An improved hybrid boundary node method for solving steady fluid flow problems

This paper describes the application of an improved hybrid boundary node method (hybrid BNM) for solving steady fluid flow problems. The hybrid BNM is a boundary type meshless method, which combined the moving least squares (MLS) approximation and the modified variational principle. It only requires nodes constructed on the boundary of the domain, and does not require any ‘mesh’ neither for the interpolation of variables nor for the integration. As the variables inside the domain are interpolated by the fundamental solutions, the accuracy of the hybrid BNM is rather high. However, shape functions for the classical MLS approximation lack the delta function property. Thus in this method, the boundary condition cannot be enforced easily and directly, and its computational cost is high for the inevitable transformation strategy of boundary condition. In the method we proposed, a regularized weight function is adopted, which leads to the MLS shape functions fulfilling the interpolation condition exactly, which enables a direct application of essential boundary conditions without additional numerical effort. The improved hybrid BNM has successfully implemented in solving steady fluid flow problems. The numerical examples show the excellent characteristics of this method, and the computation results obtained by this method are in a well agreement with the analytical solutions, which indicate that the method we introduced in this paper can be implemented to other problems.