Finite element solution of interface and free surface three-dimensional fluid flow problems using flow-condition-based interpolation

The necessity for a highly accurate simulation scheme of free surface flows is emphasized in various industrial and scientific applications. To obtain an accurate response prediction, mass conservation must be satisfied. Due to a continuously moving fluid domain, however, it is a challenge to maintain the volume of the fluid while calculating the dynamic responses of free surfaces, especially when seeking solutions for long time durations. This thesis describes how the difficulty can be overcome by proper employment of an Arbitrary Lagrangian Eulerian (ALE) method derived from the Reynolds transport theorem to compute unsteady Newtonian flows including fluid interfaces and free surfaces. The proposed method conserves mass very accurately and obtains stable and accurate results with very large solution steps and even coarse meshes. The continuum mechanics equations are formulated, and the Navier-Stokes equations are solved using a 'flow-condition-based interpolation' (FCBI) scheme. The FCBI method uses exponential interpolations derived from the analytical solution of the 1-dimensional advection-diffusion equation. The thesis revisits the 2-dimensional FCBI method with special focus on the application to flow problems in highly nonlinear moving domains with interfaces and free surfaces, and develops an effective 3-D FCBI tetrahedral element for such applications. The newly developed 3-D FCBI solution scheme can solve flow problems of a wide range since it can handle highly nonlinear and unsteady flow conditions, even when large mesh distortions occur. Various example solutions are given to show the effectiveness of the developed solution schemes.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• You, Soyoung, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Klaus-JUrgen Bathe.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/97845

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/97845