A brief review of techniques for generating irregular computational grids

This review attempts to place in perspective the wide variety of computer methods which are available for constructing irregular computational grids. Several different approaches exist for each aspect of the construction task: creation of the points, recognition of neighbouring points that define grid elements, enumeration of the points with indices, optimization of the positions of the points for computational advantage, and variation of point density throughout the grid.

[1]  Akio Arakawa,et al.  Integration of the Nondivergent Barotropic Vorticity Equation with AN Icosahedral-Hexagonal Grid for the SPHERE1 , 1968 .

[2]  Elizabeth Cuthill,et al.  Several Strategies for Reducing the Bandwidth of Matrices , 1972 .

[3]  Robert Kao,et al.  A General Finite Difference Method for Arbitrary Meshes , 1975 .

[4]  A. Bykat,et al.  Automatic generation of triangular grid: I—subdivision of a general polygon into convex subregions. II—triangulation of convex polygons , 1976 .

[5]  V. M. Fomin,et al.  Methods for the construction of moving grids for problems of fluid dynamics with big deformations , 1976 .

[6]  R. H. MacNeal,et al.  An asymmetrical finite difference network , 1953 .

[7]  J. M. Nelson.  A triangulation algorithm for arbitrary planar domains , 1978 .

[8]  W. J. Gordon,et al.  Construction of curvilinear co-ordinate systems and applications to mesh generation , 1973 .

[9]  E. G. Sewell,et al.  Automatic generation of triangulations for piecewise polynomial approximation , 1972 .

[10]  O. C. Zienkiewicz,et al.  An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co‐ordinates , 1971 .

[11]  Peter R. Eiseman,et al.  A multi-surface method of coordinate generation , 1979 .

[12]  N. Perrone,et al.  Finite difference energy techniques for arbitrary meshes applied to linear plate problems , 1979 .

[13]  R. Shaw,et al.  Modification to the Suhara‐Fukuda method of network generation , 1978 .

[14]  W. P. Crowley.  Flag: A free-Lagrange method for numerically simulating hydrodynamic flows in two dimensions , 1971 .

[15]  Thomas D. Brown,et al.  An implicit finite-difference method for solving the Navier-Stokes equation using orthogonal curvilinear coordinates , 1977 .

[16]  Jay P. Boris,et al.  The Lagrangian solution of transient problems in hydrodynamics using a triangular mesh , 1979 .

[17]  C. W. Hirt,et al.  A simple scheme for generating general curvilinear grids , 1973 .

[18]  David E Potter,et al.  The construction of discrete orthogonal coordinates , 1973 .

[19]  Lawrence L. Durocher,et al.  A versatile two-dimensional mesh generator with automatic bandwidth reduction , 1979 .

[20]  W. J. Gordon,et al.  Substructured macro elements based on locally blended interpolation , 1977 .

[21]  W. Thacker,et al.  Irregular Grid Finite-Difference Techniques: Simulations of Oscillations in Shallow Circular Basins , 1977 .

[22]  Georges Akhras,et al.  An automatic node relabelling scheme for minimizing a matrix or network bandwidth , 1976 .

[23]  B. A. Lewis,et al.  Triangulation of Planar Regions with Applications , 1978, Comput. J..

[24]  W. A. Cook.  Body oriented (natural) co-ordinates for generating three-dimensional meshes , 1974 .

[25]  Wen-Hwa Chu,et al.  Development of a general finite difference approximation for a general domain part I: Machine transformation , 1971 .

[26]  H. J. Haussling.  Boundary-fitted coordinates for accurate numerical solution of multibody flow problems , 1979 .

[27]  Werner C. Rheinboldt,et al.  Self-adaptive refinements in the finite element method , 1975 .

[28]  R. E. Jones.  A Self-Organizing Mesh Generation Program , 1974 .

[29]  C. O. Frederick,et al.  Two-dimensional automatic mesh generation for structural analysis (ijnme 2 (1970)) , 1970 .

[30]  R. Collins.  Bandwidth reduction by automatic renumbering , 1973 .

[31]  André Denayer.  Automatic generation of finite element meshes , 1978 .

[32]  W. C. Thacker.  Comparison of Finite-Element and Finite-Difference Schemes. Part II: Two-Dimensional Gravity Wave Motion , 1978 .

[33]  James C. Cavendish.  Local mesh refinement using rectangular blended finite elements , 1975 .

[34]  David L. Williamson,et al.  INTEGRATION OF THE PRIMITIVE BAROTROPIC MODEL OVER A SPHERICAL GEODESIC GRID , 1970 .

[35]  D. A. Caughey,et al.  A systematic procedure for generating useful conformal mappings , 1978 .

[36]  J. A. George.  Computer implementation of the finite element method , 1971 .

[37]  C. A. Hall,et al.  Numerical Solution of Steady State Heat Flow Problems Over Curved Domains , 1976, TOMS.

[38]  Stephen B. Pope,et al.  The calculation of turbulent recirculating flows in general orthogonal coordinates , 1978 .

[39]  R. Meyder,et al.  Solving the Conservation Equations in Fuel Rod Bundles Exposed to Parallel Flow by Means of Curvilinear-Orthogonal Coordinates , 1975 .

[40]  T. S. Murty,et al.  A Numerical Model for Wind-Driven Circulation in Lakes Michigan and Huron , 1974 .

[41]  S. K. Godunov,et al.  The use of moving meshes in gas-dynamical computations☆ , 1972 .

[42]  W. D Barfield,et al.  An optimal mesh generator for Lagrangian hydrodynamic calculations in two space dimensions , 1970 .

[43]  S. A. Coons.  SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS , 1967 .

[44]  G. Steinmueller.  Restrictions in the application of automatic mesh generation schemes by ‘isoparametric’ co-ordinates , 1974 .

[45]  Pedro V. Marcal,et al.  Optimization of Finite Element Grids Based on Minimum Potential Energy. , 1973 .

[46]  J. Cavendish.  Automatic triangulation of arbitrary planar domains for the finite element method , 1974 .

[47]  C. Wayne Mastin,et al.  TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies , 1977 .

[48]  William H. Frey,et al.  Flexible finite‐difference stencils from isoparametric finite elements , 1977 .

[49]  S. Park,et al.  Drag method as a finite element mesh generation scheme , 1979 .

[50]  P.C.M Lau.  Curvilinear finite difference method for three-dimensional potential problems , 1979 .

[51]  Roger Temam,et al.  Solution of the navier-stokes equations by finite element methods , 1975 .