An immersed boundary method for compressible flows using local grid refinement

This paper combines a state-of-the-art method for solving the three-dimensional preconditioned Navier-Stokes equations for compressible flows with an immersed boundary approach, to provide a Cartesian-grid method for computing complex flows over a wide range of the Mach number. Moreover, a flexible local grid refinement technique is employed to achieve high resolution near the immersed body and in other high-flow-gradient regions at a fraction of the cost required by a uniformly fine grid. The method is validated versus well documented steady and unsteady test problems, for a wide range of both Reynolds and Mach numbers. Finally, and most importantly, for the case of the laminar compressible steady flow past an NACA-0012 airfoil, a thorough mesh-refinement study shows that the method is second-order accurate.

[1]  Charles Merkle,et al.  Propulsion-related flowfields using the preconditioned Navier-Stokes equations , 1992 .

[2]  Michael J. Aftosmis,et al.  Aspects (and aspect ratios) of cartesian mesh methods , 1998 .

[3]  M. Mcpherson,et al.  Introduction to fluid mechanics , 1997 .

[4]  Michele Napolitano,et al.  AN IMMERSED-BOUNDARY METHOD FOR COMPRESSIBLE VISCOUS FLOWS , 2006 .

[5]  J. O´Rourke,et al.  Computational Geometry in C: Arrangements , 1998 .

[6]  Yuzhi Sun,et al.  Spectral (finite) volume method for conservation laws on unstructured grids VI: Extension to viscous flow , 2006, J. Comput. Phys..

[7]  Fue-Sang Lien,et al.  A Cartesian Grid Method with Transient Anisotropic Adaptation , 2002 .

[8]  Douglas Alan Schwer.  Numerical study of unsteadiness in non-reacting and reacting mixing layers , 1999 .

[9]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[10]  H. Fasel,et al.  A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains , 2005 .

[11]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[12]  Parviz Moin,et al.  LOCAL GRID REFINEMENT FOR AN IMMERSED BOUNDARY RANS SOLVER , 2004 .

[13]  Zdenek Travnicek,et al.  On the relationship of effective Reynolds number and Strouhal number for the laminar vortex shedding of a heated circular cylinder , 1999 .

[14]  W. Haase.  EUROVAL : an European initiative on validation of CFD codes : results of the EC/BRITE-EURAM project EUROVAL, 1990-1992 , 1993 .

[15]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[16]  M. Hafez,et al.  Computational fluid dynamics review 1995 , 1995 .

[17]  T. Pulliam,et al.  A diagonal form of an implicit approximate-factorization algorithm , 1981 .

[18]  C. Peskin.  Flow patterns around heart valves: A numerical method , 1972 .

[19]  Charles-Henri Bruneau.  Sixteenth International Conference on Numerical Methods in Fluid Dynamics , 1998 .

[20]  R. Verzicco,et al.  Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations , 2000 .

[21]  S. Dennis,et al.  Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100 , 1970, Journal of Fluid Mechanics.

[22]  J. Sodja.  Turbulence models in CFD , 2007 .

[23]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[24]  G. Iaccarino,et al.  Immersed boundary technique for turbulent flow simulations , 2003 .

[25]  V. A. Bashkin,et al.  Comparison of Calculated and Experimental Data on Supersonic Flow past a Circular Cylinder , 2002 .

[26]  Franz Durst,et al.  Flows past a tiny circular cylinder at high temperature ratios and slight compressible effects on the vortex shedding , 2003 .

[27]  B. Fornberg.  Steady viscous flow past a circular cylinder , 1984 .

[28]  R. Bouard,et al.  Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow , 1977, Journal of Fluid Mechanics.

[29]  Gianluca Iaccarino,et al.  An approach to local refinement of structured grids , 2002 .

[30]  Gianluca Iaccarino,et al.  IMMERSED BOUNDARY METHODS , 2005 .

[31]  C. Merkle,et al.  Dual time-stepping and preconditioning for unsteady computations , 1995 .

[32]  D. Tritton.  Experiments on the flow past a circular cylinder at low Reynolds numbers , 1959, Journal of Fluid Mechanics.