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An adaptive mesh refinement method for solution of the transported PDF equation. (English) Zbl 1176.80089
Summary: This paper presents the results of an investigation into a possible alternative to Monte Carlo methods for solving the transported probability density function (PDF) equation for scalars (compositions). The method uses a finite-volume approach combined with adaptive mesh refinement (AMR) in a multi-dimensional compositional space. Comparisons are made between the new method and Monte Carlo solutions for analytical test cases involving the reaction of two or three chemical species. These tests demonstrate the potential of the new method in terms of both accuracy and run time. Additional test cases involving various models for molecular mixing were also conducted with similar conclusions.

MSC:
80M12 Finite volume methods applied to problems in thermodynamics and heat transfer
80M31 Monte Carlo methods applied to problems in thermodynamics and heat transfer
80A32 Chemically reacting flows
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[1] Schildmacher, Unsteady flame and flow field interaction of a premixed model gas turbine burner, Proceedings of the Combustion Institute 31 (2) pp 3197– (2007)
[2] Pope, PDF methods for turbulent reactive flows, Progress in Energy and Combustion Science 11 pp 119– (1985)
[3] Janicka, Closure of transport equation for the probability density function of turbulent scalar fields, Journal of Non-Equilibrium Thermodynamics 4 pp 47– (1979) · Zbl 0422.76058
[4] Janicka J, Kolbe W, Kollmann W. The solution of a PDF-transport equation for turbulent diffusion. In Proceedings of the Heat Transfer and Fluid Mechanics Institute, Crowe CT, Grosshandler WL (eds). 1978; 297-312.
[5] Sabel’nikov, Rapidly decorrelating velocity-field model as a tool for solving one-point Fokker-Planck equations for probability density functions of turbulent reactive scalars, Physical Review E 72 pp 16301– (2005)
[6] Berger, Adaptive mesh refinement for hyperbolic partial differential equations, Journal of Computational Physics 53 pp 484– (1984) · Zbl 0536.65071
[7] Berger, Local adaptive mesh refinement for shock hydrodynamics, Journal of Computational Physics 82 pp 64– (1989) · Zbl 0665.76070
[8] Bell, Three dimensional adaptive mesh refinement for hyperbolic conservation laws, Society for Industrial and Applied Mathematics Journal on Scientific Computing 15 pp 127– (1994) · Zbl 0793.65072
[9] Quirk, A parallel adaptive grid algorithm for computational shock hydrodynamics, Applied Numerical Mathematics 20 pp 427– (1996) · Zbl 0856.65108
[10] Online details of CHOMBO code: http://seesar.lbl.gov/ANAG/chombo/.
[11] Online details of FLASH code: http://flash.uchicago.edu/website/home/.
[12] Online details of SAMRAI code: http://www.llnl.gov/CASC/SAMRAI/.
[13] Fromang, A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical magnetohydrodynamics, Astronomy and Astrophysics 457 pp 371– (2006)
[14] Jones, Pdf modelling of finite-rate chemistry effects in turbulent nonpremixed jet flames, Combustion and Flame 115 pp 210– (1998)
[15] Godunov, Finite difference methods for numerical computations of discontinuous solutions of the equations of fluid dynamics, Matematicheski Sbornik 47 (89) pp 271– (1959)
[16] Falle, Self-similar jets, Monthly Notices of the Royal Astronomical Society 250 pp 581– (1991)
[17] Online details of AMROC code: http://amroc.sourceforge.net/.
[18] Baum JD, Löhner R. Numerical simulation of shock-elevated box interaction using an adaptive finite shock capturing scheme. American Institute of Aeronautics and Astronautics, AIAA-1989-653, 1989.
[19] Khkhlov, Fully threaded tree algorithm for adaptive refinement fluid dynamics simulations, Journal of Computational Physics 143 pp 519– (1998)
[20] Möbus, Comparison of Eulerian and Lagrangian Monte Carlo PDF methods for turbulent diffusion flames, Combustion and Flame 124 (3) pp 519– (2001)
[21] Curl, Dispersed phase mixing: 1 theory and effects in simple reactors, AIChE Journal 9 (2) pp 175– (1963)
[22] Kosaly, Modelling of turbulent molecular mixing, Combustion and Flame 70 pp 101– (1987) · Zbl 0619.76071
[23] Dopazo, Relaxation of initial probability density functions in turbulent convection of scalar fields, Physics of Fluids 22 (1) pp 20– (1979) · Zbl 0401.76049
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