Parallel Multi-Scale Algorithms and Applications to Combustion and Turbulence

Abstract

Abstract : In this project, the main objective was to develop multi-resolution wavelet algorithm to study the flame acceleration and to understand the mechanism of the transition of deflagration to detonation. In the first half year of the project. The author completed the study of two-dimensional detonation waves based on hybrid high order methods (a combination of high order Essentially Non-oscillatory (ENO) methods and spectral methods and Shock Tracking methods). The result on the detonation waves was published in the AIAA Journal. In the remaining time of the two years, first, the author completed the theoretical and algorithmic studies of the adaptive wavelet method, which could handle non-periodic boundary conditions and non-linear time dependent PDE's (The result was published in the SIAM Journal of Numerical Analysis). Secondly, the author implemented the adaptive wavelet methods for the solution of one-dimensional flame propagation; thirdly, the author developed a Fortran code WL2D (more than 13,000 lines) for the two-dimensional multi-scale wavelet algorithms with an efficient data structure and implemented a second order implicit factorized scheme for the adaptive wavelet methods.