A Comparison of a Cell-Centre Method and a Cell-Vertex Method for the Solution of the Two-Dimensional Unsteady Euler Equations on a Moving Grid

Abstract

A moving-mesh system for the solution of two-dimensional Euler equations describing the compressible flow about an aerofoil undergoing arbitrary motions and deformations is presented. A finite volume formulation is chosen, where the volumes distort as the aerofoil moves. Independent motion of the inner and outer boundaries is permitted. By using transfinite interpolation, a fast technique for generating the required sequence of grids has been developed. Furthermore, as the flow speeds of the grid at the vertices of the finite volumes are required by any flow solver, these are also obtained by transfinite interpolation of the boundary speeds. The moving mesh has been implemented using two flow solvers, one is a cell-centre method and the other is a cell-vertex method. The flow solvers have been used to calculate a series of test cases and have produced good results in terms of detailed pressure distributions and load loops.

Keywords

computational fluid dynamics unsteady flows Euler equations grid generation

Get full access to this article

View all access options for this article.

References

Lin

C. Q.

Pahlke

Numerical solution of the Euler equations for airfoils in arbitrary unsteady motion. DLR report number DFVLR-IB 129–91/17, 1990.

Badcock

K. J.

Computation of turbulent pitching aerofoil flows. University of Glasgow, Aerospace report 9322, 1993.

Ann Williams

Fiddes

S. P.

Moving grid generation using transfinite interpolation. Bristol University Aerospace Engineering Department report number 431, 1991.

Ann Gaitonde

Fiddes

S. P.

The generation of three-dimensional moving grids using transfinite interpolation. Bristol University Aerospace Engineering Department report number 477, 1993.

Jameson

Schmidt

Turkel

Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA Paper 81–1259, 1981.

Kroll

Jain

R. K.

Solution of the two-dimensional Euler equations—experience with a finite volume code. DLR report, DFVLR-FB 87–41, 1987.

R.-H.

A multiple grid scheme for solving the Euler equations. Proceedings of AIAA Fifth Computational Fluid Dynamics Conference, Palo Alto, California, 1981, paper 81–81.

Hall

M. G.

Cell-vertex multigrid schemes for solution of the Euler equations. In Numerical methods for fluid dynamics, (Eds Morton Baines ), 1986, Vol. II, pp. 303–345 (Oxford University Press).

Eriksson

L. E.

Generation of boundary-conforming grids around wing-body configurations using transfinite interpolation. AIAA Journal, 1982, 20(10), 1313–1320.

10.

Gaitonde

Ann L.

Fiddes

S. P.

A cell-vertex method for the solution of the two-dimensional unsteady Euler equations on a structured moving grid. Bristol University Aerospace Engineering Department report number 487, 1994.

11.

Thomas

P. D.

Lombard

C. K.

Geometric conservation law and its application to flow computations on moving grids. AIAA Journal, October 1979, 17, 1030–1037.

12.

Test cases for inviscid flow field methods. AGARD Agardograph AR-211, 1985.

13.

Compendium of unsteady aerodynamic measurements. AGARD-R-702, 1982.