A CARTESIAN GRID APPROACH WITH HIERARCHICAL REFINEMENT FOR COMPRESSIBLE FLOWS

Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows which is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.

[1]  Steven K. Feiner,et al.  Computer graphics: principles and practice (2nd ed.) , 1990 .

[2]  D. P. Young,et al.  A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics , 1990 .

[3]  Bram van Leer,et al.  A simulation technique for 2-D unsteady inviscid flows around arbitrarily moving and deforming bodies of arbitrary geometry , 1993 .

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

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

[6]  Richard L. Gaffney,et al.  Euler calculations for wings using Cartesian grids , 1987 .

[7]  J. L. Steger,et al.  On the use of composite grid schemes in computational aerodynamics , 1987 .

[8]  Rainald Löhner,et al.  Adaptive H-refinement on 3-D unstructured grids for transient problems , 1989 .

[9]  Yu-Liang Chiang.  Simulation of unsteady inviscid flow on an adaptively refined Cartesian grid , 1992 .

[10]  J. J. Quirk,et al.  An adaptive grid algorithm for computational shock hydrodynamics , 1991 .

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

[12]  M. D. Salas,et al.  Euler calculations for multielement airfoils using Cartesian grids , 1986 .

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

[14]  R. LeVeque,et al.  An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries , 1989 .

[15]  John R. Rice,et al.  Numerical Computation with General Two-Dimensional Domains , 1984, TOMS.

[16]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[17]  Phillip Colella,et al.  Adaptive Cartesian grid methods for representing geometry in inviscid compressible flow , 1993 .

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

[19]  Joe F. Thompson,et al.  Aspects of numerical grid generation - Current science and art , 1993 .

[20]  Bradford Sturtevant,et al.  The focusing of weak shock waves , 1976 .