A previous transient three-dimensional ignition model is extended to enable the study of both flame spread and extinction in concurrent flows. In the non-dimensional model, the flame base stabilization zone structure is resolved. Variable grid scheme is used to accelerate the numerical computation. An automatic adaptive mesh refinement scheme is developed and implemented for the moving flame stabilization zone where fuel burnout occurs. Several examples, in both forced and buoyant flows, are shown to illustrate the model capability to predict flame growth and extinction processes. The extinction modes include both quench due to heat loss in forced flow in microgravity and blowoff due to reduced Damkohler number in buoyant flow in normal gravity. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.