FINITE-ELEMENT MULTIGRID SCHEME FOR THE NAVIER-STOKES SOLUTIONS, PART II: FORMULATION AND VALIDATION

REFERENCES

• Y. Li , J. Peiró , and C. H. Liu , Finite-Element Multigrid Scheme for the Navier-Stokes Solutions, Part I New Unstructured Mesh Generation Based on Contour Refinement , Numer. Heat Transfer B , vol. 34 , pp. 61 – 80 , 1998 .
   Web of Science ®Google Scholar
• A. Jameson , T. J. Baker , and N. P. Weatherill , Calculation of Inviscid Transonic Flow over a Complete Aircraft , AIAA Paper 86–0103 , 1986 .
   Google Scholar
• D. J. Mavriplis , A. Jameson , and L. Martinelli , Multigrid Solution of the Navier-Stokes Equations on Triangular Meshes , AIAA Paper 89–0120 , 1989 .
   Google Scholar
• J. Peraire , K. Morgan , J. Peiró , A 3D Finite Element Multigrid Solver for the Euler Equations , AIAA Paper 92–0449 , 1992 .
   Google Scholar
• J. Peraire , K. Morgan , M. Vahdati , and J. Peiró , The Construction and Behavior of Some Unstructured Grid Algorithms for Compressible Flows , Proc. ICFD Conf. on Numerical Methods for Fluid Dynamics , 1992 .
   Google Scholar
• A. Bowyer , Computing Dirichlet Tessellations , Comput. J. , vol. 24 , pp. 162 – 166 , 1981 .
   Web of Science ®Google Scholar
• P. J. Green and R. Sibson , Computing Dirichlet Tessellations in the Plane , Comput. J. , vol. 21 , pp. 168 – 173 , 1978 .
   Web of Science ®Google Scholar
• J. Peiró , A Finite Element Procedure for the Solution of the Euler Equations on Unstructured Meshes , Ph.D. thesis , University of Wales , Swansea , Wales , 1989 .
   Google Scholar
• D. F. Watson , Computing the n-Dimensional Delaunay Tessellation with Application to Voronoi Polytopes , Comput. J. , vol. 24 , pp. 167 – 172 , 1981 .
   Web of Science ®Google Scholar
• O. Hassan , K. Morgan , and J. Peraire , An Adaptive Implicit/ Explicit Finite Element Scheme for Compressible Viscous high Speed Flows , AIAA Paper 89–0363 , 1989 .
   Google Scholar
• S. Pirzadeh , Unstructured Viscous Grid Generation by the Advancing Layer Method , AIAA J. , vol. 32 , pp. 1735 – 1737 , 1989 .
   Google Scholar
• S. Soltani , An Upwind Scheme for the Equations of Compressible Flow on Unstructured Grids . Ph.D. thesis , Imperial College , London , 1991 .
   Google Scholar
• R. R. Thareja , R. K. Prabhu , K. Morgan , J. Peraire , J. Peiró , and S. Soltani , Application of an Adaptive Unstructured Solution Algorithm to the Analysis of High Speed Flows , AIAA Paper 90–0395 , 1990 .
   Google Scholar
• J. Peraire , K. Morgan , and J. Peiró , A 3D Finite Element Multigrid Solver for the Euler Equations . AIAA Paper 92–0449 , 1992 .
   Google Scholar
• H. C. Yee , Construction of Explicit and Implicit Symmetric TVD Schemes and Their Applications , J. Comput. Phys. , vol. 68 , pp. 151 – 179 , 1987 .
   Web of Science ®Google Scholar
• M. S. Liou and C. J. Steffen , A New Flux Splitting Scheme , J. Comput. Phys. , vol. 107 , pp. 23 – 39 , 1993 .
   Web of Science ®Google Scholar
• B. S. Baldwin and H. Lomax , Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows , AIAA Paper 78–257 , 1978 .
   Google Scholar
• B. S. Baldwin and T. J. Barth , A One Equation Turbulence Transport Model for High Reynolds Number Wall Bounded Flows , AIAA Paper 91–0610 , 1991 .
   Google Scholar
• D. J. Mavriplis , Algebraic Turbulence Modeling for Unstructured and Adaptive Meshes , AIAA Paper 90–1563 , 1990 .
   Google Scholar
• P. Rostand , Algebraic Turbulence Models for the Computation of Two Dimensional High Speed Flows Using Unstructured Grids , ICASE Report 88–63 , 1988 .
   Google Scholar
• B. E. Launder and D. B. Spalding , Mathematical Models of Turbulence. Academic Press , 1972 .
   Google Scholar
• M. Giles , Energy Stability Analysis of Multi-Step Methods on Unstructured Meshes , Technical Report CFDL-TR-87–1 , Massachusetts Institute of Technology , Cambridge , MA , 1987 .
   Google Scholar
• H. Schlichting , Boundary Layer Theory , McGraw-Hill , New York , 1968 .
   Google Scholar
• F. M. White , Viscous Fluid Flow , 2d ed. , McGraw-Hill , New York , 1991 .
   Google Scholar
• T. J. Barth , Numerical Aspects of Computing Viscous High Reynolds Number Flows on Unstructured Meshes , AIAA Paper 91–0721 , 1991 .
   Google Scholar
• P. H. Cook , M. A. McDonald , and M. C. P. Firmin , Airfoil RAE2822 Pressure Distributions and Boundary Layer and Wake Measurements , AGARD Advisory Report No. 139 , 1979 .
   Google Scholar
• Address correspondence to Dr. Chung-Ho Liu, Chung Cheng Institute of Technology, Department of Aeronautical Engineering, Ta-Hsi, Tao-Yuan, 33509, Taiwan, Republic of China. E-mail: [email protected].
   Google Scholar