A NOVEL ALPHA GRADIENT SMOOTHING METHOD (αGSM) FOR FLUID PROBLEMS

In this article, a novel alpha gradient smoothing method (alpha GSM) based on the strong form of governing equations for fluid problems is presented. The basic principle of alpha GSM is that the spatial derivatives at a location of interest are approximated by the gradient smoothing operation. The main difference among the piecewise-constant gradient smoothing method (PC-GSM), piecewise-linear gradient smoothing method (PL-GSM), and alpha GSM is the selection of smoothing function. In the alpha GSM, the alpha value controls the contribution of the PC-GSM and PL-GSM. The alpha GSM is also verified by the solving the Poisson equation. The proposed alpha GSM has been tested for one benchmark example. All the numerical results demonstrate that the alpha GSM is remarkably accurate, robust, and stable. Finally, the alpha GSM has been applied to analyze the flow characteristic in the diseased artery in terms of stenosis.