On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws
dc.contributor.author | Maeng, Jungyeoul | |
dc.date.accessioned | 2017-10-05T20:29:57Z | |
dc.date.available | NO_RESTRICTION | |
dc.date.available | 2017-10-05T20:29:57Z | |
dc.date.issued | 2017 | |
dc.date.submitted | 2017 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/138695 | |
dc.description.abstract | A new class of numerical methods called Active Flux (AF) is investigated for nonlinear hyperbolic conservation laws. The AF method is designed specifically to address the aspect that most modern compressible flow methods fail to do; the multidimensionality aspect. It addresses the shortcoming by employing a two stage update process. In the first stage, a nonconservative form of the system is introduced to provide the flexibility to pursue distinct numerical approaches for flow processes with differing physics. Because each process is treated separately, the numerical method can be appropriately formed to reflect each type of physics and to provide the maximal stability. The method is completed with the conservation update to produce a third-order accurate scheme. The AF advection scheme is founded on the characteristic tracing method, a semi-Lagrangian method, which has long been used for developing numerical methods for hyperbolic problems. The first known AF method for advection, Scheme V by van Leer, is revisited as a part of the development of the scheme. Details of Scheme V are examined closely, and new improvements are made for the multidimensional nonlinear advection scheme. A detailed study of the nonlinear system of equations is made possible by the pressureless Euler system, which is the advective component of the Euler system. It serves as a stepping stone for the Euler system, and all necessary details of the nonlinear system are explored. Lastly, an extension to the Euler system is presented where a novel nonlinear operator splitting method is introduced to correctly blend the contributions of the nonlinear advection and acoustic processes. The AF method, as a result, produces a maximally stable, third-order accurate method for the multidimensional Euler system. Some guiding principles of limiting are presented. Because two types of flow feature are separately treated, the limiting process must also be kept separate. Advective problems obeying natural bounding principles are treated differently from acoustic problems with no explicit bounding principles. Distinct limiting approaches are explored along with discussions. | |
dc.language.iso | en_US | |
dc.subject | Active Flux Schemes | |
dc.subject | High-order numerical method | |
dc.subject | Advection schemes | |
dc.title | On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws | |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Aerospace Engineering | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.contributor.committeemember | Roe, Philip L | |
dc.contributor.committeemember | Krasny, Robert | |
dc.contributor.committeemember | Duraisamy, Karthik | |
dc.contributor.committeemember | Fidkowski, Krzysztof J | |
dc.subject.hlbsecondlevel | Aerospace Engineering | |
dc.subject.hlbtoplevel | Engineering | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/138695/1/jmaeng_1.pdf | |
dc.identifier.orcid | 0000-0002-7798-7865 | |
dc.identifier.name-orcid | Maeng, Jungyeoul; 0000-0002-7798-7865 | en_US |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.