Adaptive continuation algorithms with application to combustion problems

We investigate the solution of parameterized nonlinear two-point boundary value problems by phase-space, pseudo-arclength, continuation methods that employ Newton-like iterations and adaptive gridding techniques. In particular, attention is focused on a modification of the basic continuation algorithm so that the Jacobian structure can be maintained both before and after the continuation raparameterization and on the determination of an adaptive mesh at each continuation step using equidistribution techniques. The numerical method is applied in the solution of counterflow premixed laminar flames with complex chemistry. We predict both strain rate and equivalence ratio extinction for a hydrogen-air system.