A study of reactive diffusion problems with stiff integrators and adaptive grids

Abstract

In the present paper the results of a comprehensive study of the numerical problems associated with flows with chemical reactions have been presented. The problems solved are simplifications of many practical problems, but they retain the key features of complex flows. Also, the time and space scaling problems are general to most problems in fluid mechanics and the results will be applicable to many areas. The major conclusions of our study are:

• 1. The use of newton-linearized block solvers with higher order difference methods has given very efficient calculations for flame propagation and stiff chemistry.

• 2. 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.

• 3. 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.