Moving least-squares aided finite element method: A powerful means to predict flow fields in the presence of a solid part

With the assistance of the moving least-squares (MLS) interpolation functions, a two-dimensional finite element code is developed to consider the effects of a stationary or moving solid body in a flow domain. At the same time, the mesh or grid is independent of the shape of the solid body. We achieve this goal in two steps. In the first step, we use MLS interpolants to enhance the pressure (P) and velocity (V) shape functions. By this means, we capture different discontinuities in a flow domain. In our previous publications, we have named this technique the PVMLS method (pressure and velocity shape functions enhanced by the MLS interpolants) and described it thoroughly. In the second step, we modify the PVMLS method (the M-PVMLS method) to consider the effect of a solid part(s) in a flow domain. To evaluate the new method's performance, we compare the results of the M-PVMLS method with a finite element code that uses boundary-fitted meshes. Many physical and industrial problems comprise one or more moving parts, which change the flow domain during a process, such as lubrication and mixing. For such problems, we have suggested a new method, which uses a fixed background mesh to avoid the time-consuming task of boundary-fitted grid generation. The new technique, which is based on the finite element method, uses the moving least-squares interpolation functions, where the solid and fluid meet each other in the flow domain. image