Two-dimensional implicit flux split steady and unsteady Euler calculations using unstructured moving grids

Two-dimensional Euler equations are solved on unstructured triangular meshes using commonly available minicomputers. The driving algorithm is an upwind biased implicit cell-centred finite volume scheme. The spatial discretisation involves a naturally dissipative flux-split approach that sharply captures Shockwaves. The grid generation method uses a type of advancing front technique which triangulates a given set of points. To demonstrate the application, the steady flow results are presented for single and two component aerofoils. The unsteady results are obtained using a dynamic mesh algorithm for an aerofoil pitching harmonically about the quarter chord. The paper presents a description of the grid generation and movement algorithm and of the Euler solver, along with results and comparison that assess their capabilities.

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

[2]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[3]  Mark S. Shephard,et al.  Automatic three‐dimensional mesh generation by the finite octree technique , 1984 .

[4]  J. Batina UNSTEADY EULER ALGORITHM WITH UNSTRUCTURED DYNAMIC MESH FOR COMPLEX – AIRCRAFT AERODYNAMIC ANALYSIS , 1991 .

[5]  Dimitri J. Mavriplis,et al.  Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes , 1988 .

[6]  J. Batina Accuracy of an Unstructured-Grid Upwind-Euler Algorithm for the ONERA M6 Wing , 1991 .

[7]  S. Lo A NEW MESH GENERATION SCHEME FOR ARBITRARY PLANAR DOMAINS , 1985 .

[8]  Rainald Löhner,et al.  Three-dimensional space-marching algorithm on unstructured grids , 1991 .

[9]  M. D. Salas,et al.  Far-field boundary conditions for transonic lifting solutions to the Euler equations , 1986 .

[10]  A. Jameson,et al.  Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh , 1985 .

[11]  David C. Slack,et al.  Time integration algorithms for the two-dimensional Euler equations on unstructured meshes , 1994 .

[12]  B. Leer,et al.  Flux-vector splitting for the Euler equations , 1997 .

[13]  J. Cavendish Automatic triangulation of arbitrary planar domains for the finite element method , 1974 .

[14]  O. C. Zienkiewicz,et al.  Adaptive remeshing for compressible flow computations , 1987 .

[15]  D. Mavriplis Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes , 1987 .

[16]  John T. Batina,et al.  Unsteady transonic small-disturbance theory including entropy and vorticity effects , 1989 .

[17]  Tohru Ogawa,et al.  A new algorithm for three-dimensional voronoi tessellation , 1983 .

[18]  Rainald Löhner,et al.  Finite elements in CFD: What lies ahead , 1987 .

[19]  John T. Batina,et al.  Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes , 1990 .