Gradient smoothing method (GSM) has been widely applied to solve partial differential equations, and we have smoothed finite element method (S-FEM) for solid mechanics and GSM-CFD for fluid mechanics. Theories and numerical examples have demonstrated that the GSM-CFD solver is accurate, efficient, robust, and insensitive to mesh distortions. However, the previous research of GSM-CFD mainly focused on 2D cases, thus the 3D version GSM-CFD solver will be developed here. First, the method for construction of smoothing domains (SDs) on 3D complex grids will be proposed, and the general data structure for SD will be devised. Then the algorithms for gradient approximation of flow field variables in 3D solution domains will be developed and verified. The Navier-Stokes equations will be discretized using GSM, and the 3D GSM-CFD solver is finally formed. The validation and verification of the proposed GSM-CFD solver will be carried out using the method of manufactured solutions, and the results will be compared with the ones obtained using conventional finite volume method.

Currently, we have finished the data structure and gradient approximation algorithms for 3D GSM, and we are working on the verification of gradient approximation for flow field variables. We will implement the 3D algorithm to the CFD solver soon, and it very promising that we can present some meaningful results at the conference.