Modeling and Verification of a RANCF Fluid Element Based on Cubic Rational Bezier Volume

Abstract

This investigation is focused on developing a novel three-dimensional rational absolute nodal coordinate formulation (RANCF) fluid element based on cubic rational Bezier volume. The new fluid element can describe liquid columns with initially curved configurations precisely, performing better than the conventional absolute nodal coordinate formulation (ANCF) fluid element. A new kinematic description, which employs a different interpolation function to describe the displacement field, makes this element a true difference. The shape function is no longer calculated by an incomplete polynomial or nonrational B-spline function, replaced by the rational Bezier function. Dynamical model or governing equation of the RANCF fluid element is built based on the constitutive equation of fluid, momentum, and constraint equation. One liquid column with initially cylindrical configuration is established by the RANCF fluid element, the position vector of control points and their weights are calculated to achieve the specific initial configuration. A simulation of the cylindrical liquid column collapsing on a plane is implemented to verify the validity of the RANCF fluid element, and numerical results are in good agreement with those obtained in the literature. The convergence of the RANCF fluid element is also checked and proved not to be influenced by mesh size. Finally, the precise description ability of the RANCF fluid element is compared with that of the conventional ANCF fluid element, the former shows a great advantage.