TECHNIQUE FOR RAPID CONVERGENCE OF THE PENALTY FINITE-ELEMENT METHOD WITH A MODIFIED GALERKIN SCHEME AND ITS APPLICATION TO NATURAL CONVECTION

REFERENCES

• H. Sayama , H. Ozoe , and Y. Kameyama , Penalty Method for Nonlinear Programming , Trans. Soc. Instrum. Control Eng. Jpn. , vol. 9 , no. 1 , pp. 100 – 107 , 1973 .
   Google Scholar
• T. J. R. Hughes , W. K. Liu , A. Brooks . Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation , J. Comp. Phys. , vol. 30 , pp. 1 – 60 , 1979 .
   Web of Science ®Google Scholar
• R. S. Marshall , J. C. Heinrich , and O. C. Zienkiewicz , Natural Convection in a Square Enclosure by a Finite Element, Penalty Function Method, Using Primitive Fluid Variables . Numer. Heat Transfer , vol. 1 , pp. 315 – 330 , 1978 .
   Google Scholar
• J. C. Heinrich and M. Strada , Penalty Finite Element Analysis of Natural Convection at High Rayleigh Numbers , in R. H. Gallagher et al., eds., Finite Elements in Fluids , vol. 4 , Wiley , New York , 1982 .
   Google Scholar
• J. N. Reddy and A. Satake , A Comparison of a Penalty Finite Element Model with the Stream Function-Vorticity Model of Natural Convection in Enclosures , J. Heat Transfer , vol. 102 , pp. 659 – 666 , 1980 .
   Web of Science ®Google Scholar
• C. D. Upson , P. M. Gresho , and R. L. Lee , Finite Element Simulations of Thermally Induced Convection in an Enclosed Cavity, in J. P. Jones and C. P. Thompson , eds., Numerical Solutions for a Comparison Problem on Natural Convection in an Enclosed Cavity , pp. 152–163, AERE Harwell , 1981.
   Google Scholar
• G. De Vahl Davis and I. P. Jones , Natural Convection in a Square Cavity A Comparison Problem , Proc. 2nd Int. Conf. on Numerical Methods in Heat Transfer , Venice , 1981 .
   Google Scholar
• E. L. Koshmieder , Benard Convection , Adv. Chem. Phys. , vol. 26 , pp. 177 – 211 , 1974 .
   Google Scholar
• R. Temam , Navier-Stokes Equations , North-Holland , Amsterdam , 1977 .
   Google Scholar
• O. C. Zienkiewicz , The Finite Element Method, , 3d ed. , McGraw-Hill , New York , 1977 .
   Google Scholar
• A. J. Baker , Finite Element Computational Fluid Mechanics , Hemisphere , Washington , D.C. , 1983 .
   Google Scholar
• S. W. Churchill , P. Chao , and H. Ozoe , Extrapolation of Finite Difference Calculations of Laminar Natural Convection in Enclosures to Zero Grid Size , Numer. Heat Transfer , vol. 4 , pp. 39 – 51 , 1981 .
   Google Scholar
• H. Ozoe , A. Mouri , M. Ohmuro , S. W. Churchill , and N. Lior , Numerical Calculations of Laminar and Turbulent Natural Convection in Water in Rectangular Channels Heated and Cooled Isothermally on the Opposing Vertical Walls , Int. J. Heat Mass Transfer , vol. 28 , no. 1 , pp. 124 – 138 , 1985
   Web of Science ®Google Scholar
• A. Emery and N. C. Chu , Heat Transfer across Vertical Layers , J. Heat Transfer , Ser. C , vol. 87 , pp. 110 – 116 , 1965 .
   Web of Science ®Google Scholar
• S. W. Churchill , Free Convection in Layers and Enclosures in E. U. Schlünder, ed. , Heat Exchanger Design Handbook , Section 2.5.8 , Hemisphere , Washington , D.C. , 1982 .
   Google Scholar
• T. Fujii , M. Takeuchi , M. Fujii , K. Suzaki , and H. Uehara , Experiments on Natural Convection Heat Transfer from the Outer Surface of a Vertical Cylinder to Liquids , Int. J. Heat Mass Transfer , vol. 13 , pp. 753 – 787 , 1970 .
   Web of Science ®Google Scholar
• R. Cheesewright , Turbulent Natural Convection from a Vertical Plane Surface , J, Heat Transfer , vol. 90C , pp. 1 – 8 , 1968 .
   Web of Science ®Google Scholar
• A. Pirovano , S. Viannay , and M. Jannot , Convection naturelle en regime turbulent le long d'une plaque plane verticale , Heat Transfer 1970 , vol. 4 , NC.1.8, Paris-Versailles , 1970 .
   Google Scholar
• H. Ozoe , M. Ohmuro , A. Mouri , S. Mishima , H. Sayama , and S. W. Churchill , Laser-Doppler Measurement of the Velocity along a Heated Vertical Wall of a Rectangular Enclosure , J. Heat Transfer, Trans. ASME , vol. 105 , no. 4 , pp. 782 – 788 , 1983 .
   Web of Science ®Google Scholar
• P. L. Silveston , Wärmedurchgang in wargerechten flüssigheitsschichten , Forsch. Ingenieurwes. , vol. 24 , pp. 59 – 69 , 1958 .
   Google Scholar
• H. Bertin and H. Ozoe , Numerical Study of Two-Dimensional Natural Convection in a Horizontal Fluid Layer Heated from Below Influence of Prandtl Number , Int. J. Heat Mass Transfer , vol. 29 , no. 3 , pp. 439 – 449 , 1986 .
   Web of Science ®Google Scholar