A Third-Order Unconditionally Positivity-Preserving Scheme for Production–Destruction Equations with Applications to Non-equilibrium Flows

In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018 . https://doi.org/10.1007/s10915-018-0852-1 ) and develop a third-order unconditionally positivity-preserving modified Patankar Runge–Kutta method for production–destruction equations. The necessary and sufficient condit...

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Veröffentlicht in:	Journal of scientific computing Jg. 79; H. 2; S. 1015 - 1056
Hauptverfasser:	Huang, Juntao, Zhao, Weifeng, Shu, Chi-Wang
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.05.2019 Springer Nature B.V
Schlagworte:	Algorithms Chemical reactions Computational Mathematics and Numerical Analysis Equilibrium Essentially non-oscillatory schemes Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonequilibrium flow Numerical analysis Runge-Kutta method Theoretical Time integration Production–destruction equations Finite difference Chemical reactions Positivity-preserving Compressible Euler equations Third-order accuracy
ISSN:	0885-7474, 1573-7691
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Abstract	In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018 . https://doi.org/10.1007/s10915-018-0852-1 ) and develop a third-order unconditionally positivity-preserving modified Patankar Runge–Kutta method for production–destruction equations. The necessary and sufficient conditions for the method to be of third-order accuracy are derived. With the same approach as Huang and Shu ( 2018 ), this time integration method is then generalized to solve a class of ODEs arising from semi-discrete schemes for PDEs and coupled with the positivity-preserving finite difference weighted essentially non-oscillatory schemes for non-equilibrium flows. Numerical experiments are provided to demonstrate the performance of our proposed scheme.
AbstractList	In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018 . https://doi.org/10.1007/s10915-018-0852-1 ) and develop a third-order unconditionally positivity-preserving modified Patankar Runge–Kutta method for production–destruction equations. The necessary and sufficient conditions for the method to be of third-order accuracy are derived. With the same approach as Huang and Shu ( 2018 ), this time integration method is then generalized to solve a class of ODEs arising from semi-discrete schemes for PDEs and coupled with the positivity-preserving finite difference weighted essentially non-oscillatory schemes for non-equilibrium flows. Numerical experiments are provided to demonstrate the performance of our proposed scheme. In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018. https://doi.org/10.1007/s10915-018-0852-1) and develop a third-order unconditionally positivity-preserving modified Patankar Runge–Kutta method for production–destruction equations. The necessary and sufficient conditions for the method to be of third-order accuracy are derived. With the same approach as Huang and Shu (2018), this time integration method is then generalized to solve a class of ODEs arising from semi-discrete schemes for PDEs and coupled with the positivity-preserving finite difference weighted essentially non-oscillatory schemes for non-equilibrium flows. Numerical experiments are provided to demonstrate the performance of our proposed scheme.
Author	Zhao, Weifeng Shu, Chi-Wang Huang, Juntao
Author_xml	– sequence: 1 givenname: Juntao surname: Huang fullname: Huang, Juntao email: huangj75@msu.edu organization: Department of Mathematics, Michigan State University – sequence: 2 givenname: Weifeng surname: Zhao fullname: Zhao, Weifeng organization: Department of Applied Mathematics, University of Science and Technology Beijing – sequence: 3 givenname: Chi-Wang surname: Shu fullname: Shu, Chi-Wang organization: Division of Applied Mathematics, Brown University
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Cites_doi	10.1137/151005798 10.1016/j.jcp.2018.01.051 10.1016/S0168-9274(03)00101-6 10.1016/j.jcp.2010.08.016 10.1016/0021-9991(88)90177-5 10.1016/j.jcp.2010.10.036 10.1007/978-3-642-05221-7 10.1137/17M1144362 10.1007/s10915-018-0852-1 10.1016/j.jcp.2011.10.002 10.1142/S0218202517500099 10.1016/j.jcp.2011.11.020 10.1007/s10543-018-0705-1 10.1016/j.jcp.2009.05.028 10.1006/jcph.1996.0130 10.1017/CBO9780511624100 10.1137/S003614450036757X 10.1007/978-3-319-57397-7_1 10.1016/j.apnum.2017.09.004 10.1016/j.jcp.2009.12.030 10.1002/fld.4023 10.1137/18M1226774
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Keywords	Production–destruction equations Finite difference Chemical reactions Positivity-preserving Compressible Euler equations Third-order accuracy
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References	ChertockACuiSKurganovAWuTWell-balanced positivity preserving central-upwind scheme for the shallow water system with friction termsInt. J. Numer. Methods Fluids2015786355383335017810.1002/fld.4023 KopeczSMeisterAOn order conditions for modified Patankar–Runge–Kutta schemesAppl. Numer. Math.2018123159179371199610.1016/j.apnum.2017.09.0041377.65089 HuangJShuC-WBound-preserving modified exponential Runge–Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source termsJ. Comput. Phys.2018361111135377117810.1016/j.jcp.2018.01.05106882515 GottliebSShuC-WTadmorEStrong stability-preserving high-order time discretization methodsSIAM Rev.200143189112185464710.1137/S003614450036757X0967.65098 ZhangXShuC-WOn maximum-principle-satisfying high order schemes for scalar conservation lawsJ. Comput. Phys.2010229930913120260109110.1016/j.jcp.2009.12.0301187.65096 ZhangXShuC-WOn positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshesJ. Comput. Phys.20102292389188934272538010.1016/j.jcp.2010.08.0161282.76128 AxelssonOIterative Solution Methods1994CambridgeCambridge University Press10.1017/CBO97805116241000795.65014 Huang, J., Shu, C.-W.: Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. J. Sci. Comput. (2018). https://doi.org/10.1007/s10915-018-0852-1 WangWShuC-WYeeHSjögreenBHigh-order well-balanced schemes and applications to non-equilibrium flowJ. Comput. Phys.20092281866826702256786810.1016/j.jcp.2009.05.0281261.76024 ShuC-WOsherSEfficient implementation of essentially non-oscillatory shock-capturing schemesJ. Comput. Phys.198977243947110.1016/0021-9991(88)90177-50653.65072 HuangJShuC-WA second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye modelMath. Mod. Methods Appl. Sci.20172703549579362133710.1142/S02182025175000991360.65235 ZhangXShuC-WPositivity-preserving high order finite difference WENO schemes for compressible Euler equationsJ. Comput. Phys.2012231522452258287663610.1016/j.jcp.2011.11.02006036596 JiangG-SShuC-WEfficient implementation of weighted ENO schemesJ. Comput. Phys.19961261202228139162710.1006/jcph.1996.01300877.65065 HairerEWannerGSolving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems1996BerlinSpringer10.1007/978-3-642-05221-70859.65067 WangCZhangXShuC-WNingJRobust high order discontinuous Galerkin schemes for two-dimensional gaseous detonationsJ. Comput. Phys.20122312653665287209610.1016/j.jcp.2011.10.0021243.80011 Shu, C.-W.: Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. In: Cances, C., Omnes, P. (eds.) Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects, Proceedings of the Eighth Conference on Finite Volumes for Complex Applications (FVCA8), Springer Proceedings in Mathematics and Statistics, vol. 199, pp. 3–14. Springer, Switzerland (2017) ZhangXShuC-WPositivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source termsJ. Comput. Phys.2011230412381248275335910.1016/j.jcp.2010.10.0361391.76375 HuJShuRZhangXAsymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equationSIAM J. Numer. Anal.2018562942973378411510.1137/17M11443621388.82023 Hu, J., Shu, R.: A second-order asymptotic-preserving and positivity-preserving exponential Runge–Kutta method for a class of stiff kinetic equations. arXiv:1807.03728 (2018) XuZZhangXBound-preserving high-order schemesHandb. Numer. Anal.2017188110236453891368.65149 BurchardHDeleersnijderEMeisterAA high-order conservative Patankar-type discretisation for stiff systems of production-destruction equationsAppl. Numer. Math.2003471130200314410.1016/S0168-9274(03)00101-61028.80008 ChertockACuiSKurganovAWuTSteady state and sign preserving semi-implicit Runge–Kutta methods for ODEs with stiff damping termSIAM J. Numer. Anal.201553420082029338483510.1137/1510057981327.65128 HairerENørsettSPWannerGSolving Ordinary Differential Equations I: Nonstiff Problems1993BerlinSpringer0789.65048 KopeczSMeisterAUnconditionally positive and conservative third order modified Patankar–Runge–Kutta discretizations of production-destruction systemsBIT Numer. Math.201858691728385568810.1007/s10543-018-0705-11397.65102 X Zhang (881_CR23) 2011; 230 J Huang (881_CR11) 2018; 361 C-W Shu (881_CR17) 1989; 77 S Kopecz (881_CR15) 2018; 123 X Zhang (881_CR24) 2012; 231 881_CR12 S Kopecz (881_CR14) 2018; 58 X Zhang (881_CR21) 2010; 229 A Chertock (881_CR3) 2015; 53 E Hairer (881_CR6) 1993 O Axelsson (881_CR1) 1994 S Gottlieb (881_CR5) 2001; 43 881_CR8 J Huang (881_CR10) 2017; 27 J Hu (881_CR9) 2018; 56 C Wang (881_CR18) 2012; 231 W Wang (881_CR19) 2009; 228 881_CR16 E Hairer (881_CR7) 1996 X Zhang (881_CR22) 2010; 229 H Burchard (881_CR2) 2003; 47 A Chertock (881_CR4) 2015; 78 G-S Jiang (881_CR13) 1996; 126 Z Xu (881_CR20) 2017; 18
References_xml	– reference: KopeczSMeisterAOn order conditions for modified Patankar–Runge–Kutta schemesAppl. Numer. Math.2018123159179371199610.1016/j.apnum.2017.09.0041377.65089 – reference: AxelssonOIterative Solution Methods1994CambridgeCambridge University Press10.1017/CBO97805116241000795.65014 – reference: ZhangXShuC-WOn maximum-principle-satisfying high order schemes for scalar conservation lawsJ. Comput. Phys.2010229930913120260109110.1016/j.jcp.2009.12.0301187.65096 – reference: ZhangXShuC-WPositivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source termsJ. Comput. Phys.2011230412381248275335910.1016/j.jcp.2010.10.0361391.76375 – reference: ShuC-WOsherSEfficient implementation of essentially non-oscillatory shock-capturing schemesJ. Comput. Phys.198977243947110.1016/0021-9991(88)90177-50653.65072 – reference: GottliebSShuC-WTadmorEStrong stability-preserving high-order time discretization methodsSIAM Rev.200143189112185464710.1137/S003614450036757X0967.65098 – reference: JiangG-SShuC-WEfficient implementation of weighted ENO schemesJ. Comput. Phys.19961261202228139162710.1006/jcph.1996.01300877.65065 – reference: ChertockACuiSKurganovAWuTWell-balanced positivity preserving central-upwind scheme for the shallow water system with friction termsInt. J. Numer. Methods Fluids2015786355383335017810.1002/fld.4023 – reference: HairerENørsettSPWannerGSolving Ordinary Differential Equations I: Nonstiff Problems1993BerlinSpringer0789.65048 – reference: KopeczSMeisterAUnconditionally positive and conservative third order modified Patankar–Runge–Kutta discretizations of production-destruction systemsBIT Numer. Math.201858691728385568810.1007/s10543-018-0705-11397.65102 – reference: Shu, C.-W.: Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. In: Cances, C., Omnes, P. (eds.) Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects, Proceedings of the Eighth Conference on Finite Volumes for Complex Applications (FVCA8), Springer Proceedings in Mathematics and Statistics, vol. 199, pp. 3–14. Springer, Switzerland (2017) – reference: BurchardHDeleersnijderEMeisterAA high-order conservative Patankar-type discretisation for stiff systems of production-destruction equationsAppl. Numer. Math.2003471130200314410.1016/S0168-9274(03)00101-61028.80008 – reference: Hu, J., Shu, R.: A second-order asymptotic-preserving and positivity-preserving exponential Runge–Kutta method for a class of stiff kinetic equations. arXiv:1807.03728 (2018) – reference: HuJShuRZhangXAsymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equationSIAM J. Numer. Anal.2018562942973378411510.1137/17M11443621388.82023 – reference: Huang, J., Shu, C.-W.: Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. J. Sci. Comput. (2018). https://doi.org/10.1007/s10915-018-0852-1 – reference: WangWShuC-WYeeHSjögreenBHigh-order well-balanced schemes and applications to non-equilibrium flowJ. Comput. Phys.20092281866826702256786810.1016/j.jcp.2009.05.0281261.76024 – reference: ChertockACuiSKurganovAWuTSteady state and sign preserving semi-implicit Runge–Kutta methods for ODEs with stiff damping termSIAM J. Numer. Anal.201553420082029338483510.1137/1510057981327.65128 – reference: WangCZhangXShuC-WNingJRobust high order discontinuous Galerkin schemes for two-dimensional gaseous detonationsJ. Comput. Phys.20122312653665287209610.1016/j.jcp.2011.10.0021243.80011 – reference: ZhangXShuC-WPositivity-preserving high order finite difference WENO schemes for compressible Euler equationsJ. Comput. Phys.2012231522452258287663610.1016/j.jcp.2011.11.02006036596 – reference: HuangJShuC-WBound-preserving modified exponential Runge–Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source termsJ. Comput. Phys.2018361111135377117810.1016/j.jcp.2018.01.05106882515 – reference: ZhangXShuC-WOn positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshesJ. Comput. Phys.20102292389188934272538010.1016/j.jcp.2010.08.0161282.76128 – reference: HuangJShuC-WA second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye modelMath. Mod. Methods Appl. Sci.20172703549579362133710.1142/S02182025175000991360.65235 – reference: HairerEWannerGSolving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems1996BerlinSpringer10.1007/978-3-642-05221-70859.65067 – reference: XuZZhangXBound-preserving high-order schemesHandb. Numer. Anal.2017188110236453891368.65149 – volume: 53 start-page: 2008 issue: 4 year: 2015 ident: 881_CR3 publication-title: SIAM J. Numer. Anal. doi: 10.1137/151005798 – volume: 361 start-page: 111 year: 2018 ident: 881_CR11 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2018.01.051 – volume: 47 start-page: 1 issue: 1 year: 2003 ident: 881_CR2 publication-title: Appl. Numer. Math. doi: 10.1016/S0168-9274(03)00101-6 – volume: 229 start-page: 8918 issue: 23 year: 2010 ident: 881_CR22 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.08.016 – volume: 77 start-page: 439 issue: 2 year: 1989 ident: 881_CR17 publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(88)90177-5 – volume: 230 start-page: 1238 issue: 4 year: 2011 ident: 881_CR23 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.10.036 – volume-title: Solving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems year: 1996 ident: 881_CR7 doi: 10.1007/978-3-642-05221-7 – volume: 56 start-page: 942 issue: 2 year: 2018 ident: 881_CR9 publication-title: SIAM J. Numer. Anal. doi: 10.1137/17M1144362 – ident: 881_CR12 doi: 10.1007/s10915-018-0852-1 – volume: 231 start-page: 653 issue: 2 year: 2012 ident: 881_CR18 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2011.10.002 – volume-title: Solving Ordinary Differential Equations I: Nonstiff Problems year: 1993 ident: 881_CR6 – volume: 27 start-page: 549 issue: 03 year: 2017 ident: 881_CR10 publication-title: Math. Mod. Methods Appl. Sci. doi: 10.1142/S0218202517500099 – volume: 18 start-page: 81 year: 2017 ident: 881_CR20 publication-title: Handb. Numer. Anal. – volume: 231 start-page: 2245 issue: 5 year: 2012 ident: 881_CR24 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2011.11.020 – volume: 58 start-page: 691 year: 2018 ident: 881_CR14 publication-title: BIT Numer. Math. doi: 10.1007/s10543-018-0705-1 – volume: 228 start-page: 6682 issue: 18 year: 2009 ident: 881_CR19 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.05.028 – volume: 126 start-page: 202 issue: 1 year: 1996 ident: 881_CR13 publication-title: J. Comput. Phys. doi: 10.1006/jcph.1996.0130 – volume-title: Iterative Solution Methods year: 1994 ident: 881_CR1 doi: 10.1017/CBO9780511624100 – volume: 43 start-page: 89 issue: 1 year: 2001 ident: 881_CR5 publication-title: SIAM Rev. doi: 10.1137/S003614450036757X – ident: 881_CR16 doi: 10.1007/978-3-319-57397-7_1 – volume: 123 start-page: 159 year: 2018 ident: 881_CR15 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2017.09.004 – volume: 229 start-page: 3091 issue: 9 year: 2010 ident: 881_CR21 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.12.030 – volume: 78 start-page: 355 issue: 6 year: 2015 ident: 881_CR4 publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.4023 – ident: 881_CR8 doi: 10.1137/18M1226774
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Snippet	In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018 . https://doi.org/10.1007/s10915-018-0852-1 ) and develop a third-order... In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018. https://doi.org/10.1007/s10915-018-0852-1) and develop a third-order...
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SubjectTerms	Algorithms Chemical reactions Computational Mathematics and Numerical Analysis Equilibrium Essentially non-oscillatory schemes Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonequilibrium flow Numerical analysis Runge-Kutta method Theoretical Time integration
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Title	A Third-Order Unconditionally Positivity-Preserving Scheme for Production–Destruction Equations with Applications to Non-equilibrium Flows
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