2026-09-19T00:59:01Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1599432026-07-08T12:57:06Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Van Rees, Wim M.
Shen, Changxiao Nigel
Massachusetts Institute of Technology. Center for Computational Science and Engineering
2025-07-07T17:39:49Z
2025-07-07T17:39:49Z
2025-05
2025-05-20T21:15:21.468Z
https://hdl.handle.net/1721.1/159943
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.
S.M.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright retained by author(s)
https://rightsstatements.org/page/InC-EDU/1.0/
High-Order and Wavelet-Adaptive Immersed Methods for PDEs on Complex Domain Geometries
Thesis
application/pdf
Master
Master of Science in Computational Science and Engineering
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="19dfb438-1c25-4f53-a370-65bc3728ae80">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>High-Order and Wavelet-Adaptive Immersed Methods for PDEs on Complex Domain Geometries</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2025-05</PublicationDate>
<Authors>
<Author>
<DisplayName>Shen, Changxiao Nigel</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>https://rightsstatements.org/page/InC-EDU/1.0/</License>
<Abstract>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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>