Adaptive Distribute Points Technique for Convection Dominated Problems Combined with Meshless Method

It is well known that the numerical solutions of conventional methods may be corrupted by non-physical oscillations when the convection action dominates the diffusion action in the transport problems.The adaptive distribute points technique was developed to overcome the instability issues in convection dominated problems simulated by radial point interpolation method.In the adaptive process of meshless method,the background mesh was considered as the cell to control the grads adaptively.The grads of the cell was regarded as Grads Index,and it decided whether or not to refine the cell by comparing with Grads Bounds.Two numerical examples were presented and the numerical results show that this technique is effective to solve convection dominated problems.In addition,these methods have high accuracy and good stabilization,the computational algorithms can be easily implemented,the preprocess and post process are very convenient.