Adaptive finite element methods for low-Mach-number flows with chemical reactions

We describe recent developments in the design and implementation of finite element methods for the Navier-Stokes equations modelling chemically reactive flows. The emphasize is on the low-Mach number regime including the limit case of incompressible flow. The most important ingredients are residual driven a posteriori mesh refinement, fully coupled defect-correction iteration for linearization, and optimal multigrid preconditioning. These computational techniques are systematically developed for several linearized sub-problems and are then applied to the full model of compressible low-Mach number flow including chemical reactions. The potential of automatic mesh adaptation together with multilevel techniques is illustrated by various examples. In Chapters 1, we discuss the governing equations of compressible flow in the low-Mach-number regime and the particularities introduced by the inclusion of chemical reactions. Then, Chapter 2 presents our finite element discretization of the resulting models with emphasize on the description of pressure stabilization and numerical diffusion by least-squares techniques. Chapter 3 introduces into a new approach to error control and adaptive mesh design which is based on weighted a posteriori error estimates derived by duality techniques. In Chapter 4, the solution process involving defect-correction and multigrid techniques is described. Chapter 5 presents some applications of our methods to solving compressible flow problems including chemical reaction systems of different complexity. In the Appendix, we collect some details about the models of chemical reactions used in our simulations. (orig.)Available from TIB Hannover: RR 1606(99-20) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman