스펙트랄요소법을 이용한 점성 자유표면 유동에 대한 수치해석기법 개발

Abstract

An accurate and efficient numerical modelling of viscous free surface flows is introduced in this paper. The governing equation of the flow is based on the Navier-Stokes equations incorporating the velocity-pressure formulation. In order to deal with the free surface motion, an Arbitrary Lagrangian-Eulerian (ALE) description is adopted. The paper addresses the solution procedure and characteristic aspects of the present modeling and its numerical implementation. For higher-order accuracy, the Spectral Element Method (SEM), which possesses the property of high-order spatial accuracy as proposed by Karniadakis & Sherwin (2005), is utilized. It is shown that the present SEM produces very accurate and convergent solutions to the Poisson equation, the Helmholtz equation, and a manufactured problem of the N-S equations that are originally devised by Johnston and Liu (2004). Numerical results of the lid-driven cavity flow are compared with other numerical results. As for the viscous free surface flows, viscous sloshing with a prescribed initial free surface profile is simulated and it is shown that the present methodology gives very reasonable results for the small-amplitude problem. As for the nonlinear waves, propagation of soliton and run-up on the vertical wall is evaluated with a very high level of accuracy.