Generation of adaptive finite element meshes for the sluicegate problem

Abstract

The investigation of two-dimensional steady-state viscid incompressible flow in a sluicegate is presented in this paper. Navier - Stokes equations describing the sluicegate problem are solved by the finite element method. There are specific subdomains near the lower free surface and the pick of the gate. In such subdomains flow is complicated and computational errors are large. Methods of an adaptive analysis help to reach the best accuracy with minimal computational resources. The residuals of three Navier - Stokes equations are calculated for the purpose of adaptive analysis. The residual of every Navier - Stokes equation represents independent criteria for the finite element mesh refinement. The error of computational solution is estimated by these criteria in every finite element. The appropriate norms of residuals estimates computational error in the whole solution domain. Four adaptive finite element meshes are generated considering the calculated residuals. The convergence of the calculated norms of residuals is shown. This convergence shows efficiency of the adaptive analysis.