Adaptive mesh refinement by the reproducing kernel element method applied to the immersed finite element method

Work prepared at Departement of Mechanical Engineering of Northwestern University, Evanston, Illinois, USA.

In order to efficiently simulate the interaction between fluid and solids, the Immersed Finite Element Method (IFEM) [3] was proposed. With IFEM, the momentum equations are rewritten so that the computational fluid domain encompasses fluid and solid domain. Both domains interact by an interpolation scheme using the shape function of the Reproducing Kernel Particle Method (RKPM) [1]. IFEM does not require any fluid mesh update due to the solid surface movement, which makes this method particularly suitable for flow interaction with moving and deforming structures. In order to provide sufficient grid resolution near the moving body, however, a grid-refinement algorithm is necessary. For this purpose an adaptive meshing algorithm for the fluid domain will be developed based on the Kernel Element Method (RKEM) [2]. Unlike many meshfree methods, RKEM shape functions are interpolants. Also, the use of global conforming shape functions allows simple sub-division of elements, which reduces the time required for the remeshing process and simplifies the implementation of the adaptive meshing algorithm.