Two meshless methods for solving fluid problems in two dimensions

Two meshless methods, namely the Meshless Local Petrov Galerkin (MLPG) method and the Local Boundary Integral Equation (LBIE) method, for solving two dimensional fluid flow problems are presented. A cloud of distributed points without any connectivity requirement is employed for the approximation of the unknown fluid velocity $u(x)$. In both methodologies the interpolation of $u(x)$ is accomplished with the aid of a Moving Least Squares Approximation scheme. The weak integral formulation of MLPG and LBIE methodologies is presented in detail. The treatment of terms involving possible nonlinearities and time derivatives is explained and the numerical implementation of both techniques is addressed. Some representative examples that demonstrate the potentiality of using the aforementioned meshless methods to flow problems are shown.