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Solving multidimensional reactive flow problems with adaptive finite elements. (English) Zbl 1398.76096
Jäger, Willi (ed.) et al., Reactive flows, diffusion and transport. From experiments via mathematical modeling to numerical simulation and optimization. Final report of SFB (Collaborative Research Center) 359. Berlin: Springer (ISBN 3-540-28379-X/hbk). 93-112 (2007).
Summary: We describe recent developments in the design and implementation of finite element methods for the compressible Navier-Stokes equations modeling chemically reactive flows. The emphasize is on the low-Mach number regime including the limit case of incompressible flow. The most important ingredients are appropriate finite element discretizations, residual driven a posteriori mesh refinement, fully coupled defect-correction iteration for linearization, and optimal multigrid preconditioning. The potential of automatic mesh adaptation together with multilevel techniques is illustrated by 2D and 3D simulations of laminar methane combustion including detailed reaction mechanisms.
For the entire collection see [Zbl 1103.76004].

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76V05 Reaction effects in flows 80A25 Combustion
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##### References:
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