Moving Weight Galerkin Methods for Turbulent Reactive Flows
Please always quote using this URN: urn:nbn:de:0297-zib-1646
- Adopting a statistical approach for the computation of turbulent combustion flows an approximation for the probability density function (PDF) of the composition variables is often required to treat the highly non-linear reaction term in a satisfactory way. One class of methods currently being used are the moment methods which employ transport equations for low order statistical moments and use a parametrized shape of the PDF. A second class solves a transport equation for the joint PDF by a Monte Carlo method. In the present paper we develop an intermediate algorithm based on a Galerkin method for the PDF transport equation. The solution is developed in terms of an orthogonal or bi-orthogonal basis of a suitable Hilbert space. The unconventional use of the related weight function as a prefactor (moving weight approach) permits adaptivity and results in a generalization of the $\beta-$closure for bounded scalar quantities. We present the approximation procedure in detail and apply it to the evolution of the composition in a homogeneous well-stirred reactor. The extension to non-homogeneous flow simulations is straightforward.
Author: | Jochen Fröhlich, Peter Deuflhard |
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Document Type: | ZIB-Report |
Date of first Publication: | 1994/12/20 |
Series (Serial Number): | ZIB-Report (SC-94-36) |
ZIB-Reportnumber: | SC-94-36 |
Published in: | Appeared in: Topics in Industrial Mathematics. Proc. 8th Conf. of the European Consortium for Mathematics in Industry (ECMI 94). H. Neunzert (ed.) Wiley; Teubner 1996, pp. 176-184 |