Two-dimensional implicit time-dependent calculations on adaptive unstructured meshes with time evolving boundaries

An implicit multigrid-driven algorithm for two-dimensional incompressible laminar viscous flows has been coupled with a solution adaptation method and a mesh movement method for boundary movement. Time-dependent calculations are performed implicitly by regarding each time step as a steady-state problem in pseudo-time. The method of artificial compressibility is used to solve the flow equations. The solution mesh adaptation method performs local mesh refinement using an incremental Delaunay algorithm and mesh coarsening by means of edge collapse. Mesh movement is achieved by modeling the computational domain as an elastic solid and solving the equilibrium equations for the stress field. The solution adaptation method has been validated by comparison with experimental results and other computational results for low Reynolds number flow over a shedding circular cylinder. Preliminary validation of the mesh movement method has been demonstrated by a comparison with experimental results of an oscillating airfoil and with computational results for an oscillating cylinder.

[1]  Charles H. K. Williamson,et al.  Measurements of base pressure in the wake of a cylinder at low Reynolds numbers , 1990 .

[2]  Timothy J. Baker,et al.  Mesh Movement and Metamorphosis , 2002, Engineering with Computers.

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

[4]  Russ D. Rausch,et al.  Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations , 1993 .

[5]  Juan J. Alonso,et al.  Multigrid unsteady Navier-Stokes calculations with aeroelastic applications , 1995 .

[6]  Tayfun E. Tezduyar,et al.  Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces , 1994 .

[7]  R. L. Halfman.  Experimental aerodynamic derivatives of a sinusoidally oscillating airfoil in two-dimensional flow , 1952 .

[8]  Mark D. Sanetrik,et al.  Time-accurate Navier-Stokes calculations with multigrid acceleration , 1993 .

[9]  S. Rebay.  Efficient Unstructured Mesh Generation by Means of Delaunay Triangulation and Bowyer-Watson Algorithm , 1993 .

[10]  N. Weatherill,et al.  Unstructured grid generation using iterative point insertion and local reconnection , 1995 .

[11]  Timothy J. Baker,et al.  Mesh adaptation strategies for problems in fluid dynamics , 1997 .

[12]  M Delanaye,et al.  An accurate finite volume scheme for Euler and Navier-Stokes equations on unstructured adaptive grids , 1995 .

[13]  A. Jameson.  Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

[14]  Brian T. Helenbrook,et al.  A two-fluid spectral-element method , 2001 .

[15]  T. Sarpkaya.  Vortex-Induced Oscillations: A Selective Review , 1979 .

[16]  Arthur Rizzi,et al.  Computation of inviscid incompressible flow with rotation , 1985, Journal of Fluid Mechanics.

[17]  Rainald Löhner,et al.  Numerical Simulation of Shock Interaction With a Modern Main Battlefield Tank , 1991 .

[18]  Charles H. K. Williamson,et al.  A SERIES IN 1/√Re TO REPRESENT THE STROUHAL–REYNOLDS NUMBER RELATIONSHIP OF THE CYLINDER WAKE , 1998 .

[19]  S. Mittal,et al.  A finite element study of incompressible flows past oscillating cylinders and aerofoils , 1992 .

[20]  R. Löhner.  An adaptive finite element scheme for transient problems in CFD , 1987 .

[21]  DimitriJ.,et al.  TURBULENT FLOW CALCULATIONS USING UNSTRUCTURED AND ADAPTIVE MESHES , 2022 .

[22]  Timothy J. Baker,et al.  Dynamic adaptation for deforming tetrahedral meshes , 1999 .

[23]  Biing-Horng Liou,et al.  AN IMPLICIT UNSTRUCTURED ADAPTIVE-GRID APPROACH FOR COMPRESSIBLE FLOWS WITH MOVING BOUNDARIES , 2001 .

[24]  Peter A. Cavallo,et al.  DYNAMIC UNSTRUCTURED GRID METHODOLOGY WITH APPLICATION TO AERO/PROPULSIVE FLOWFIELDS , 1997 .

[25]  John Vassberg,et al.  A fast, implicit unstructured-mesh Euler method , 1992 .

[26]  Rainald Loehner,et al.  A new ALE adaptive unstructured methodology for the simulation of moving bodies , 1994 .

[27]  Luigi Martinelli,et al.  Calculation of Plunging Breakers with A Fully-Implicit Adaptive-Grid Method , 1998 .

[28]  T. Barth.  Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations , 1994 .

[29]  Stuart Connell,et al.  A 3D unstructured adaptive multigrid scheme for the Euler equations , 1993 .

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

[31]  T. Baker.  Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation , 1989, Engineering with Computers.

[32]  Dimitri J. Mavriplis,et al.  Multigrid solution of the Navier-Stokes equations on triangular meshes , 1989 .

[33]  Charles Merkle,et al.  Time-accurate unsteady incompressible flow algorithms based on artificial compressibility , 1987 .

[34]  R. Peyret,et al.  Unsteady evolution of a horizontal jet in a stratified fluid , 1976, Journal of Fluid Mechanics.

[35]  Rupak Biswas,et al.  A new procedure for dynamic adaption of three-dimensional unstructured grids , 1993 .

[36]  Antony Jameson,et al.  Solution of three-dimensional supersonic flowfields via adapting unstructured meshes , 1993 .

[37]  Dimitri J. Mavriplis,et al.  TURBULENT FLOW CALCULATIONS USING UNSTRUCTURED AND ADAPTIVE MESHES , 1991 .

[38]  V. Venkatakrishnan,et al.  IMPLICIT METHOD FOR THE COMPUTATION OF UNSTEADY FLOWS ON UNSTRUCTURED GRIDS , 1995 .

[39]  Stuart E. Rogers,et al.  Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations , 1990 .

[40]  Rainald Löhner,et al.  An adaptive finite element solver for transient problems with moving bodies , 1988 .

[41]  Tayfun E. Tezduyar,et al.  Simulation of multiple spheres falling in a liquid-filled tube , 1996 .

[42]  C. Williamson.  Defining a Universal and Continuous Strouhal-Reynolds Number Relationship for the Laminar Vortex She , 1988 .

[43]  Y. Kallinderis,et al.  Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes , 1993 .

[44]  K. Morgan,et al.  Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing , 1993 .

[45]  Mark S. Shephard,et al.  Parallel refinement and coarsening of tetrahedral meshes , 1999 .

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

[47]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .