SUMMARYThe primary objective of this work is to extend the capability of the arbitrary Lagrangian-Eulerian (ALE)-based strategy for solving fluid-structure interaction problems. This is driven by the fact that the ALE mesh movement techniques will not be able to treat problems in which fluid-structure interface experiences large motion. In addition, for certain problems the need arises to capture accurately flow features, such as a region with high gradients of the solution variables. This can be achieved by incorporating an adaptive remeshing procedure into the solution strategy.As , here, the fluid flow is governed by the incompressible NavierStokes equations and modelled by using stabilized low order velocity-pressure finite elements. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. The flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics. For temporal discretization of both fluid and solid bodies, the discrete implicit generalized-method is employed. The resulting strongly coupled set of non-linear equations is then solved by means of a novel partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates full linearization of the overall incremental problem.Within the adaptive solution strategy, the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required. The adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field. For the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross-sections. To be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution. The numerical examples demonstrate the robustness and efficiency of the methodology.
This paper describes variational formulation and finite element discretization of surface tension. The finite element formulation is cast in the Lagrangian framework, which describes explicitly the interface evolution. In this context surface tension formulation emerges naturally through the weak form of the Laplace-Young equation.The constitutive equations describing the behaviour of Newtonian fluids are approximated over a finite time step, leaving the governing equations for the free surface flow function of geometry change rather than velocities. These nonlinear equations are then solved by using Newton-Raphson procedure.Numerical examples have been executed and verified against the solution of the ordinary differential equation resulting from a parameterization of the Laplace-Young equation for equilibrium shapes of drops and liquid bridges under the influence of gravity and for various contact angle boundary conditions.
SUMMARYThis work is concerned with the numerical modelling of incompressible Newtonian uid ows on moving domains in the presence of surface tension. The solution procedure presented is based on the stabilized equal order mixed velocity-pressure ÿnite element formulation of the incompressible Navier-Stokes equations, which is adapted to a moving domain by means of an arbitrary Lagrangian-Eulerian (ALE) technique. The accurate and very robust integration in time is achieved by employing the generalizedmethod. The surface tension boundary condition is rephrased appropriately within the framework of linear ÿnite elements. The solution procedure is veriÿed by comparing numerical solutions with the corresponding analytical solutions and experimental data. The overall solution procedure proves to be accurate, robust and e cient. It allows the simulation of extensive deformation of the uid domain without remeshing.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.