Variational multiscale method for coupled systems: free-surface flows and stratified turbulence

This dissertation presents a robust numerical method for the class of coupled systems comprised of multiple interacting partial differential equations (PDE). Particular emphasis is placed on incompressible Navier-Stokes equations that are coupled with a hyperbolic scalar PDE. The method is derived based on the variational multiscale (VMS) framework. Specifically, two classes of coupled systems are considered: free-surface flows with a sharp interface marker and stratified turbulence with a smooth temperature field. The additional nonlinearity introduced by the active scalar field to the nonlinear Navier-Stokes equation system is effectively accounted for by variationally derived stabilization term. In the context of the free-surface flows that are modeled by immiscible two-phase fluids, the dependency of fluid mechanical properties (i.e., density and viscosity) on the implicit interface marker (e.g., signed distance field) results in an interface that traverses through the elements. Applying VMS method to the coupled system results in an interface stabilization term. It is shown that the structure of the stabilization term leads to the so-called Ghost-Penalty method. In the context of internal dissipation in thermodynamics for incompressible flow with Boussinesq approximation, an energy conservation equation is appended that gives rise to a thermomechanically coupled system. The coupled fine-scale sub-problem is locally resolved to yield the closure model. The fine-scale turbulence features are accounted for by the VMS strategy wherein the hierarchical application of VMS results in further enhancement of the mass conservation. The new method for coupled systems is implemented using hexahedral and tetrahedral elements, and the code is parallelized for the distributed memory system. A range of problems is presented to show the mathematical and computational features of the method.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Zhu, Lixing

Contributors dc:contributor

• Masud, Arif
• Duarte, C. Armando
• Lopez-Pamies, Oscar
• Yan, Jinhui

• Turbulent modelling
• Variational Multiscale method
• Arbitrary Lagrangian-Eulerian
• Level-set method
• Stratification
• Free surfaces
• Interface stabilization

Statement dc:rights

• Copyright 2019 Lixing Zhu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/106470

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106470