The grid-aligned shock instability prevents an accurate computation of high Mach number flows using low-dissipation shock-capturing methods. In particular one manifestation, the so-called carbuncle phenomenon, has been investigated by various different groups over the past decades. Nevertheless, the mechanism of this instability is still not fully understood and commonly is suppressed by the introduction of additional numerical dissipation. However, present approaches may either significantly deteriorate the resolution of complex flow evolutions or involve additional procedures to limit stabilization measures to the shock region. Instead of increasing the numerical dissipation, in this paper, we present an alternative approach that relates the problem to the low Mach number in transverse direction of the shock front. We show that the inadequate scaling of the acoustic dissipation in the low Mach number limit is the prime reason for the instability. Our approach is to increase the "numerical" Mach
Most technological advancements in medicine, process and energy engineering, life and food science, mobility and environmental engineering involve mastering fluid mechanical effects. In particular, compressible flow physics including shockwaves and phase‐interface interactions exhibit multi‐scale phenomena spanning several orders of magnitude upwards from nanometer and nanosecond time scales. Clearly, detailed analysis of such effects is impossible by means of experimental techniques. On the contrary, numerical modeling and simulations allow to capture the aforementioned mechanisms and provide non‐invasive access to any quantity of interest. Yet, the complex fluid physics require powerful computational methods utilizing recent advancements for high‐order schemes. In this work, we provide an overview on latest high‐order low‐dissipation schemes using level sets to model discontinuous phase‐interface interactions.
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