Cartesian-like grids using a novel grid-stitching algorithm for viscous flow computations

A novel grid-stitching algorithm has been developed for generating Cartesian-like grids for viscous flow calculations. A grid is generated by recursive division of Cartesian cells. Unlike the conventional Cartesian-mesh calculations that involve unit aspect ratio cells, stretching is used to get the high aspect ratio cells and smooth grid near the body. The grid data are collected in an unstructured format. This novel approach, along with an unstructured mesh-based flow solver (HIFUN-2D, developed in-house), has been successfully used for numerical simulations. This grid is successfully used for Euler and laminar flowcomputations. Partial success has been achieved for turbulent flow simulations.

[1]  Hassan Hassan,et al.  Navier-Stokes calculations using Cartesian grids. I - Laminar flows , 1988 .

[2]  Rainald Löhner,et al.  A hybrid Cartesian grid and gridless method for compressible flows , 2005, J. Comput. Phys..

[3]  M. D. Salas,et al.  Euler calculations for multielement airfoils using Cartesian grids , 1986 .

[4]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

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

[6]  M. S. Milgram Does a point lie inside a polygon , 1988 .

[7]  D. Holmes,et al.  Solution of the 2D Navier-Stokes equations on unstructured adaptive grids , 1989 .

[8]  P. A. Newman,et al.  Unsteady viscous-inviscid interaction procedures for transonic airfoils using Cartesian grids , 1988 .

[9]  W. Coirier An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ. , 1994 .

[10]  K. Powell,et al.  Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows , 1996 .

[11]  Zhi J. Wang,et al.  Anisotropic Cartesian grid method for viscous turbulent flow , 2000 .

[12]  N. Balakrishnan,et al.  Wall boundary conditions for inviscid compressible flows on unstructured meshes , 1998 .

[13]  Michael J. Aftosmis,et al.  Automatic hybrid-cartesian grid generation for high-reynolds number flows around complex geometries , 1999 .

[14]  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.

[15]  Feng Liu,et al.  A gridless boundary condition method for the solution of the Euler equations on embedded Cartesian meshes with multigrid , 2004 .

[16]  Michael A. Leschziner,et al.  Automatic grid generation for complex geometries , 1996, The Aeronautical Journal (1968).

[17]  H. Kamath,et al.  A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids , 2000 .

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

[19]  W. Shyy,et al.  Regular Article: An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries , 1999 .

[20]  Zhi J. Wang,et al.  A Quadtree-based adaptive Cartesian/Quad grid flow solver for Navier-Stokes equations , 1998 .

[21]  D. D. Zeeuw,et al.  An adaptively refined Cartesian mesh solver for the Euler equations , 1993 .

[22]  K. Morinishi A Gridless Type Solver for Parallel Simulation of Compressible Flow , 1999 .

[23]  Vedat S. Arpaci,et al.  Conduction Heat Transfer , 2002 .

[24]  M. Berger,et al.  An Adaptive Version of the Immersed Boundary Method , 1999 .

[25]  A. Jameson,et al.  Lower-upper Symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations , 1988 .

[26]  V. Venkatakrishnan,et al.  Viscous computations using a direct solver , 1990 .

[27]  Clinton P. T. Groth,et al.  A Mesh Adjustment Scheme for Embedded Boundaries , 2006 .

[28]  N. Balakrishnan,et al.  New Migratory Memory Algorithm for Implicit Finite Volume Solvers , 2004 .

[29]  J. Ferziger,et al.  A ghost-cell immersed boundary method for flow in complex geometry , 2002 .

[30]  V. Venkatakrishnan Convergence to steady state solutions of the Euler equations on unstructured grids with limiters , 1995 .