Coupling multimodelling with local mesh refinement for the numerical computation of laminar flames

In this work, we propose a twofold adaptive method for the simulation of steady reactive flows. On the one hand, locally refined meshes are used. On the other hand, two types of diffusion models are applied: a simple Fick law and a more accurate multicomponent diffusion model. The diffusion model is changed locally throughout the computational domain. An analytically derived a posteriori error estimator provides reliable information on where to refine the mesh and where to choose the appropriate diffusion model. During the adaptation process, discretization and modelling errors are equilibrated. Numerical results are presented for ozone and hydrogen laminar flames.

[1]  T. Richter,et al.  SOLUTIONS OF 3D NAVIER-STOKES BENCHMARK PROBLEMS WITH ADAPTIVE FINITE ELEMENTS , 2006 .

[2]  Rolf Rannacher,et al.  Numerical simulation of laminar flames at low Mach number by adaptive finite elements , 1999 .

[3]  J. Warnatz,et al.  Calculation of the Structure of Laminar Flat Flames I: Flame Velocity of Freely Propagating Ozone Decomposition Flames , 1978 .

[4]  Alfio Quarteroni,et al.  MULTIMODELS FOR INCOMPRESSIBLE FLOWS: ITERATIVE SOLUTIONS FOR THE NAVIER-STOKES/OSEEN COUPLING , 2001 .

[5]  Alexandre Ern,et al.  Multicomponent transport algorithms , 1994 .

[6]  S. Ohnimus,et al.  Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems , 1999 .

[7]  Rolf Rannacher,et al.  An optimal control approach to a posteriori error estimation in finite element methods , 2001, Acta Numerica.

[8]  Roland Becker,et al.  A finite element pressure gradient stabilization¶for the Stokes equations based on local projections , 2001 .

[9]  J. Warnatz,et al.  Calculation of the Structure of Laminar Flat Flames III: Structure of Burner‐Stabilized Hydrogen‐Oxygen and Hydrogen‐Fluorine Flames , 1978 .

[10]  J. Guermond.  Stabilization of Galerkin approximations of transport equations by subgrid modelling , 1999 .

[11]  Alexandre Ern,et al.  Thermal diffusion effects in hydrogen-air and methane-air flames , 1998 .

[12]  Alexandre Ern,et al.  A Posteriori Control of Modeling Errors and Discretization Errors , 2003, Multiscale Model. Simul..

[13]  Christine Bernardi,et al.  Choix du paramètre de pénalisation pour la discrétisation par éléments finis des équations de Navier–Stokes , 2003 .

[14]  Roland Becker,et al.  A Two-Level Stabilization Scheme for the Navier-Stokes Equations , 2004 .

[15]  Alexandre Ern,et al.  Impact of Detailed Multicomponent Transport on Planar and Counterflow Hydrogen/Air and Methane/Air Flames , 1999 .

[16]  J. Tinsley Oden,et al.  Estimation of modeling error in computational mechanics , 2002 .

[17]  Alexandre Ern,et al.  Multicomponent transport impact on turbulent premixed H2/O2 flames , 2002 .