The simulation of inviscid, compressible flows using an upwind kinetic method on unstructured grids

SUMMARY A kinetic flux-vector-splitting method has been used to solve the Euler equations for inviscid, compressible flow on unstructured grids. This method is derived from the Boltzmann equation and is an upwind, cellcentred, finite volume scheme with an explicit time-stepping procedure. The Delaunay triangulation has been used to generate the grids. The approach is demonstrated for three flow field simulations, namely the subsonic flow over a two-component high-lift aerofoil, the transonic flow over an aerofoil and the supersonic flow in a channel.

[1]  N. Weatherill.  Delaunay triangulation in computational fluid dynamics , 1992 .

[2]  O. Zienkiewicz,et al.  Finite element Euler computations in three dimensions , 1988 .

[3]  N. Weatherill.  A method for generating irregular computational grids in multiply connected planar domains , 1988 .

[4]  S. M. Deshpande,et al.  A second-order accurate kinetic-theory-based method for inviscid compressible flows , 1986 .

[5]  S. M. Deshpande,et al.  On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations , 1986 .

[6]  A Jameson,et al.  CALCULATION OF IN VISCID TRANSONIC FLOW OVER A COMPLETE AIRCRAFT , 1986 .

[7]  N. P. Weatherill,et al.  Grid generation and flow calculations for aircraft geometries , 1985 .

[8]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[9]  J. Steger,et al.  Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods , 1981 .

[10]  R. Lindsay,et al.  Elements of gasdynamics , 1957 .

[11]  Timothy J. Barth,et al.  The design and application of upwind schemes on unstructured meshes , 1989 .

[12]  Philip L. Roe,et al.  The use of the Riemann problem in finite difference schemes , 1989 .

[13]  J. C. Mandal,et al.  Higher Order Accurate Kinetic Flux Vector Splitting Method for Euler Equations , 1989 .

[14]  Timothy J. Baker,et al.  Three dimensional mesh generation by triangulation of arbitrary point sets , 1987 .

[15]  S. M. Deshpande,et al.  Kinetic theory based new upwind methods for inviscid compressible flows , 1986 .

[16]  P. Eiseman.  Grid Generation for Fluid Mechanics Computations , 1985 .

[17]  Joe F. Thompson,et al.  Numerical grid generation: Foundations and applications , 1985 .

[18]  S. Osher.  Numerical Solution of Singular Perturbation Problems and Hyperbolic Systems of Conservation Laws , 1981 .

[19]  R. Maccormack,et al.  A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions , 1975 .