High-Order and Wavelet-Adaptive Immersed Methods for PDEs on Complex Domain Geometries

The development of immersed methods brings a promising solution to the numerical simulation of interface-coupled multi-physics problems, such as multi-phase flows and fluidstructure interactions. This renders necessitates the design of novel high-order and efficient solvers based on immersed methods. This thesis examines two pivotal aspects of these methods: firstly, the acceleration of computational processes via adaptive resolution strategies; and secondly, the enhancement of accuracy order while sustaining numerical stability. To achieve the former, we develop a novel wavelet transform algorithm applicable to computational domains with arbitrary geometries. This wavelet transform maintains the order of the wavelet and serves as an indicator for local truncation error (LTE), resulting in an adaptive resolution strategy with explicit error control. To address the latter, we introduce a fifth-order upwind finite difference (FD) scheme that sustains numerical stability across any immersed interface discretization.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Center for Computational Science and Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2025

Author dc:creator

• Shen, Changxiao Nigel

Advisor dc:contributor.advisor

• Van Rees, Wim M.

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/159943

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/159943