Nonstandard High Order Multigrid Techniques with Applications to Laminar Diffusion Flame Simulations

This project will design efficient geometric multigrid methods using intermediate grids to solve convection diffusion problems discretized by high order compact schemes. The use of intermediate grids aims at reducing discrepancy between the solutions obtained on different grids. Symbolic computation packages will be used to derive a fourth order finite difference scheme on the intermediate grids. Special relaxation schemes and intergrid transfer operators will be developed. The nonstandard multigrid method with high order discretization schemes will be used in the numerical simulation of laminar diffusion flames. The use of intermediate grids is expected to alleviate the problem haunting existing multigrid methods in the flame simulation, in which the converged coarse grid correction is not in the convergence domain of the fine grid Newton iteration. This project requires both symbolic and numerical computation techniques. The successful development of a useful symbolic computation procedure will greatly promote the awareness and use of symbolic computation packages in numerical computation community. The results of this research project will make important contribution to the understanding of geometric multigrid solution of convection diffusion problems, and of the applications of high order compact schemes to realistic flow simulations. Efficient solution of such problems is central to many numerical simulations in computational fluid dynamics. The fast laminar diffusion flame code is useful in combustion and environment protection. Certain U.S. industries related to commercial burners, pollutant tracking, car and airplane manufacturing, combustion, can benefit from this research.