Numerical study and comparison of alternative time discretization schemes for an ultrasonic guided wave propagation problem coupled with fluid-structure interaction

摘要

Discretization is a crucial step in the numerical treatment of coupled multiphysics problems. In the present paper, we focus on the numerical solution of ultrasonic guided waves (UGWs) propagation problem coupled with fluid-structure interaction. We track UGWs propagation through fluid, solid and their interface, where the structure is in motion. Discretization is done via a Finite Element method. For this, we follow the Rothe method, in which discretization in time is followed by space discretization, solving the resulting problem according to the monolithic approach. Further, we provide a systematic analysis of alternative discretization schemes, time-steps, and mesh refinements. Specifically, we contrast one first-order time discretization scheme (cf. backward Euler) and three second-order schemes (cf. Crank-Nicolson, shifted Crank-Nicolson, and fractional-step-theta). First, we establish the robustness of the convergence result. Second, we estimate the experimental order of convergence for alternative schemes and space-time discretization combinations. (C) 2019 Elsevier Ltd. All rights reserved.