Accuracy and convergence of a finite element algorithm for turbulent boundary layer flow
Abstract
The GalerkinWeighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in doubleprecision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 August 1981
 DOI:
 10.1016/00457825(81)900281
 Bibcode:
 1981CMAME..28...81S
 Keywords:

 Boundary Layer Equations;
 Computational Fluid Dynamics;
 Finite Element Method;
 Turbulent Boundary Layer;
 Accuracy;
 Algorithms;
 Convergence;
 Matrices (Mathematics);
 Newton Methods;
 Partial Differential Equations;
 Fluid Mechanics and Heat Transfer