The goal of this on-going work is to show that a high order adaptive Spectral Element Method is an effective technique for the simulation of complex physical phenomena, in particular fluid flow. Atmospheric, oceanographic, biological and other flows contain so many different features over a wide range of scales, that adaptive refinement has become a necessity in order to resolve these features efficiently. The spectral element method lends itself naturally to adaptivity by its hybrid nature of a finite element method and a spectral method. Both h- (finite element) and p- (spectral) refinement and coarsening are used in this method to improve resolution in a cost effective way. The adaptivity criteria are based on elemental a posteriori error estimators that analyze the quality of the solution as well as give an estimated value of the error. A tree data structure has been implemented to simplify the refinement and especially the coarsening algorithms. Two-dimensional simulations of a thin premixed flame front wrinkled by synthetic turbulent velocity fields illustrate the resolution capabilities of the adaptive spectral element method. In the figure below, results of three cases are shown: a flame deformed by (a) a sin shear flow, (b) a periodic array of vortices, and (c) the combination of shear and vortices. The starting grid is the same for all the three cases with K =12 elements and N =4th order polynomials or 5 × 5 collocation points in each element. Adaptive spectral element simulations of thin flame front deformations (closeup view). (a) Case One: a sine shear flow (K = 200, DoF=12180) (b) Case Two: a vortex flow (K = 150, DoF=10746) (c) Case Three: a flow with sine shear and vortices (K = 232, DoF=14300). Element boundaries are indicated by white lines. Red represents burnt gases, blue unburnt gases. DoF refers to the total number of degrees of freedom, while K is the number of elements. Three-dimensional simulations of a moving heat source will also be shown. A parallel adaptive spectral element method is currently being developed. Load balancing, data movement and access are important issues that need to be resolved for unstructured dynamically adaptive methods. Some preliminary work in this area will be discussed if time permits.