ON A NETWORK METHOD FOR UNSTEADY INCOMPRESSIBLE FLUID FLOW ON TRIANGULAR GRIDS

The dual variable method for Delaunay triangulations is a network-theoretic method that transforms a set of primitive variable finite difference or finite element equations for incompressible flow into an equivalent system which is one-fifth the size of the original. Additionally, it eliminates the pressures from the system and produces velocities that are exactly discretely divergence-free. In this paper new discretizations of the convection term are presented for Delaunay triangulations, the dual variable method is extended to tessellations that contain obstacles, and an efficient algorithm for the solution of the dual variable system is described.

[1]  Karl Gustafson,et al.  Graph Theory and Fluid Dynamics , 1985 .

[2]  T. Porsching.  A network model for two‐fluid, two‐phase flow , 1985 .

[3]  On the Dimension of a Finite Difference Approximation to Divergence-Free Vectors , 1981 .

[4]  T. A. Porsching,et al.  Stable Numerical Integration of Conservation Equations for Hydraulic Networks , 1971 .

[5]  A. Segal.  The implementation of boundary conditions of the type u equals unknown constant in finite element codes , 1985 .

[6]  J. Cavendish,et al.  The dual variable method for solving fluid flow difference equations on Delaunay triangulations , 1991 .

[7]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[8]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[9]  R. Nicolaides.  Direct discretization of planar div-curl problems , 1992 .

[10]  O. Burggraf.  Analytical and numerical studies of the structure of steady separated flows , 1966, Journal of Fluid Mechanics.

[11]  T. Porsching,et al.  An application of network' theory to the solution of implicit Navier-Stokes difference equations , 1981 .

[12]  So-Hsiang Chou,et al.  A network model for incompressible two‐fluid flow and its numerical solution , 1989 .

[13]  C. Hall.  Numerical Solution of Navier–Stokes Problems by the Dual Variable Method , 1985 .

[14]  J. Doster,et al.  Parallel processing algorithms for the finite difference solution to the Navier-Stokes equations , 1986 .

[15]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[16]  R. A. Nicolaides,et al.  Flow discretization by complementary volume techniques , 1989 .

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