A stabilized cell-based smoothed finite element method against severe mesh distortion in non-Newtonian fluid-structure interaction

Failure is an inevitability for the finite element method (FEM) to be performed on seriously degenerated four-node quadrilateral (Q4) elements whose Jacobians become negative. This article proposes a stabilized selective integration formulation of the cell-based smoothed FEM (CSFEM) for modeling non-Newtonian fluid-structure interaction (NNFSI) where that acute mesh distortion arises. The Carreau-Yasuda and Oldroyd-B fluids, respectively, interact with a geometrically nonlinear solid in NNFSI. The CSFEM is applied to discretize both the fluid and solid media in space. As the fluid mesh accounts for a substantial part of the discretized NNFSI system, seriously distorted Q4 elements are specified exclusively for the fluid field. In this case, each convex Q4 element is subdivided into four smoothing cells (SCs) whereas its concave counterpart is regarded as one single SC. In the meantime, the solid elements are treated as usual. To stabilize the one-SC integral in smoothed Galerkin weak form, an hourglass control is subsequently introduced into the fluid momentum equations as well as the viscoelastic constitutive equation. The transient non-Newtonian fluid equations are advanced with dual time steps of the characteristic-based split scheme in time to further enhance the numerical stability and accuracy. After discussing other aspects of computational NNFSI, two benchmark problems are presented to demonstrate the effectiveness and performance of the developed methodology under the harsh environment.

Automated summary

This article proposes a stabilized selective integration formulation for handling severely distorted four-node quadrilateral elements. The method is applied to model non-Newtonian fluid-structure interaction and its effectiveness and performance are demonstrated through two benchmark problems.