An Alternative Strategy for the Solution of Heat and Incompressible Fluid Flow Problems via the Finite Volume Method

REFERENCES

• A. Ashrafizadeh , R. Mehdipour , and M. Rezvani , An Efficient and Accurate Numerical Simulation Method for the Paint Curing Process in Auto Industries, ICADME 2009: Proc. Int. Conf. on Applications and Design in Mechanical Eng. , Penang , Malaysia , pp. 3A1 – 3A6 , 2009 .
   Google Scholar
• S. Acharya , B. R. Baliga , K. Karki , J. Y. Murthy , C. Prakash , and S. P. Vanka , Pressure-Based Finite-Volume Methods in Computational Fluid Dynamics , J. of Heat Transfer , vol. 129 , pp. 407 – 424 , 2007 .
   Web of Science ®Google Scholar
• E. Isaacson , R. Courant , and M. Rees , On the Solution of Non-Linear Hyperbolic Differential Equations by Finite Differences , Comm. Pure Appl. Math. , vol. 5 , pp. 243 – 255 , 1952 .
   Web of Science ®Google Scholar
• D. B. Spalding , A Novel Finite Difference Formulation for Differential Equations Involving both First and Second Derivatives , Int. J. Numer. Meth. Eng. , vol. 4 , pp. 551 – 559 , 1972 .
   Google Scholar
• O. C. Zienkiewicz , R. L. Taylor , and P. Nithiarasu , The Finite Element Method for Fluid Dynamics, , 6th ed. , Butterworth and Heinemann , Oxford , 2005 .
   Google Scholar
• A. J. Chorin , Numerical Solution of Navier–Stokes Equations , Mathematics of Computation , vol. 22 , pp. 745 – 762 , 1968 .
   Web of Science ®Google Scholar
• G. E. Schneider , G. D. Raithby , and M. M. Yovanovich , Finite Element Analysis of Incompressible Flow Incorporating Equal Order Pressure and Velocity Interpolation , in C. Taylor , K. Morgan , and C. A. Rebbia (eds.), Numerical Methods in Laminar and Turbulent Flow, Proceedings of the First International Conference, University College Swansea , Swansea , UK , 1978 .
   Google Scholar
• B. Ramaswamy , Finite Element Solution for Advection and Natural Convection Flows, Comp. Fluids , vol. 16, pp. 349–388, 1988.
   Web of Science ®Google Scholar
• R. Rannacher , On Chorin Projection Method for the Incompressible Navier–Stokes Equations , Lecture Notes in Mathematics , vol. 1530 , pp. 167 – 183 , 1993 .
   Web of Science ®Google Scholar
• O. C. Zienkiewicz and R. Codina , A General Algorithm for Compressible, and Incompressible Flow, Part I. The split Characteristic Based Scheme , Int. J. Numer. Meth. Fluids , vol. 20 , pp. 869 – 85 , 1995 .
   Web of Science ®Google Scholar
• O. C. Zienkiewicz , P. Nithiarasu , R. Codina , M. Vázque , and P. Ortiz , The Characteristic Based Split Procedure: An Efficient and Accurate Algorithm for Fluid Problems , Int. J. Numer. Meth. Fluids , vol. 31 , pp. 359 – 392 , 1999 .
   Web of Science ®Google Scholar
• P. Nithiarasu , R. Codina , and O. C. Zienkiewicz , The Characteristic-Based Split (CBS) Scheme—A Unified Approach to Fluid Dynamics , Int. J. Numer. Meth. Eng. , vol. 66 , pp. 1514 – 1546 , 2006 .
   Web of Science ®Google Scholar
• P. Nithiarasu , A Unified Fractional Step Method for Compressible and Incompressible Flows , Heat Transfer and Incompressible Solid Mechanics , vol. 18 , pp. 111 – 130 , 2008 .
   Web of Science ®Google Scholar
• A. Shamekhi and K. Sadeghy , On the use of Characteristic-Based Split Mesh-Free Method for Solving Flow Problems , Int. J. Numer. Meth. Fluids , vol. 56 , pp. 1885 – 1907 , 2008 .
   Web of Science ®Google Scholar
• M. Nickaeen and A. Ashrafizadeh , A Semi-Implicit CBS Finite Volume Algorithm for the Solution of Incompressible Flow Problems, CFDSC2010: Proc. 18th Annual Conf. of the CFD Society of Canada , London , Canada , vol. 1 , 2010 .
   Google Scholar
• M. Nickaeen and A. Ashrafizadeh , A Characteristic-Based Split Finite Volume Algorithm for the Solution of Incompressible Flow Problems, ECCOMAS CFD 2010: Proc. 5th European Conf. on Computational Fluid Dynamics , Lisbon , Portugal , vol. 1 , pp. 177 , 2010 .
   Google Scholar
• M. Nickaeen and A. Ashrafizadeh , Comparison between Two Characteristic-Based Split Finite Volume Methods for the Solution of Incompressible Flow Problems, FD2010: Proc. 13th Annual & 2nd International Fluid Dynamics Conf. , Shiraz , Iran , vol. 1 , pp. 33 , 2010 .
   Google Scholar
• R. W. Lewis , P. Nithiarasu , and K. N. Seetharamu , Fundamentals of the Finite Element Method for Heat and Fluid Flow , Wiley , Chichester, West Sussex , England , 2004 .
   Google Scholar
• U. Ghia , K. N. Ghia , and C. T. Shin , High-Resolution for Incompressible Flow using the Navier–Stokes Equations and Multigrid Method , J. Comp. Phys. , vol. 48 , pp. 387 – 411 , 1982 .
   Web of Science ®Google Scholar
• B. F. Armaly , F. Durst , J. C. F. Pereira , and B. Schoenung , Experimental and Theoretical Investigation of Backward-Facing Step Flow , J. Fluid Mech. , vol. 127 , pp. 473 – 496 , 1983 .
   Web of Science ®Google Scholar
• D. de Vahl Davis , Natural Convection of Air in a Square Cavity: A Benchmark Solution , Int. J. Numer. Meth. Fluids , vol. 3 , pp. 249 – 264 , 1983 .
   Web of Science ®Google Scholar
• D. C. Wan , B. S. V. Patnaik , and G. W. Wei , A New Benchmark Quality Solution for the Buoyancy-Driven Cavity by Discrete Singular Convolution , Numer. Heat Transfer B , vol. 40 , pp. 199 – 228 , 2001 .
   Web of Science ®Google Scholar