Extending a Hybrid Finite-Volume-Element Method to Solve Laminar Diffusive Flame

REFERENCES

• S. V. Patankar and D. B. Spalding , A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows , Int. J. Heat Mass Transfer , vol. 15 , pp. 1787 – 1806 , 1972 .
   Web of Science ®Google Scholar
• G. E. Schneider and M. J. Raw , Control Volume Finite Element Method for Heat Transfer and Fluid Flow Using Co-located Variables—1. Computational Procedure, Numer. Heat Transfer , vol. 11, pp. 363–390, 1987.
   Web of Science ®Google Scholar
• M. Darbandi and G. E. Schneider , Momentum Variable Procedure for Solving Compressible and Incompressible Flows , AIAA J. , vol. 35 , pp. 1801 – 1805 , 1997 .
   Google Scholar
• M. Darbandi and G. E. Schneider , Analogy-Based Method for Solving Compressible and Incompressible Flows , J. Thermophys. Heat Transfer B , vol. 12 , pp. 239 – 247 , 1998 .
   Web of Science ®Google Scholar
• M. Darbandi and S. M. Bostandoost , A New Formulation toward Unifying the Velocity Role in Collocated Variable Arrangement , Numer. Heat Transfer B , vol. 47 , pp. 361 – 382 , 2005 .
   Web of Science ®Google Scholar
• W. E and C. W. Shu , A Numerical Resolution Study of High Order Essentially Non-oscillatory Schemes Applied to Incompressible Flow , J. Comput. Phys. , vol. 110 , pp. 39 – 46 , 1994 .
   Web of Science ®Google Scholar
• J. Y. Yang , S. C. Yang , Y. N. Chen , and C. A. Hsu , Implicit Weighted ENO Schemes for the Three-Dimensional Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 146 , pp. 464 – 487 , 1998 .
   Web of Science ®Google Scholar
• A. Sbaibi and W. P. Manno , On the Accuracy of Upwind and Symmetric TVD Schemes in Simulating Low Mach Number Flow , Int. J. Comput. Fluid Dynam. , vol. 13 , pp. 125 – 142 , 2000 .
   Web of Science ®Google Scholar
• J. Luo , L. Xuan , and K. Xu , Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation , Commun. Comput. Phys. , vol. 14 , pp. 599 – 620 , 2013 .
   Web of Science ®Google Scholar
• P. Tsoutsanis , A. F. Antoniadis , and D. Drikakis , WENO Schemes on Arbitrary Unstructured Meshes for Laminar, Transitional and Turbulent Flows , J. Comput. Phys. , vol. 256 , pp. 254 – 276 , 2014 .
   Web of Science ®Google Scholar
• B. R. Baliga and S. V. Patankar , A New Finite-Element Formulation for Convection-Diffusion Problems , Numer. Heat Transfer , vol. 3 , pp. 393 – 409 , 1980 .
   Google Scholar
• G. D. Raithby , Skew Upstream Differencing Schemes for Problems Involving Fluid Flow , J. Comput. Meth. Appl. Mech. Eng. , vol. 9 , pp. 153 – 164 , 1976 .
   Google Scholar
• B. R. Baliga and S. V. Patankar , A Control Volume Finite-Element Method for Two-Dimensional Fluid Flow and Heat Transfer , Numer. Heat Transfer , vol. 6 , pp. 245 – 261 , 1983 .
   Google Scholar
• C. Prakash and S. V. Patankar , A Control Volume-Based Finite Element Method for Solving the Navier-Stokes Equations Using Equal-Order Velocity-Pressure Interpolation , Numer. Heat Transfer , vol. 8 , pp. 259 – 280 , 1985 .
   Web of Science ®Google Scholar
• N. A. Hookey , B. R. Baliga , and C. Prakash , Evaluation and Enhancemenets of Some Control Volume Finite-Element Methods. Part 1. Convection-Diffusion Problems , Numer. Heat Transfer , vol. 14 , pp. 255 – 272 , 1988 .
   Web of Science ®Google Scholar
• N. A. Hookey and B. R. Baliga , Evaluation and Enhancemenets of Some Control Volume Finite-Element Methods. Part 2. Incompressible Fluid Flow Problems , Numer. Heat Transfer , vol. 14 , pp. 273 – 293 , 1988 .
   Web of Science ®Google Scholar
• C. F. Kettleborough , S. R. Husain , and C. Prakash , Solution of Fluid Flow Problems with the Vorticity-Streamfunction Formulation and the Control-Volume-Based Finite-Element Method , Numer. Heat Transfer B , vol. 16 , pp. 31 – 58 , 1989 .
   Web of Science ®Google Scholar
• D. Elkaim , M. Reggio , and R. Camarero , Numerical Solution of Reactive Laminar Flow by a Control Volume Based Finite Element Method and the Vorticity-Streamfunction Formulation , Numer. Heat Transfer B , vol. 20 , pp. 223 – 240 , 1991 .
   Web of Science ®Google Scholar
• G. E. Schneider and S. M. H. Karimian , Advances in Control-Volume Based Finite-Element Methods for Compressible Flows , Comput. Mech. , vol. 14 , pp. 431 – 446 , 1994 .
   Web of Science ®Google Scholar
• M. Darbandi , and G. E. Schneider , Application of an All-Speed Flow Algorithm to Heat Transfer Problems , Numer. Heat Transfer A , vol. 35 , pp. 695 – 715 , 1999 .
   Web of Science ®Google Scholar
• M. Darbandi and G. E. Schneider , Performance of an Analogy-Based All-Speed Procedure without any Explicit Damping, Comput. Mech. , vol. 26, pp. 459–469, 2000.
   Web of Science ®Google Scholar
• M. Darbandi and A. Naderi , Multiblock Hybrid Grid Finite Volume Method to Solve Flow in Irregular Geometries , Comput. Meth. Appl. Mech. Eng. , vol. 196 , pp. 321 – 336 , 2006 .
   Web of Science ®Google Scholar
• L. D. Tran , C. Masson , and A. Smaili , A Stable Second-Order Mass-Weighted Upwind Scheme for Unstructured Meshes , Int. J. Numer. Meth. Fluids , vol. 51 , pp. 749 – 771 , 2006 .
   Web of Science ®Google Scholar
• M. Darbandi , S. Vakili , and G. E. Schneider , Efficient Multilevel Restriction-Prolongation Expressions for Hybrid Finite Volume Element Method , Int. J. Comput. Fluid Dynam. , vol. 22 , pp. 29 – 38 , 2008 .
   Web of Science ®Google Scholar
• A. Naderi , M. Darbandi , and M. Taeibi-Rahni , Developing a Unified FVE-ALE Approach to Solve Unsteady Fluid Flow with Moving Boundaries , Int. J. Numer. Meth. Fluids , vol. 63 , pp. 40 – 68 , 2010 .
   Web of Science ®Google Scholar
• H. Tan and K. M. Pillai , Numerical Simulation of Reactive Flow in Liquid Composite Molding Using Flux-Corrected Transport (FCT) Based Finite Element/Control Volume (FE/CV) Method , Int. J. Heat Mass Transfer , vol. 53 , pp. 2256 – 2271 , 2010 .
   Web of Science ®Google Scholar
• P. Theeraek , S. Phongthanapanich , and P. Dechaumphai , Solving Convection-Diffusion-Reaction Equation by Adaptive Finite Volume Element Method , Math. Comput. Simul. , vol. 82 , pp. 220 – 233 , 2011 .
   Web of Science ®Google Scholar
• R. Nasrin and M. A. Alim , Control Volume Finite Element Simulation of MHD Forced and Natural Convection in a Vertical Channel with a Heat-Generating Pipe , Int. J. Heat Mass Transfer , vol. 55 , pp. 2813 – 2821 , 2012 .
   Web of Science ®Google Scholar
• M. Darbandi and G. E. Schneider , Thermobuoyancy Treatment for Electronic Packaging Using an Improved Advection Scheme , ASME J. Electron. Packaging , vol. 125 , pp. 244 – 250 , 2003 .
   Web of Science ®Google Scholar
• M. Darbandi and S. F. Hosseinizadeh , A Two-Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows , J. Aerospace Sci. Technol. , vol. 2 , pp. 37 – 44 , 2005 .
   Google Scholar
• H. Paillere , P. Le Quere , C. Weisman , J. Vierendeels , E. Dick , M. Braack , F. Dabbene , A. Beccantini , E. Studer , T. Kloczko , C. Corre , V. Heuveline , M. Darbandi , and S. F. Hosseinizadeh , Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers , Math. Model. Numer. Anal. , vol. 39 , pp. 617 – 621 , 2005 .
   Web of Science ®Google Scholar
• M. Darbandi and S. F. Hosseinizadeh , Numerical Simulation of Thermobuoyant Flow with Large Temperature Variation , J. Thermophys. Heat Transfer , vol. 20 , pp. 285 – 296 , 2006 .
   Web of Science ®Google Scholar
• M. Alipanah , P. Hasannasab , S. F. Hosseinizadeh , and M. Darbandi , Entropy Generation for Compressible Natural Convection with High Gradient Temperature in a Square Cavity , Int. Commun. Heat Mass Transfer , vol. 37 , pp. 1388 – 1395 , 2010 .
   Web of Science ®Google Scholar
• S. F. Hosseinizadeh , M. Darbandi , and M. Heidarnataj , Numerical Study of High Gradient Thermobuoyant Flow in a Tilted Cavity Using a Novel Non-Boussinesq Algorithm , Numer. Heat Transfer A , vol. 58 , pp. 984 – 1003 , 2010 .
   Web of Science ®Google Scholar
• R. Knikker , A Comparative Study of High-Order Variable-Property Segregated Algorithms for Unsteady Low Mach Number Flows , Int. J. Numer. Meth. Fluids , vol. 66 , pp. 403 – 427 , 2011 .
   Web of Science ®Google Scholar
• S. R. Lee and J. S. Kim , Analysis of Premixed-Flame Propagation in Media with Periodic Flame-Speed Variations Using the Level-Set Equation , Combustion Theory Model. , vol. 8 , pp. 123 – 140 , 2004 .
   Web of Science ®Google Scholar
• B. Lessani and M. V. Papalexanddris , Time-Accurate Calculation of Variable Density Flows with Strong Temperature Gradients and Combustion , J. Comput. Phys. , vol. 212 , pp. 218 – 246 , 2006 .
   Web of Science ®Google Scholar
• E. Barrios , J. C. Prince , and C. Trevino , The Role of Duct Thickness on the Quenching Process of Premixed Flame Propagation , Combustion Theory Model. , vol. 12 , pp. 115 – 133 , 2008 .
   Web of Science ®Google Scholar
• J. Li , S. K. Chou , Z. W. Li , and W. M. Yang , A Comparative Study of H2-Air Premixed Flame in Micro Combustors with Different Physical and Boundary Conditions, Combustion Theory Model. , vol. 12, pp. 325–347, 2008.
   Web of Science ®Google Scholar
• G. Ni , S. Jiang , and K. Xu , A DGBGK Scheme Based on WENO Limiters for Viscous and Inviscid Flows , J. Comput. Phys. , vol. 227 , pp. 5799 – 5815 , 2008 .
   Web of Science ®Google Scholar
• C. Duwig , A Filtered Flame Approach for Simulation of Unsteady Laminar Premixed Flames , Combustion Theory Model. , vol. 13 , pp. 251 – 268 , 2009 .
   Web of Science ®Google Scholar
• C. E. Zambra , N.O. Moraga , and M. Escudey , Heat and Mass Transfer in Unsaturated Porous Media: Moisture Effects in Compost Piles Self-Heating , Int. J. Heat Mass Transfer , vol. 54 , pp. 2801 – 2810 , 2011 .
   Web of Science ®Google Scholar
• S. Chander and A. Ray , Experimental and Numerical Study on the Occurrence of Off-Stagnation Peak in Heat Flux for Laminar Methane/Air Flame Impinging on a Flat Surface , Int. J. Heat Mass Transfer , vol. 54 , pp. 1179 – 1186 , 2011 .
   Web of Science ®Google Scholar
• H. Ebrahimi-Kebria , M. Darbandi , and S. F. Hosseinizadeh , Numerical Simulation of Low-Mach-Number Laminar Mixing and Reacting Flows Using a Dual-Purpose Pressure-Based Algorithm , Numer. Heat Transfer B , vol. 59 , pp. 495 – 514 , 2011 .
   Web of Science ®Google Scholar
• J. L. Ziegler , R. Deiterding , J. E. Shepherd , and D. I. Pullin , An Adaptive High-Order Hybrid Scheme for Compressive, Viscous Flows with Detailed Chemistry , J. Comput. Phys. , vol. 230 , pp. 7598 – 7630 , 2011 .
   Web of Science ®Google Scholar
• P. Gerlinger , Multi-Dimensional Limiting for High-Order Schemes Including Turbulence and Combustion , J. Comput. Phys. , vol. 231 , pp. 2199 – 2228 , 2012 .
   Web of Science ®Google Scholar
• C. Wang , W. Han , J. Ning , and Y. Yang , High Resolution Numerical Simulation of Methane Explosion in Bend Ducts , Safety Sci. , vol. 50 , pp. 709 – 717 , 2012 .
   Web of Science ®Google Scholar
• M. Karaca , N. Lardjane , and I. Fedioun , Implicit Large Eddy Simulation of High-Speed Non-Reacting and Reacting Air/H2 Jets with a 5th Order WENO Scheme , Comput. Fluids , vol. 62 , pp. 25 – 44 , 2012 .
   Web of Science ®Google Scholar
• K. Luo , T. Jin , S. Lu , and J. Fan , DNS Analysis of a Three-Dimensional Supersonic Turbulent Lifted Jet Flame , Fuel , vol. 108 , pp. 691 – 698 , 2013 .
   Web of Science ®Google Scholar
• D. G. Elliman , D. E. Fussey , and N. Hay , Predictions, and Measurements of a Turbulent Axisymmetric Ducted Diffusion Flame , Int. J. Heat Mass Transfer , vol. 21 , pp. 1393 – 1402 , 1978 .
   Web of Science ®Google Scholar
• X. Zhou , Z. Sun , G. Brenner , and F. Durst , Combustion Modeling of Turbulent Jet Diffusion H2/Air Flame with Detailed Chemistry , Int. J. Heat Mass Transfer , vol. 43 , pp. 2075 – 2088 , 2000 .
   Web of Science ®Google Scholar
• X. Xu , Y. Chen , and H. Wang , Detailed Numerical Simulation of Thermal Radiation Influence in Sandia Flame D , Int. J. Heat Mass Transfer , vol. 49 , pp. 2347 – 2355 , 2006 .
   Web of Science ®Google Scholar
• L. Y. Jiang and I. Campbell , Reynolds Analogy in Combustor Modeling , Int. J. Heat Mass Transfer , vol. 51 , pp. 1251 – 1263 , 2008 .
   Web of Science ®Google Scholar
• K. H. Lee and S. W. Baek , Inverse Estimation of Inlet Parameters in An Axi-symmetric Cylindrical Combustor with Thermal Radiation Effect , Int. J. Heat Mass Transfer , vol. 54 , pp. 5386 – 5394 , 2011 .
   Web of Science ®Google Scholar
• K. K. Kuo , Principles of Combustion , pp. 366 – 368 , John Wiley , New York , 1987 .
   Google Scholar
• C. E. Baukal , Jr. , V. Y. Gershtein , and X. Li , Computational Fluid Dynamics in Industrial Combustion , CRC Press , Boca Raton , FL , 2001 .
   Google Scholar
• M. Darbandi and V. Mokarizadeh , A Modified Pressure-Based Algorithm to Solve the Flow Fields with Shock and Expansion Waves , Numer. Heat Transfer B , vol. 46 , pp. 497 – 504 , 2004 .
   Web of Science ®Google Scholar
• M. Darbandi , E. Roohi , and V. Mokarizadeh , Conceptual Linearization of Euler Governing Equations to Solve High Speed Compressible Flow Using a Pressure-Based Method , Numer. Meth. Part D. E., No. 2 , vol. 24 , pp. 583 – 604 , 2008 .
   Web of Science ®Google Scholar
• B. Epstein and S. Peigin , Short Communication: Application of WENO (Weighted Essentially Non-oscillatory) Approach to Navier–Stokes Computations, Int. J. Comput. Fluid Dynam. , vol. 18, pp. 289–293, 2004.
   Web of Science ®Google Scholar
• V. Daru and C. Tenaud , High Order One-Step Monotonicity Preserving Schemes for Unsteady Flow Calculations , J. Comput. Phys. , vol. 193 , pp. 563 – 594 , 2004 .
   Web of Science ®Google Scholar
• D. Kim and J. H. Kwon , A High-Order Accurate Hybrid Scheme Using a Central Flux Scheme and a WENO Scheme for Compressible Flowfield Analysis , J. Comput. Phys. , vol. 210 , pp. 554 – 583 , 2005 .
   Web of Science ®Google Scholar
• S. Kurioka and D. R. Dowling , Numerical Simulation of Free Surface Flows with the Level Set Method Using an Extremely High-Order Accuracy WENO Advection Scheme , Int. J. Comput. Fluid Dynam. , vol. 23 , pp. 233 – 243 , 2009 .
   Web of Science ®Google Scholar
• T. Driessen and R. Jeurissen , A Regularised One-Dimensional Drop Formation and Coalescence Model Using a Total Variation Diminishing (TVD) Scheme on a Single Eulerian Grid , Int. J. Computat. Fluid Dynam. , vol. 25 , pp. 333 – 343 , 2011 .
   Web of Science ®Google Scholar
• C. M. Rhie and W. L. Chow , Numerical Study of the Turbulent Flow past an Airfoil with Trailing Edge Separation , AIAA J. , vol. 21 , pp. 1525 – 1532 , 1983 .
   Google Scholar
• T. F. Miller and F. W. Schmidt , Use of a Pressure-Weighted Interpolation Method for the Solution of the Incompressible Navier-Stokes Equations on a Nonstaggered Grid System , Numer. Heat Transfer , vol. 14 , pp. 213 – 233 , 1988 .
   Web of Science ®Google Scholar
• M. Peric , R. Kessler , and G. Scheuerer , Comparison of Finite-Volume Numerical Methods with Staggered and Colocated Grids , Comput. Fluids , vol. 16 , pp. 389 – 403 , 1988 .
   Web of Science ®Google Scholar
• S. Majumdar , Role of Underrelaxation in Momentum Interpolation for Calculation of Flow with Nonstaggered Grids , Numer. Heat Transfer , vol. 13 , pp. 125 – 132 , 1988 .
   Web of Science ®Google Scholar
• M. Darbandi and S. Vakilipour , Developing Implicit Pressure-Weighted Upwinding Scheme to Calculate Steady and Unsteady Flows on Unstructured Grids , Int. J. Numer. Meth. Fluids , vol. 56 , pp. 115 – 141 , 2008 .
   Web of Science ®Google Scholar
• M. Darbandi and N. Fouladi , A Reduced Domain Strategy for Local Mesh Movement Application in Unstructured Grids , Appl. Numer. Math. , vol. 61 , pp. 1001 – 1016 , 2011 .
   Web of Science ®Google Scholar
• M. Darbandi and N. Fouladi , Developing an Ordering-Based Renumbering Approach for Triangular Unstructured Grids , Eng. Comput. , vol. 29 , pp. 225 – 243 , 2013 .
   Web of Science ®Google Scholar
• K. A. Hoffmann and S. T. Chiang , Computational Fluid Dynamics , 4th ed., vol. 1, chapter 2, Engineering Education System, Wichita, Kansas, 2000 .
   Google Scholar
• F. Durst and T. Loy , Investigation of Laminar Flow in Pipe with Sudden Contraction of Cross Sectional Area , Comput. Fluids , vol. 13 , pp. 15 – 36 , 1985 .
   Web of Science ®Google Scholar
• R. E. Mitchell , A. F. Sarofim , and L. A. Clomburg , Experimental and Numerical Investigation of Confined Laminar Flames , Combustion & Flame , vol. 37 , pp. 227 – 244 , 1980 .
   Web of Science ®Google Scholar
• T. Poinsot and D. Veynante , Theoretical and Numerical Combustion , Chapter 3 , R.T. Edwards Inc , Philadelphia, PA , 2001 .
   Google Scholar
• C. K. Law , Combustion Physics , p. 195 , Cambridge University Press , New York , 2006 .
   Google Scholar