Propagation of premixed laminar flames in 3D narrow open ducts using RBF-generated finite differences

Combustion Theory and Modelling

Volumn 17, Issue 5, 2013, Pages 789-803

  Bayona, Victor ^a   Kindelan, Manuel ^a  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

flame velocity; laminar flames; meshless methods; radial basis functions (RBF); RBF FD

Indexed keywords

FLAME VELOCITY; LAMINAR FLAME; MESH-LESS METHODS; RADIAL BASIS FUNCTION(RBF); RBF-FD;

COMBUSTION; FINITE DIFFERENCE METHOD; FLAMMABILITY TESTING; GEOMETRY; IMAGE SEGMENTATION; NUMERICAL METHODS; NUMERICAL MODELS; RADIAL BASIS FUNCTION NETWORKS; THREE DIMENSIONAL;

DUCTS;

EID: 84886415461     PISSN: 13647830     EISSN: 17413559     Source Type: Journal    
DOI: 10.1080/13647830.2013.801519     Document Type: Article

References (35)

1. G.F. Carrier, F.E. Fendell, and P.S. Feldman, Laminar flame propagation/quench for a parallel-wall duct, Symp. (Int.) Combust. 20 (1985), pp. 67-74.
2. B. Larrouturou, Adaptive numerical simulation of premixed flame propagation, in Numerical Modeling in Combustion, Ed. T. J. Chung, Taylor & Francis (1993), 177-230 (http://bookshop.blackwell.co.uk/jsp/display_product_info.jsp?isbn=9780891168225).
3. N. Peters and J. Warnatz, Numerical Methods in Laminar Flame Propagation, Notes on Numerical Fluid Mechanics, Proceedings of the Combustion Institute, Volume 28 (2000), pp. 1883-1889, Vieweg & Sohn, 1982.
4. V.N. Kurdyumov, E. Fernández, and A. Liñán, Flame flashback and propagation of premixed flames near a wall, Symp. (Int.) Combust. 28 (2000), pp. 1883-1889.
5. V.N. Kurdyumov and E. Fernández-Tarrazo, Lewis number effect on the propagation of premixed laminar flames in narrow open ducts, Combust. Flame 128 (2002), pp. 382-394.
6. J. Fröhlich and J. Lang, Two-dimensional cascadic finite element computations of combustion problems, Computer Meth. Appl. Mech. Engng 158 (1998), pp. 255-267.
7. J.I. Ramos, Finite element methods for one-dimensional flame propagation problems, in Numerical Modeling in Combustion, T.J. Chung, ed., Hemishpere, New York, 1990.
8. E.J. Kansa, Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics - II: Solutions to parabolic, hyperbolic and elliptic partial differential equations, Comput. & Math. Appls 19 (1990a), pp. 147-161.
9. E.J. Kansa, Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics - I: Surface approximations and partial derivative estimates, Comput. & Math. Appls 19 (1990b), pp. 127-145.
10. E. Larsson and B. Fornberg, A numerical study of some radial basis function based solution methods for elliptic PDEs, Comput. & Math. Appls 46 (2003), pp. 891-902.
11. G.E. Fasshauer and J.G. Zhang, On choosing 'optimal' shape parameters for RBF approximation, Numer. Algorithms 45 (2007), pp. 345-368.
12. S.A. Sarra and E.J. Kansa, Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations, Adv. Comput. Mech. 2 (2009). Available at http://www.techscience.com/acm/2009/v2.htm.
13. G.B. Wright and B. Fornberg, Scattered node compact finite difference-type formulas generated from radial basis functions, J. Comput. Phys. 212 (2006), pp. 99-123.
14. A.I. Tolstykh and D.A. Shirobokov, On using radial basis functions in a 'finite difference mode' with applications to elasticity problems, Comput. Mech. 33 (2003), pp. 68-79.
15. C. Shu, H. Ding, and K.S. Yeo, Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations, Computer Meth. Appl. Mech. Engng 192 (2003), pp. 941-954.
16. Y.Y. Shan, C. Shu, and Z.L. Lu, Application of local MQ-DQ method to solve 3D incompressible viscous flows with curved boundary, Comput. Model. Engng & Sci. 25 (2008), pp. 99-114.
17. Y.V.S.S. Sanyasiraju and G. Chandhini, Local radial basis function based gridfree scheme for unsteady incompressible viscous flows, J. Comput. Phys. 227 (2008), pp. 8922-8948.
18. N. Flyer, E. Lehto, S. Blaise, G.B. Wright, and A. St-Cyr, A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere, J. Comput. Phys. 231 (2012), pp. 4078-4095.
19. B. Fornberg and E. Lehto, Stabilization of RBF-generated finite difference methods for convective PDEs, J. Comput. Phys. 230 (2011), pp. 2270-2285.
20. S.A. Sarra, A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains, Appl. Math. Comput. 218 (2012), pp. 9853-9865.
21. E.F. Bollig, N. Flyer, and G. Erlebacher, Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs, J. Comput. Phys. 231 (2012), pp. 7133-7151.
22. D.G. Lasseigne, T.L. Jackson, and L. Jameson, Stability of freely propagating flames revisited, Combust. Theory Model. 3 (1999), pp. 591-611.
23. V. Bayona, M. Moscoso, M. Carretero, and M. Kindelan, RBF-FD formulas and convergence properties, J. Comput. Phys. 229 (2010), pp. 8281-8295.
24. I.J. Schoenberg, Metric spaces and completely monotone functions, Ann. Math. 39 (1938), pp. 811-841.
25. C.A. Micchelli, Interpolation of scattered data: distance matrices and conditionally positive definite functions, Constr. Approx. 2 (1986), pp. 11-22.
26. C. Mairhuber, On Haar's theorem concerning Chebyshev approximation problems having unique solutions, Proc. Amer. Math. Soc. 7 (1956), pp. 609-615.
27. R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Adv. Comput. Math. 3 (1995), pp. 251-264.
28. C.-S. Huang, C.-F. Lee, and A.H.-D. Cheng, Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method, Engng Anal. with Bound. Elements 31 (2007), pp. 614-623.
29. B. Fornberg and G. Wright, Stable computation of multiquadric interpolants for all values of the shape parameter, Comput. & Math. Appls 48 (2004), pp. 853-867.
30. B. Fornberg and C. Piret, A stable algorithm for flat radial basis functions on a sphere, SIAM J. Sci. Comput. 30 (2007), pp. 60-80.
31. B. Fornberg, E. Larsson, and N. Flyer, Stable computations with Gaussian radial basis functions, SIAM J. Sci. Comput. 33 (2011), pp. 869-892.
32. B. Fornberg, E. Lehto, and C. Powell, Stable calculation of Gaussian-based RBF-FD stencils, Comput. & Math. Appls 65 (2013), pp. 627-637.
33. R.F. Heinemann, K.A. Overholser, and G.W. Reddien, Multiplicity and stability of premixed laminar flames: an application of bifurcation theory, Chem. Engng Sci. 34 (1979), pp. 833-840.
34. S. Galant, Multiplicity and stability of burner stabilized premixed laminar flames: a general proof, Symp. (Int.) Combust. 18 (1981), pp. 1343-1353.
35. V. Bayona, M. Moscoso, and M. Kindelan, Gaussian RBF-FD weights and its corresponding local truncation errors, Engng Anal. with Bound. Elements 36 (2012), pp. 1361-1369.