No abstract

Numerical solution of steady state partial differential equation (PDE) model is proposed using a stabilized local meshless method (SLMM). The PDE model under consideration is used to approximate longitudinal dispersion of suspended particles of turbulent flow moving with both zero and nonzero settling velocities. In the proposed technique, a shape parameter based SLMM is used to calculate effects of mean velocity and variable eddy diffusivity accurately. In the case of zero settling velocity, when particles are injected from a line source located at some height, numerical results confirm the experimental results. Numerical results of the SLMM also confirm numerical results produced by finite difference method (FDM) as well.

A stable localized meshless method (SLMM) is proposed for convection dominated PDEs exhibiting boundary layer. Some cases of continuous and discontinuous boundary data as well as continuous and discontinuous source function with constant and variable convection coefficients are considered. In this approach, the localized meshless method is implemented on specialized sub-domains embedded with flow direction of underlying fluid. The proposed method is based on flow featured overlapping sub-domains, called stencils. The concept of flow direction is used to construct good quality stencils having the ability to capture flow features, such as boundary layer, accurately. Numerical experiments are presented to compare the proposed method with the finite-difference method on special grid (FDSG), the standard finite-element method, hybridized SUPG method, hybridized upwind method, residual-free bubbles (RFB) method and other meshless methods. Numerical results confirm that the new approach is accurate and efficient for solving a wide class of one-, two-, and three-dimensional convection-dominated PDEs. In some cases, performance of the SLMM is comparable and sometimes better than the mesh-based finite-element and finite-difference methods.