A novel variational multiscale interpolating element-free Galerkin method for generalized Oseen problems. (15th October 2018) - Zhang, Tao; Li, Xiaolin
Highlights: A stabilized Galerkin meshless method was developed to generalized Oseen problems. The method allows equal-order basis for velocity and pressure. The method is efficient for advection-dominated and reaction-dominated problems. Numerical studies for generalized Stokes problem, Oseen problem and generalized Oseen problem were investigated. Numerical results reveal that the method has higher accuracy than other methods. Abstract: In this paper, a novel variational multiscale interpolating element-free Galerkin (VMIEFG) method is developed for the numerical solution of generalized Oseen problems. The moving Kriging interpolation is used to generate shape functions with Kronecker delta function property, then essential boundary conditions can be enforced easily and directly. The present method is based on a decomposition of the velocity and its weighting function into coarse scales and fine scales. The fine scale problem is solved analytically, and the stabilization parameter appears naturally. Then, the coarse scale problem is solved numerically. The VMIEFG method allows equal-order basis for velocity and pressure, which is fairly easy to implement from an application point of view. Numerical examples involving generalized Stokes problem, Oseen problem and generalized Oseen problem are provided to demonstrate the efficiency of the method.