Numerical simulation of shock diffraction on unstructured meshes

Shock diffraction over geometric obstacles is performed on two-dimensional unstructured triangular meshes using the AUSM+ flux-vector splitting scheme. Numerical simulations of shock diffraction using structured grids are reviewed in the literature, as are experimental results corresponding to the flow conditions studied. Present unstructured grid results for popular and challenging two-dimensional shock diffraction problems are presented and compared to experimental data and photographs. Benchmark and example test cases were chosen to cover a wide variety of Mach numbers for weak and strong shock waves, and for square and circular geometries. Both single and multiple obstacles are considered, as are obstacles located in the free field and confined in a channel.

[1]  Thomas L. Jackson,et al.  Combustion in high-speed flows , 1994 .

[2]  Uniformly second order accurate ENO schemes for the Euler equations of gas dynamics , 1987 .

[3]  E. Toro.  Godunov Methods: Theory and Applications , 2001 .

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

[5]  M. Sun,et al.  A Simple Smoothing TVD Scheme on Structured and Unstructured Grids , 2001 .

[6]  John B. Bell,et al.  Cartesian grid method for unsteady compressible flow in irregular regions , 1995 .

[7]  R. Hillier,et al.  Computation of shock wave diffraction at a ninety degrees convex edge , 1991 .

[8]  T. V. Bazhenova,et al.  Change in the shape of the diffracting shock wave at a convex corner , 1979 .

[9]  Kyu Hong Kim,et al.  An improvement of AUSM schemes by introducing the pressure-based weight functions , 1998 .

[10]  Kazuyoshi Takayama,et al.  The formation of a secondary shock wave behind a shock wave diffracting at a convex corner , 1997 .

[11]  J. Kaca.  An interferometric investigation of the diffraction of a planar shock wave over a semicircular cylinder , 1988 .

[12]  C. Hirsch.  Computational methods for inviscid and viscous flows , 1990 .

[13]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[14]  B. K. Karamete,et al.  UNSTRUCTURED GRID GENERATION AND A SIMPLE TRIANGULATION ALGORITHM FOR ARBITRARY 2-D GEOMETRIES USING OBJECT ORIENTED PROGRAMMING , 1997 .

[15]  M. Liou.  A Sequel to AUSM , 1996 .

[16]  M. A. Nettleton,et al.  Unsteady interactions of shock waves , 1984 .

[17]  A. E. Bryson,et al.  Diffraction of strong shocks by cones, cylinders, and spheres , 1961, Journal of Fluid Mechanics.

[18]  C. Hirsch.  Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows , 1990 .

[19]  James J. Quirk,et al.  Godunov-Type Schemes Applied to Detonation Flows , 1994 .

[20]  B. W. Skews,et al.  The perturbed region behind a diffracting shock wave , 1967, Journal of Fluid Mechanics.

[21]  Randall J. LeVeque.  Hyperbolic conservation laws and numerical methods , 1990 .

[22]  James J. Quirk,et al.  A Contribution to the Great Riemann Solver Debate , 1994 .

[23]  R. Hillier,et al.  Computation of shock wave diffraction and unsteady shock-boundary layer interaction , 1990 .