K-Kernel Regularization of Mach 2000 Astrophysical Jets: Eliminating Gibbs Phenomenon in Supersonic Flows

The simulation of extreme Mach 2000 astrophysical flows traditionally encounters numerical instabilities, such as the Gibbs phenomenon and spurious oscillations, due to non-unique entropy solutions in turbulent regimes. Building upon recent computational explorations of statistical solutions (Simonis & Wissocq, 2026), this paper presents a deterministic alternative using the K-Kernel framework. By introducing a non-Markovian memory field that accumulates at the shock front, we demonstrate that memory acts as a self-regulating adaptive filter. This dynamic viscosity completely eliminates the spurious oscillations, enforcing a unique, physically admissible solution while maintaining the sharpness of the shock.