A reduced smoothed integration scheme of the cell-based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

This article describes an inexpensive partitioned coupling strategy for computational fluid–structure interaction (FSI) admitting negative-Jacobian elements. The emphasis is very much on a reduced smoothed integration (RSI) scheme of the cell-based smoothed finite element method (CSFEM) using four-node quadrilateral (Q4) elements for a cost-effective solution to the Navier–Stokes (NS) equations. In the discrete fluid field, each Q4 element is considered as one single smoothing cell so as to diminish the smoothed integration loops substantially. However, the RSI scheme does not respect the stability condition of smoothed Galerkin weak-form integral in the CSFEM. To tackle this issue, a simple hourglass control is introduced to the under-integrated formulation of the NS solver. Importantly, the stabilized RSI scheme has an inbuilt advantage of its enormous tolerance towards negative-Jacobian elements. The developed technique is easy-to-implement and has been tested in various FSI examples adopting both fine and distorted meshes.