A study of reactive diffusion problems with stiff integrators and adaptive grids
The use of newton-linearized block solvers with higher order difference methods has given very efficient calculations for flame propagation and stiff chemistry.
Adaptive gridding based on gradients of the dependent variables has yielded very large efficiencies for problems with large spatial and temporal gradients. As these temporal gradients decrease there is less advantage to be gained with adaptive techniques.
Adaptive gridding techniques offer the promise of very large economies for multi-dimensional problems. However, the problem of grid cell geometry is not completely under control, and a need for additional research is necessary in this area.
KeywordsModel Problem Flame Propagation Flame Speed Adaptive Grid Computational Space
Unable to display preview. Download preview PDF.
- R.M. Beam and R.F. Warming, 1977, “On the Construction and Application of Implicit Factored Schemes for Conservation Laws, SIAM-AMS Proceedings, Vol.11, April.Google Scholar
- W.R. Birley and H. McDonald, 1977, “Solution of the Multidimensional Compressible Navier-Stokes Equations by a Generalized Implicit Method,” J. Computational Physics, Vol.24, August, pp.373–392.Google Scholar
- W.C. Gear, 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
- Z. Kopal, 1961, Numerical Analysis, John Wiley and Sons, New York.Google Scholar
- N.K. Madsen and R.F. Sincovic, 1976, “PDECOL: General Collocation Software for Partial Differential Equations,” Univ. of Calif., LLL, Report UCRL-51186, May.Google Scholar
- G.R. Otey, 1978, “Numerical Methods for Solving Reaction Diffusion Problems,” Ph.D. Thesis, Dept. of Mechanical Engineering, Univ. of Calif., Davis, July.Google Scholar
- G.R. Otey and H.A. Dwyer, 1979, “Numerical Study of the Interaction of Fast Chemistry and Diffusion,” AIAA J., Vol.17, No.6, June, p.606.Google Scholar
- R. Peyret and H. Viviand, 1975, “Computation of Viscous Compressible Flows Based on the Navier-Stokes Equations,” AGARD-AG212, 1975.Google Scholar
- N.N. Yanenko, 1971, The Method of Fractional Steps, Springer Verlag, New York.Google Scholar