Aniruddha Choudhary and Christopher J. Roy

Truncation Error (TE) acts as the local source for the transport of the discretization error (DE) in the domain. Mesh adaption based upon TE is performed for 1D and 2D Burgers equations. Examination of the analytically derived TE expressions in generalized coordinates provides insight into the effects of mesh quality on the DE. For a 1D model function, adaption based upon TE equidistribution is explored with different relocation techniques.

1D Burgers Equation

For 65 nodes and a Reynolds number of 128, a TE reduction of 79.5 times and DE reduction of 154.8 times was obtained relative to a uniform mesh. TE-based adaptation was also shown to out-perform other mesh adaptation strategies.

2D Burgers Equation

For 65 nodes in each direction and a Reynolds number of 128, TE reduction of 1.44 times and DE reduction of 42.9 times from the uniform mesh was obtained for total TE-based adaption. Note that the flow solver failed to converge on the mesh obtained by Hessian-based adaption.

Key Findings

Mesh adaption driven by TE is found to be superior compared with feature-based adaption for 1D and 2D Burgers equations. Generalized TE expression include terms for mesh resolution, mesh quality (metric terms), and solution features (solution derivatives). Thus, geometric mesh quality alone is not the best measure of “goodness” of the mesh. Mesh relocation with a center of mass-based approach is found to be more effective than other techniques. 

References

  • C. J. Roy, “Strategies for Driving Mesh Adaptation in CFD,” AIAA 2009-1302, invited paper for session on Error Estimation and Control, 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, January 5-8, 2009.
  • A. Choudhary and C. J. Roy, “Efficient Residual-Based Mesh Adaptation for 1D and 2D CFD Applications,” AIAA Paper 2011-214, 49th AIAA Aerospace Sciences, Jan. 4-7, 2011, Orlando, Florida.
  • A. Choudhary and C. J. Roy, “A Truncation Error-Based Approach to Understanding and Improving Mesh Quality in CFD,” AIAA Paper 2012-0607, 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 09 - 12 January 2012, Nashville, Tennessee.