Multi-scale analysis on fluid and fluid-structure interactions using meshfree and finite element methods

A parallel computational implementation of a meshfree method, Reproducing Kernel Particle Method (RKPM), is used for 3-D implicit CFD analysis. A novel procedure for implementing the essential boundary condition using the bridging-scale hierarchical enrichment method is presented. Using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results than does either the finite element method or other meshfree methods. Furthermore, matrix inversions are not required in this boundary treatment. The performance of the parallelization technique and the accuracy of the implicit CFD algorithm are demonstrated in two example problems: the flow past a cylinder and the flow past the San Francisco Transamerica Pyramid.; The RKPM method also plays an important role in the Immersed Finite Element Method (IFEM), a new approach in solving complex fluid-structure interaction problems. The interpolations of the variables between the fluid and the solid domains are calculated via the RKPM shape functions. This RKPM delta functions can handle nonuniform grids for the fluid domain, which allows the definition of arbitrary geometry shapes and boundary conditions. It broadens the flexibilities in treating typical fluid-structure interactions with detailed and realistic stress analysis. Particulate flows of rigid and deformable spheres are illustrated as examples. Future research and potential possible applications in the field of bio-engineering mechanics are stated.