On the mesh insensitivity of the edge-based smoothed finite element method for moving-domain problems

Abstract

Although much less sensitive to mesh distortion, the edge-based smoothed finite element method (ESFEM) can become ineffective on severely distorted elements whose Jacobians are less than or equal to zero, especially in transient cases. In this work, we first prove that the ESFEM may be unable to get over severe mesh distortion occurring even in a very simple mesh of four four-node quadrilateral (Q4) elements. We then propose a slight modification that makes the ESFEM inherently applicable to negative-Jacobian Q4 elements without requiring any ad hoc stabilization. For the ESFEM, a smoothing cell (SC) attached to negative-Jacobian Q4 element is rebuilt on the midpoint of the shorter diagonal of the damaged element. Thus, the SC has a positive area that accounts correctly for inertial effects of transient problems. Such a treatment is compatible with the regular procedure for constructing an edge-based SC in normal Q4 elements. The mesh insensitivity of the ESFEM is highlighted by solving fluid–structure interaction on negative-Jacobian Q4 elements. Importantly, the present scheme can be generalized to other linear $n$-sided elements which are more likely to be badly distorted in complex moving-domain problems.