Lagrangian Approach of BEM for Incompressible Unsteady Viscous Flow

Abstract

A Lagrangian approach of boundary element method is presented for the numerical simulation of unsteady viscous flow. The time-dependent fundamental solutions are used for the transformation of the Navier-Stokes equations into the boundary integral equations in primitive variables. The method is based on the Lagrangian description of the fluid motion which localizes the variables to a finite number of fluid particles; the material acceleration is then the time derivative considering the change of the location of a fluid particle. Since the boundary element method has the advantage of the unlimited analytical resolution within the fluid body, a velocity correction approach can be obtained for a more accurate approximation. While the advantage is based on the accuracy of the boundary elements, an approximation function for the singularity of E₁(s)–S1(s) and a replacing integral for the other singularity on the collocated element integral are given.