Converging shocks have long been a topic of interest in theoretical fluid mechanics,
and are of prime importance in inertial confinement fusion. However, tracking
converging shocks in numerical schemes poses several challenges. Numerical schemes
based on shock capturing inherently diffuse out shocks to multiple grid cells, making
it hard to track the shock. Converging shocks are significantly harder to track, as
this numerical smearing is much more significant when converging shocks approach
the axis of convergence. To mitigate this problem, we transform the conservation
laws to a non-inertial frame of reference in which the accelerating shock is stationary.
A system of equations is derived based on the transformed conservation laws
coupled to the shock speed obtained from jump conditions and a characteristic-based
derivation of a relation governing shock acceleration. We solve these equations using
a finite volume method. Our numerical results compare favorably with the analytical
value of Guderley exponent for self-similarly converging cylindrical hydrodynamic
shocks. Results for fast magnetosonic shock in MHD are also presented and compared
with results from geometrical shock dynamics (GSD). Results from our shock
fitting method, developed without any approximation to the original ideal magnetohydrodynamics
equations, provide further credibility to GSD applied to converging
fast magnetosonic shocks. This sort of shock fitting is a precursor to future multidimensional
stability analysis of imploding shocks.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/670162 |
| Date | 07 1900 |
| Creators | Arshad, Talha |
| Contributors | Samtaney, Ravi, Physical Science and Engineering (PSE) Division, Farooq, Aamir, Parsani, Matteo, Bakhsh, Abeer |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | 2023-07-12, At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis will become available to the public after the expiration of the embargo on 2023-07-12. |
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