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A Lagrangian/Eulerian Approach for Capturing Topological Changes in Moving Interface Problems

Grabel, Michael Z
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563527241172213

Abstract Details

2019, MS, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
In this thesis, a numerical method for capturing topological changes as two moving interfaces intersect is presented. A moving interface is a co-dimension one set of points embedded within an N-dimensional space whose position evolves in time. In a Lagrangian framework, the interface can be approximated by a discrete set of points called marker particles that explicitly define the interface's position. The marker particle approach is straightforward to implement and is efficient but if two interfaces intersect, the interfaces will overlap and the approximation becomes invalid. The method proposed in this thesis addresses the difficulty of capturing topological changes when using marker particles through the use of local projections to and from an Eulerian frame of reference. This approach allows topological changes to be resolved naturally without arbitrary rules or ad-hoc reconstruction of the interface. This method is applied to benchmark problems that exhibit topological changes and numerical results suggest that this approach shows convergence.
Benjamin Vaughan, Ph.D. (Committee Chair)
Donald French, Ph.D. (Committee Member)
Stephan Pelikan, Ph.D. (Committee Member)
90 p.
Applied Mathematics
Moving Interfaces; Front Tracking; Topological Change; Marker Particle Methods; Numerical Methods; Frame of Reference

Recommended Citations

Citations

  • Grabel, M. Z. (2019). A Lagrangian/Eulerian Approach for Capturing Topological Changes in Moving Interface Problems [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563527241172213

    APA Style (7th edition)

  • Grabel, Michael. A Lagrangian/Eulerian Approach for Capturing Topological Changes in Moving Interface Problems. 2019. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563527241172213.

    MLA Style (8th edition)

  • Grabel, Michael. "A Lagrangian/Eulerian Approach for Capturing Topological Changes in Moving Interface Problems." Master's thesis, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563527241172213

    Chicago Manual of Style (17th edition)

ucin1563527241172213
206
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This open access ETD is published by University of Cincinnati and OhioLINK.