Application of DAE solvers to nonlinear sloshing problems based on the ALE finite element method

Abstract

This study addresses the nonlinear sloshing in the two-dimensional problem based on the Arbitrary Eulerian–Lagrangian finite element formulation (ALE). In particular, this paper focuses on a technique to control the computation mesh in the ALE formulation for preventing mesh distortion. Since this technique introduces algebraic relations for nodal coordinates, this study treats these relations as constrained equations. Then, we introduce formulation for constrained systems with the Lagrange’s method of undetermined multipliers to derive equations of motion. As a result of this formulation, it can be found that equations of motion of this system is given by the differential algebraic equations (DAEs) consisting of differential equations for time evolution of sloshing and algebraic equations (constraints) regarding the nodal coordinates. In order to calculate the DAEs formulated by the present method, this study employed a numerical integration technique based on the mid-point schemes with the Newton-Raphson iterative procedures. The proposed approach is validated by comparisons with an existing model in the time domain analysis.