反应流模拟的有限体积法的比较
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摘要
针对自催化反应流模型的计算,推导了基于有限体积方法的统一通量格式以及十种常用格式的具体形式,并通过数值实验比较了其数值特性。结果表明:无论是一阶精度的迎风格式和Lax-Friedrichs格式,二阶精度的二阶向前差分、Lax-Wendroff、Beam-Warming和Fromm格式还是三阶精度的QUICK格式都会引起较严重的数值耗散和数值震荡,严重降低了数值精度,而带有通量限制器的MTVDLF格式可以消除数值耗散和数值震荡,并且带有Superbee限制器的MTVDLF最适合模拟自催化反应流问题。
For the numerical simulation of reacting flow, a unified flux scheme is deduced according to the finite volume method. Fluxes corresponding to ten different methods are obtained and their numerical behavior is systematically compared. It is shown that the first-order accuratemethods like the upwind and Lax-Friedrichs(LF)schemes, the secondorder accuratemethods including the second order upwind, Lax-Wendroff, Beam-Warming and Fromm schemes, and the third-order accurate QUICK scheme, will cause serious either numericaldissipation orunphysical oscillation, due to which numerical accuracy is remarkably reduced. The modified TVD-LF(MTVDLF)scheme with a flux limiter can eliminate both the numerical dissipation and unphysical oscillation, and the Superbee limiter is most suitable for the simulation of reacting flow.
For the numerical simulation of reacting flow, a unified flux scheme is deduced according to the finite volume method. Fluxes corresponding to ten different methods are obtained and their numerical behavior is systematically compared. It is shown that the first-order accuratemethods like the upwind and Lax-Friedrichs(LF)schemes, the secondorder accuratemethods including the second order upwind, Lax-Wendroff, Beam-Warming and Fromm schemes, and the third-order accurate QUICK scheme, will cause serious either numericaldissipation orunphysical oscillation, due to which numerical accuracy is remarkably reduced. The modified TVD-LF(MTVDLF)scheme with a flux limiter can eliminate both the numerical dissipation and unphysical oscillation, and the Superbee limiter is most suitable for the simulation of reacting flow.
引文
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[2]Vande Wouwer A,Saucez P,Schiesser W E,et al.Adaptive method of lines[M].London:Chapman&Hall/CRC Press,2001.
[3]张勇,赵成宏,杨光源,等.多尺度径向基无单元法求解电磁对流扩散问题[J].华中科技大学学报:自然科学版,2009(12):72-75.
[4]Wang Y,Hutter K.Comparisons of numerical methods with respect to convectively dominated problems[J].International Journal for Numerical Methods in Fluids,2001,37(6):721-745.
[5]Ewing R E,Wang H.A summary of numerical methods for time-dependent advection-dominated partial differential equations[J].Journal of Computational&Applied Mathematics,2001,128(1/2):423-445.
[6]Alhumaizi K I,Abasaeed A E.On mutating autocatalytic reactions in a CSTR.I:Multiplicity of steady states[J].Chemical Engineering Science,2000,55(18):3919-3928.
[7]Alhumaizi K.Comparison of finite difference methods for the numerical simulation of reacting flow[J].Com-puters&Chemical Engineering,2004,28(9):1759-1769.
[8]Boris J P,Book D L.Flux-corrected transport I SHASTA,a fluid transport algorithm that works[J].Journal of Computational Physics,1973,11(1):38-69.
[9]Suratanakavikul V,Marquis A J.A comparative study of flux-limiters in unsteady and steady flows[C]//Proceeding of the 13th National Mechanical Engineering Conference,South Pattaya,Cholburi,2-3 December,1999.
[10]Mac Kinnon R J,Carey G F.Positivity-preserving,flux limited finite-difference and finite-element methods for reactive transport[J].International Journal for Numerical Methods in Fluids,2003,41(2):151-183.
[11]Yee H C.Construction of explicit and implicit symmetric TVD schemes and their applications[J].Journal of Computational Physics,1987,68(1):151-179.
[12]戴厚平,郑洲顺,段丹丹.一类偏微分方程的格子Boltzmann模型[J].计算机工程与应用,2016,52(3):21-26.
[13]彭碧涛,郑洲顺,刘红娟,等.求解二维对流扩散方程的格子Boltzmann方法[J].计算机工程与应用,2015,51(23):68-73.
[14]袁冬芳,曹富军,葛永斌.求解二维对流扩散方程的投影迭代法[J].计算机工程与应用,2013,49(4):39-42.
[15]Finlayson B A.Numerical methods for problems with moving fronts[M].Washington:Ravenna Park Publishing,1992.