Analysis of a-posteriori error indicator in viscous flows

An a-posteriori error indicator for solving viscous incompressible flow problems is analyzed in this paper. The indicator named "velocity angle error estimator" is based on the spatial derivative of velocity direction fields and it can detect local flow features, such as vortices and separation, and resolve flow details precisely. The refinement indicator corresponds to the antisymmetric part of the deformation-rate-tensor, and it is sensitive to the second derivative of the velocity angle field. Rationality discussions reveal that the a-posteriori error indicator is a curvature error indicator, and its value reflects the accuracy of streamline curves. It is also found that the velocity angle error indicator contains the nonlinear convective term of the Navier-Stokes equations, and it identifies and computes the direction difference when the convective acceleration direction and the flow velocity direction have a disparity. Numerical simulation is presented to illustrate the use of the velocity angle error indicator.