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 origin. To mitigate this problem, we transform the conservation laws in 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. Preliminary results for fast magnetosonic shock in MHD are presented and compared with results from geometrical shock dynamics. This sort of shock fitting is a precursor to future multi-dimensional stability analysis of imploding shocks.
Talha Arshad received his bachelor's degree in Aerospace Engineering from National University of Sciences and Technology, Pakistan in 2018. In 2019 he joined the Mechanical Engineering Program of PSE, KAUST as a MS/PhD student. He is currently associated with the Fluid and Plasma Simulation Laboratory (FPSL) working under the supervision of Dr. Ravi Samtaney. His research interests include computational magnetohydrodynamics, computational fluid dynamics, shock capturing and tracking methods.
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