A computational study of the effect of unstructured mesh quality on solution efficiency

It is well known that mesh quality affects both efficiency and accuracy of CFD solutions. Meshes with distorted elements make solutions both more difficult to compute and less accurate. We review a recently proposed technique for improving mesh quality as measured by element angle (dihedral angle in three dimensions) using a combination of optimization-based smoothing techniques and local reconnection schemes. Typical results that quantify mesh improvement for a number of application meshes are presented. We then examine effects of mesh quality as measured by the maximum angle in the mesh on the convergence rates of two commonly used CFD solution techniques. Numerical experiments are performed that quantify the cost and benefit of using mesh optimization schemes for incompressible flow over a cylinder and weakly compressible flow over a cylinder.

[1]  S. Canann,et al.  Optismoothing: an optimization-driven approach to mesh smoothing , 1993 .

[2]  P. Plassmann,et al.  An Eecient Parallel Algorithm for Mesh Smoothing , 1995 .

[3]  E. Amezua,et al.  A method for the improvement of 3D solid finite-element meshes , 1995 .

[4]  Barry Joe,et al.  Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations , 1995, SIAM J. Sci. Comput..

[5]  Mark T. Jones,et al.  An efficient parallel algorithm for mesh smoothing , 1995 .

[6]  I. Babuska,et al.  ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD , 1976 .

[7]  Mark S. Shephard,et al.  Automatic three‐dimensional mesh generation by the finite octree technique , 1984 .

[8]  R. K. Smith,et al.  Mesh Smoothing Using A Posteriori Error Estimates , 1997 .

[9]  M. Rivara.  Mesh Refinement Processes Based on the Generalized Bisection of Simplices , 1984 .

[10]  Mark S. Shephard,et al.  Automatic three-dimensional mesh generation by the finite octree technique , 1984 .

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

[12]  B. Joe.  Three-dimensional triangulations from local transformations , 1989 .

[13]  V. Parthasarathy,et al.  A constrained optimization approach to finite element mesh smoothing , 1991 .

[14]  Randolph E. Bank,et al.  PLTMG - a software package for solving elliptic partial differential equations: users' guide 8.0 , 1998, Software, environments, tools.

[15]  Timothy J. Barth,et al.  Recent developments in high order K-exact reconstruction on unstructured meshes , 1993 .

[16]  B. Joe,et al.  GEOMPACK — a software package for the generation of meshes using geometric algorithms☆ , 1991 .

[17]  Carl Ollivier-Gooch,et al.  Tetrahedral mesh improvement using swapping and smoothing , 1997 .

[18]  C. Ollivier-Gooch.  Quasi-ENO Schemes for Unstructured Meshes Based on Unlimited Data-Dependent Least-Squares Reconstruction , 1997 .

[19]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[20]  Carl Ollivier-Gooch,et al.  A comparison of tetrahedral mesh improvement techniques , 1996 .

[21]  Carl Ollivier-Gooch,et al.  High-order ENO schemes for unstructured meshes based on least-squares reconstruction , 1997 .

[22]  I. Fried.  Condition of finite element matrices generated from nonuniform meshes. , 1972 .

[23]  C. Ollivier-Gooch.  Multigrid acceleration of an upwind Euler solver on unstructured meshes , 1995 .

[24]  David Eppstein,et al.  Optimal point placement for mesh smoothing , 1997, SODA '97.

[25]  Lori A. Freitag,et al.  On combining Laplacian and optimization-based mesh smoothing techniques , 1997 .