Adaptive Cartesian mesh generation

The last decade has witnessed a resurgence of interest in Cartesian mesh methods for CFD. In contrast to body-fitted structured or unstructured methods, Cartesian grids are inherently non-body-fitted; i.e. the volume mesh structure is independent of the surface discretization and topology. This characteristic promotes extensive automation, dramatically eases the burden of surface preparation, and greatly simplifies the re-analysis processes when the topology of a configuration changes. By taking advantage of these important characteristics, well-designed Cartesian approaches virtually eliminate the difficulty of grid generation for complex configurations. Typically, meshes with millions of cells can be generated in minutes on moderately powerful workstations.

[1]  A. R. Forrest,et al.  Application Challenges to Computational Geometry: CG Impact Task Force Report , 1999 .

[2]  John B. Bell,et al.  Cartesian grid method for unsteady compressible flow in irregular regions , 1995 .

[3]  Randall J. LeVeque,et al.  Stable boundary conditions for Cartesian grid calculations , 1990 .

[4]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[5]  Michael J. Aftosmis,et al.  Accuracy, Adaptive Methods and Complex Geometry , 1996 .

[6]  Marsha Berger,et al.  An accuracy test of a Cartesian grid method for steady flow in complex geometries , 1996 .

[7]  Michael J. Aftosmis,et al.  Adaptation and surface modeling for cartesian mesh methods , 1995 .

[8]  Kenneth G. Powell,et al.  An adaptively-refined Cartesian mesh solver for the Euler equations , 1991 .

[9]  J. W. Boerstoel,et al.  Test Cases for Inviscid Flow Field Methods. , 1985 .

[10]  J. Bonet,et al.  An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems , 1991 .

[11]  M. Berger,et al.  Robust and efficient Cartesian mesh generation for component-based geometry , 1998 .

[12]  Ivan E. Sutherland,et al.  Reentrant polygon clipping , 1974, Commun. ACM.

[13]  Jonathan Richard Shewchuk,et al.  Robust adaptive floating-point geometric predicates , 1996, SCG '96.

[14]  Jonathan Richard Shewchuk,et al.  Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates , 1997, Discret. Comput. Geom..

[15]  Bernard Chazelle The Computational Geometry Impact Task Force Report: An Executive Summary , 1996, WACG.

[16]  S. Sloan A fast algorithm for generating constrained delaunay triangulations , 1993 .

[17]  D. Du,et al.  Computing in Euclidean Geometry: (2nd Edition) , 1995 .

[18]  Herbert Edelsbrunner,et al.  Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms , 1988, SCG '88.

[19]  Robert L. Meakin,et al.  ADVANCES TOWARDS AUTOMATIC SURFACE DOMAIN DECOMPOSITION AND GRID GENERATION FOR OVERSET GRIDS , 1997 .

[20]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[21]  Francis Y. Enomoto,et al.  3D automatic Cartesian grid generation for Euler flows , 1993 .

[22]  H. Forrer Second order accurate boundary treatment for Cartesian grid methods , 1996 .

[23]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[24]  D. D. Zeeuw,et al.  An adaptively refined Cartesian mesh solver for the Euler equations , 1993 .

[25]  Eric F. Charlton,et al.  An Octree Solution to Conservation-laws over Arbitrary Regions (OSCAR) with Applications to Aircraft , 1997 .

[26]  Chee Yap,et al.  The exact computation paradigm , 1995 .

[27]  Robert F. Sproull,et al.  Principles of interactive computer graphics (2nd ed.) , 1979 .

[28]  A. Harten ENO schemes with subcell resolution , 1989 .

[29]  K. G. Powell,et al.  Solution of the euler and magnetohydrodynamic equations on solution-adaptive cartesian grids , 1996 .

[30]  Viktoria Schmitt,et al.  Pressure distributions on the ONERA M6 wing at transonic Mach numbers , 1979 .

[31]  M. Aftosmis Solution adaptive cartesian grid methods for aerodynamic flows with complex geometries , 1997 .

[32]  Chee-Keng Yap,et al.  A geometric consistency theorem for a symbolic perturbation scheme , 1988, SCG '88.

[33]  Douglas M. Priest,et al.  Algorithms for arbitrary precision floating point arithmetic , 1991, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic.

[34]  H. Forrer,et al.  Boundary treatment for a Cartesian grid method , 1996 .

[35]  D. F. Watson Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[36]  Steve L. Karman,et al.  SPLITFLOW - A 3D unstructured Cartesian/prismatic grid CFD code for complex geometries , 1995 .

[37]  Robert F. Sproull,et al.  Principles in interactive computer graphics , 1973 .

[38]  Thomas Ertl,et al.  Computer Graphics - Principles and Practice, 3rd Edition , 2014 .

[39]  E. R. Keener Pressure-distribution measurements on a transonic low-aspect ratio wing , 1985 .

[40]  李幼升,et al.  Ph , 1989 .

[41]  Leila De Floriani,et al.  An on-line algorithm for constrained Delaunay triangulation , 1992, CVGIP Graph. Model. Image Process..

[42]  Randall J. LeVeque,et al.  Cartesian meshes and adaptive mesh refinement for hyperbolic partial differential equations , 1990 .

[43]  Tracy Welterlen,et al.  Rapid assessment of F-16 store trajectories using unstructured CFD , 1995 .

[44]  Chee-Keng Yap Geometric Consistency Theorem for a Symbolic Perturbation Scheme , 1990, J. Comput. Syst. Sci..

[45]  K. Powell,et al.  An accuracy assessment of Cartesian-mesh approaches for the Euler equations , 1993 .

[46]  Michael J. Aftosmis,et al.  3D applications of a Cartesian grid Euler method , 1995 .

[47]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[48]  Elaine Cohen Some mathematical tools for a modeler's workbench , 1983, IEEE Computer Graphics and Applications.

[49]  Brian A. Barsky,et al.  An analysis and algorithm for polygon clipping , 1983, CACM.

[50]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[51]  J. Quirk An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies , 1994 .