反应、扩散化学动力学方程的有效解法

Effective Solution Method of Chemical Reaction Kinetics With Diffuse

1.
Department of Engineering Mechanics, Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China;

摘要: 对扩散、化学反应或瞬态温度场问题，给出了具有4阶精度、自起步的隐式时间积分算法．算例显示,其精度和稳定性都好于四阶Runge-Kutta法，并且保留了原系数矩阵的稀疏存储方式和稀疏矩阵的运算规则,使紧缩存储技术和减少计算时间有效的结合．以旋转填充床内的竞争串联反应为算例，表明该算法是有效的．
- 逐步时间积分 /
- 扩散 /
- 化学反应动力学 /
- 旋转填充床 /
- 微观混合
Abstract: The time integration method with four-order accuracy,self-starting and implicit for the diffuse chemical reaction kinetics equation or the transient instantaneous temperature filed equation was presented.The examples show that both accuracy and stability are better than Runge-Kutta method with four-order.The coefficients of the equation are stored with sparse matrix pattern,so an algorithm is presented which combines a compact storage scheme with reduced computation cost.The computation of the competitive and consecutitive reaction in the rotating packed bed is taken as examples which shows that the method is effective.
- step-by-step integration /
- diffuse /
- chemical reaction kinetics /
- rotating packed bed /
- micro-mixing

[1]	Fried Isaac.Numerical Solution of Differential Equations[M].New York,San Francisco,London:Academic Press,1979.
[2]	Brooks Alexander N.Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J].Comput Methods Appl Mech Engrg,1982,32(1/3)：199—259. doi: 10.1016/0045-7825(82)90071-8
[3]	Russo Alessandro.Bubble stabilization of finite element methods for the linearized incompressible Navier-Stokes equations[J].Comput Methods Appl Mech Engrg,1996,132(3/4)：335—343. doi: 10.1016/0045-7825(96)01020-1
[4]	Baiocchi Claudio,Brezzi Franco.Virtual bubbles and Galerkin-least-squares type methods(GaLS)[J].Comput Methods Appl Mech Engrg,1993,105(1)：125—141. doi: 10.1016/0045-7825(93)90119-I
[5]	钟万勰.计算结构力学与最优控制[M].大连：大连理工大学出版社，1993.
[6]	吕和祥，于洪洁，裘春航.精细积分的非线性动力学积分方程及其解法[J].固体力学学报，2001，22（3）：303—308.
[7]	陈建峰，等.超重力技术及应用——新一代反应与分离技术[M].北京：化学工业出版社，材料科学与工程出版中心，2002.
[8]	刘骥.旋转填充床内微观混合研究及液-液相法制备碳酸锶纳米粉体[D].博士学位论文.北京：北京化工大学，2000.
[9]	监凯维奇 O C.有限元法[M].北京：科学出版社，1985.