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Stabilized finite elements for 3D reactive flows
Author(s) -
Braack M.,
Richter Th.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1160
Subject(s) - solver , galerkin method , finite element method , mathematics , discontinuous galerkin method , multigrid method , ansatz , linear system , robustness (evolution) , system of linear equations , computer science , mathematical optimization , partial differential equation , geometry , mathematical analysis , physics , mathematical physics , thermodynamics , biochemistry , chemistry , gene
Objective of this work is the numerical solution of chemically reacting flows in three dimensions described by detailed reaction mechanism. The contemplated problems include, e.g. burners with 3D geometry. Contrary to the usual operator splitting method the equations are treated fully coupled with a Newton solver. This leads to the necessity of the solution of large linear non‐symmetric, indefinite systems. Due to the complexity of the regarded problems we combine a variety of numerical methods, as there are goal‐oriented adaptive mesh refinement, a parallel multigrid solver for the linear systems and economical stabilization techniques for the stiff problems. By blocking the solution components for every ansatz function and applying special matrix structures for each block of degrees of freedom, we can significantly reduce the required memory effort without worsening the convergence. Considering the Galerkin formulation of the regarded problems this is established by using lumping of the mass matrix and the chemical source terms. However, this technique is not longer feasible for ‘standard’ stabilized finite elements as for instance Galerkin least squares techniques or streamline diffusion. Those stabilized schemes are well established for Navier–Stokes flows but for reactive flows, they introduce many further couplings into the system compared to Galerkin formulations. In this work, we discuss this issue in connection with combustion in more detail and propose the local projection stabilization technique for reactive flows. Beside the robustness of the arising linear systems we are able to maintain the problem‐adapted matrix structures presented above. Finally, we will present numerical results for the proposed methods. In particular, we simulate a methane burner with a detailed reaction system involving 15 chemical species and 84 elementary reactions. Copyright © 2005 John Wiley & Sons, Ltd.