Comparison of r-Adaptation Techniques for 2-D CFD Applications

This paper examines the effectiveness of several 2-D r-adaptation schemes in reducing discretization error in numerical solutions. The adaptation schemes used include an adaptive Poisson grid generator, a variational grid generator, a center of mass based scheme, and a scheme based on deforming maps. These schemes are applied to Mach 1.2 flow around a 12◦ downward turn and Mach 0.2 flow over a Karman-Trefftz airfoil. Discretization error is computed using known exact solutions for each case. Discretization error reductions of up to six times are achieved on adapted grids relative to the discretization error present on a uniform grid of the same size.

[1]  J. Brackbill,et al.  Adaptive zoning for singular problems in two dimensions , 1982 .

[2]  D. Scott McRae,et al.  r-Refinement grid adaptation algorithms and issues , 2000 .

[3]  W. K. Anderson,et al.  Grid convergence for adaptive methods , 1991 .

[4]  Christopher J. Roy,et al.  SENSEI Computational Fluid Dynamics Code: A Case Study in Modern Fortran Software Development , 2013 .

[5]  Aniruddha Choudhary,et al.  Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation , 2015 .

[6]  Krishnamurty Karamcheti,et al.  Principles of ideal-fluid aerodynamics , 1966 .

[7]  Dale A. Anderson.  Grid cell volume control with an adaptive grid generator , 1990 .

[8]  Christopher J. Roy,et al.  Verification and Validation in Scientific Computing: Design and execution of validation experiments , 2010 .

[9]  Christopher J. Roy,et al.  Structured Mesh r-Refinement using Truncation Error Equidistribution for 1D and 2D Euler Problems , 2013 .

[10]  Christopher J. Roy,et al.  Finite Volume Solution Reconstruction Methods For Truncation Error Estimation , 2013 .

[11]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis: Oden/A Posteriori , 2000 .

[12]  J. Brackbill.  An adaptive grid with directional control , 1993 .

[13]  Joe F. Thompson,et al.  Numerical grid generation: Foundations and applications , 1985 .

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

[15]  Guojun Liao,et al.  A new approach to grid generation , 1992 .

[16]  X. Zhang,et al.  A posteriori error estimation for finite-volume solutions of hyperbolic conservation laws , 2000 .

[17]  Robert D. Russell,et al.  Adaptive Moving Mesh Methods , 2010 .

[18]  Rusty A. Benson,et al.  A solution-adaptive mesh algorithm for dynamic/static refinement of two and three dimensional grids , 1991 .

[19]  Brian H. Dennis,et al.  A comparison between local h-refinement and a novel r-refinement method , 2015 .

[20]  J. Hansen,et al.  Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations , 1991 .

[21]  Christopher J. Roy,et al.  Verification and Validation in Scientific Computing: Planning, management, and implementation issues , 2010 .

[22]  J. Moser.  On the volume elements on a manifold , 1965 .

[23]  Kelly R. Laflin.  Solver-independent r-refinement adaptation for dynamic numerical simulations , 1997 .

[24]  William J. Rider,et al.  On sub-linear convergence for linearly degenerate waves in capturing schemes , 2008, J. Comput. Phys..

[25]  Xubin Gu.  Differentiating between Source and Location of Error for Solution-Adaptive Mesh Refinement , 2001 .

[26]  C. J. Roy.  Strategies for Driving Mesh Adaptation in CFD (Invited) , 2009 .