Stabilization meshless method for convection-dominated problems

It is well-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several tech- niques are proposed to overcome the instability issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal re- finement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.