Implicit time discretization schemes for mixed least-squares finite element formulations

摘要

This work is an extension of the ideas in Averweg et al. (2019) with the focus on a detailed investigation of implicit time discretization schemes to model instationary fluid flow, based on the incompressible Navier-Stokes equations, and linear elastodynamic structural behavior. The variational approaches for fluid and solid mechanics are based on a mixed least-squares finite element method. The L-2-norm minimization of the residuals of the constructed first-order systems of the governing differential equations is based on two-field stress-velocity (SV) functionals. For the time discretization of the SV-fluid formulation, four different types of implicit integration schemes are investigated, namely the Houbolt method, the Crank-Nicolson method and two explicit, singly diagonally implicit Runge-Kutta methods (ESDIRK). The SV-formulation for the solid is discretized applying the Houbolt method. The presented time integration schemes are validated investigating an unsteady fluid flow and an elastodynamic structural benchmark. Since both (fluid and solid) SV formulations are discretized using conforming finite element spaces in H(div) and H-1, respectively, the inherent fulfillment of coupling conditions, when modeling fluid-structure interaction problems, is given a priori. Therefore, the applicability is also examined by two simplified FSI problems for small deformations, in order to represent the main characteristics of the presented approach. (C) 2020 Elsevier B.V. All rights reserved.