Comparison between continuous and discontinuous boundary elements in the multidomain dual reciprocity method for the solution of the two-dimensional Navier–Stokes equations

Abstract

Multidomain decomposition techniques are an alternative to improve the performance of the dual reciprocity boundary element method (DRBEM) in the BEM numerical solution of the Navier–Stokes equations. In the traditional DRBEM, the domain integrals that arise from the non-linear terms in the Navier–Stokes equations are approximated by a series of particular solutions and a set of collocation nodes distributed over the integration domain. In the present approach a subdomain technique is used in which the integration domain is divided into small quadrilateral elements whose four edges are either isoparametric linear discontinuous or linear continuous boundary elements. The domain integrals in each subdomain are transformed into boundary integrals by dual reciprocity with augmented thin-plate splines, i.e. r 2 log(r), plus three additional linear terms from a Pascal triangle expansion. In the present work we compare the numerical results obtained by using both kind of boundary elements, continuous and discontinuous, in each subdomain.