [1]. This method uses an approximation of compressibility factors to estimate a coherent value of the speed of sound at the Roe averaged state.This Roe averaged state is introduced in the One-Step Monotonicity-Preserving (OSMP) scheme, originally developed by Daru and Tenaud [2], to obtain an extension to the high-order with Lax-Wendroff procedure adequate for dealing with non-ideal gas flows. To avoid thermodynamic inconsistencies in the evolution of the Roe average state over a large stencil, we propose to reformulate the discrete total energy flux of the initial solver. This new formulation uses a combination of Riemann invariants related to the species mass fractions and avoids the influence of the independent values of the compressibility factors in the total energy flux computation. An additional M-P constraint on this new combination allows dealing with discontinuities. Based on the averaged speed of sound estimated by our proposed extension of the Vinokur & Montagné method, we demonstrate that this new formulation is equivalent to selecting a new combination of compressibility factors that completely fulfill the jump relationships of the Riemann problem.To properly capture discontinuities while optimizing the number of numerical cells, the new high-order OSMP scheme is combined with an Adaptive Multiresolution [3] procedure to automatically refine grid in regions where steep gradients occur and coarsen grid elsewhere. The order of the numerical method is evaluated on the convection of density and mass fraction waves. Its capability of capturing discontinuities is validated on a 1-D shock tube problem with a mixture of Nitrogen, Oxygen and dense refrigerant R22 gases. We show that smooth solutions, as well as discontinuities, are recovered with high accuracy. The 2-D interaction between a shock wave in Air with a cylindrical bubble initially filled with dense refrigerant R22 gas is also considered. Present results compare very well with both a recent fully resolved numerical solution of ideal gases and experimental results obtained with real gases. Compared to ideal gas solutions corresponding to calorically perfect gas, drastic changes are recorded on the predicted temperature and the bubble flow patterns that fully justify the use of relevant thermodynamics and the proposed numerical method to account for real gas properties. •Generalization of the Roe approximate Riemann solver to Multicomponent Real Gas Flow.•High-order accuracy with One Step Monotonicity Preserving scheme.•Additional OSMP scheme on a combination of characteristic variables.•Accurate R22 bubble/shock interaction test case with detailed thermodynamic model. The purpose of this paper is to develop a high-order shock-capturing scheme capable of predicting flows where shock waves with high-temperature jumps interact with multi-component real gas mixtures, assuming a local thermodynamic equilibrium. We first propose a generalization of the Roe solver for distinct species with non-ideal thermodynamic properties that relies on the original method proposed by Vinokur & Montagné [1]. This method uses an approximation of compressibility factors to estimate a coherent value of the speed of sound at the Roe averaged state. This Roe averaged state is introduced in the One-Step Monotonicity-Preserving (OSMP) scheme, originally developed by Daru and Tenaud [2], to obtain an extension to the high-order with Lax-Wendroff procedure adequate for dealing with non-ideal gas flows. To avoid thermodynamic inconsistencies in the evolution of the Roe average state over a large stencil, we propose to reformulate the discrete total energy flux of the initial solver. This new formulation uses a combination of Riemann invariants related to the species mass fractions and avoids the influence of the independent values of the compressibility factors in the total energy flux computation. An additional M-P constraint on this new combination allows dealing with discontinuities. Based on the averaged speed of sound estimated by our proposed extension of the Vinokur & Montagné method, we demonstrate that this new formulation is equivalent to selecting a new combination of compressibility factors that completely fulfill the jump relationships of the Riemann problem. To properly capture discontinuities while optimizing the number of numerical cells, the new high-order OSMP scheme is combined with an Adaptive Multiresolution [3] procedure to automatically refine grid in regions where steep gradients occur and coarsen grid elsewhere. The order of the numerical method is evaluated on the convection of density and mass fraction waves. Its capability of capturing discontinuities is validated on a 1-D shock tube problem with a mixture of Nitrogen, Oxygen and dense refrigerant R22 gases. We show that smooth solutions, as well as discontinuities, are recovered with high accuracy. The 2-D interaction between a shock wave in Air with a cylindrical bubble initially filled with dense refrigerant R22 gas is also considered. Present results compare very well with both a recent fully resolved numerical solution of ideal gases and experimental results obtained with real gases. Compared to ideal gas solutions corresponding to calorically perfect gas, drastic changes are recorded on the predicted temperature and the bubble flow patterns that fully justify the use of relevant thermodynamics and the proposed numerical method to account for real gas properties.
ArticleNumber	110821
Author	Kudriakov, Sergey Studer, Etienne Lecointre, Luc Vicquelin, Ronan Tenaud, Christian
Author_xml	– sequence: 1 givenname: Luc orcidid: 0000-0003-3309-8836 surname: Lecointre fullname: Lecointre, Luc email: luc.lecointre@centraliens.net organization: Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191, Gif-sur-Yvette, France – sequence: 2 givenname: Ronan surname: Vicquelin fullname: Vicquelin, Ronan organization: Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C, 91190, Gif-sur-Yvette, France – sequence: 3 givenname: Sergey surname: Kudriakov fullname: Kudriakov, Sergey organization: Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191, Gif-sur-Yvette, France – sequence: 4 givenname: Etienne surname: Studer fullname: Studer, Etienne organization: Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191, Gif-sur-Yvette, France – sequence: 5 givenname: Christian orcidid: 0000-0002-2024-485X surname: Tenaud fullname: Tenaud, Christian organization: Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C, 91190, Gif-sur-Yvette, France
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Copyright	2021 Elsevier Inc. Copyright Elsevier Science Ltd. Feb 1, 2022 Distributed under a Creative Commons Attribution 4.0 International License
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Keywords	Multi-component real gas flow Monotonicity-Preserving constraints Roe approximate Riemann solver High-order numerical scheme Multi-component Real Gas Flow
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Snippet	•Generalization of the Roe approximate Riemann solver to Multicomponent Real Gas Flow.•High-order accuracy with One Step Monotonicity Preserving... The purpose of this paper is to develop a high-order shock-capturing scheme capable of predicting flows where shock waves with high-temperature jumps interact...
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SubjectTerms	Approximation Compressibility Computational physics Discontinuity Flow distribution Fluid mechanics Gas flow Gas mixtures Gases High temperature High-order numerical scheme Ideal gas Local thermodynamic equilibrium Mechanics Monotonicity-Preserving constraints Multi-component real gas flow Numerical analysis Numerical methods Physics Real gases Refrigerants Riemann solver Roe approximate Riemann solver Shock waves Sound Thermodynamic properties Thermodynamics
Title	High-order numerical scheme for compressible multi-component real gas flows using an extension of the Roe approximate Riemann solver and specific Monotonicity-Preserving constraints
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