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Supersonic Euler and Magnetohydrodynamic Flow Past Cones

Holloway, Ian C.
http://rave.ohiolink.edu/etdc/view?acc_num=wright157653243620814

Abstract Details

2019, Doctor of Philosophy (PhD), Wright State University, Interdisciplinary Applied Science and Mathematics PhD.
This work contains the derivation and type analysis of the conical Euler and Ideal Magnetohydrodynamic equations. The 3 dimensional Euler equations and the Ideal MHD equations with Powell source terms, subject to the assumption that the solution is conically invariant, are projected onto a unit sphere using tools from tensor calculus. Conical flows provide valuable insight into supersonic and hypersonic flow past bodies, but are simpler to analyze and solve numerically. Previously, work has been done on conical inviscid flows governed by the compressible Euler equations with great success. It is known that some flight regimes involve flows of ionized gases, and thus there is motivation to extend the study of conical flows to the case where the gas is electrically conducting. This thesis shows that steady conical flows for these cases do exist mathematically and that the governing systems of partial differential equations are of mixed type. Throughout the domain they can be either hyperbolic or elliptic depending on the solution. A numerical scheme is also developed to solve the conical Euler and Ideal Magnetohydrodynamic equations. Special care had to be taken in developing the method because these equations contain geometric source terms which account for the fact that they are defined on a curved surface. In order for a numerical method to accurately capture the behavior of the system it is solving, any source terms must be discretized in a way which preserves the appropriate behavior. For a partial differential equation which has been formulated on a curved manifold using tensor calculus, it is desirable for the discretization to preserve the tensorial transformation relationships. Such discretizations are presented in this work, and a numerical method involving them is developed and demonstrated.
Sivaguru Sritharan, Ph.D. (Committee Co-Chair)
Qun Li, Ph.D. (Committee Co-Chair)
Qingbo Huang, Ph.D. (Committee Member)
Mohammed Sulman, Ph.D. (Committee Member)
135 p.
Applied Mathematics
systems of mixed type; Euler equations; supersonic flows; PDE on a manifold; Magnetohydrodynamics; Magnetoaerodynamics

Recommended Citations

Citations

  • Holloway, I. C. (2019). Supersonic Euler and Magnetohydrodynamic Flow Past Cones [Doctoral dissertation, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright157653243620814

    APA Style (7th edition)

  • Holloway, Ian. Supersonic Euler and Magnetohydrodynamic Flow Past Cones. 2019. Wright State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright157653243620814.

    MLA Style (8th edition)

  • Holloway, Ian. "Supersonic Euler and Magnetohydrodynamic Flow Past Cones." Doctoral dissertation, Wright State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=wright157653243620814

    Chicago Manual of Style (17th edition)

wright157653243620814
229
© 2019, all rights reserved.
This open access ETD is published by Wright State University and OhioLINK.