H-adaptive Boundary Element Schemes ForFree Surface Flow Problems

Abstract

An analysis of free boundary value problems for the steady, irrotational, plane flow of an inviscid, incompressible fluid was performed using an h-adaptive boundary element method. The error estimator and indicator used in the adaptive scheme are based on computation of the residual function. Two approaches for computing predicted errors were used: Gauss quadrature [1] and Rank's scheme [2], with errors defined either in the L* or H* norms. Adjustment of the free surface has been made using iterative numerical procedures [3, 4]. Numerical results for two different cases: a sluice gate flow and a torrential flow, are presented at the end of the paper. INTRODUCTION The difficulty of modelling free surface problems is associated to the nonlinearity of the free surface boundary conditions, the unknown location of the free surface which has to be determined as part of the solution, and to possible singularities or discontinuities at the intersection between free surfaces and fixed ones. Boundary element methods are very well suited to the modelling of this class of problems due to their ability to confine all approximations to the boundary of the region under consideration, and the ease of mesh updating. However, as with any numerical method, the quality of the solution largely depends on the mesh used to model the free boundary, so the discretization must be refined during the iteration process to properly represent the variation of geometry and functions. Discretization of the boundary can be made either based on knowledge of the engineer or automatically, based on results from an initial mesh, with the program adjusting it until a desirable accuracy for the problem is obtained. In this paper, an b-adaptive scheme based on calculation of a residual function to define the predicted error, is Transactions on Modelling and Simulation vol 6, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X