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Nonlinear Evolution of Weak Discontinuity Waves in Darcy-Type Porous Media
Published in Ziya Uddin, Mukesh Kumar Awasthi, Rishi Asthana, Mangey Ram, Computing and Simulation for Engineers, 2022
Across a characteristic shock, the Rankine–Hugoniot conditions are given as [u]=0,[ρ]=0,[p]=0,t=βatα=0.
Wave-Dielectric Interactions II: Growth Estimates and Existence of Smooth Solutions
Published in Frederick Bloom, Mathematical problems of classical nonlinear electromagnetic theory, 2020
The singular surface I’ is then said to satisfy the viscosity-capillarity admissibility condition if there exists û, ŵ such that (3.7.13), (3.7.14) are satisfied at all points (γ(t), t) ∈ Γ. For A > 0, Slemrod [158] establishes the equivalence of the above admissibility criterion and the standard Lax shock condition for the case of a strictly hyperbolic, genuinely nonlinear system; he also establishes conditions under which, for a propagating phase boundary Γ, a state “on the left” in the liquid phase determines a state “on the right” so as to make Γ (and the weak solution) admissible according to the viscosity-capillarity criteria. This latter result differs from the standard shock wave theorem, for materials which do not undergo phase transitions, where one state can be connected by a shock to any other state, as long as the Rankine-Hugoniot conditions are satisfied and the shock is compressive.
Evolution of turbulent mixing driven by implosion in spherical geometry
Published in Journal of Turbulence, 2023
Tao Wang, Min Zhong, Bing Wang, Ping Li, Jingsong Bai
An air shock wave with match number M = 1.25 moves towards the centre and impacts the initial perturbed interface. The shock wave satisfies the Rankine–Hugoniot conditions, which illustrates that the flow behind the incident shock is uniform. The two gases have a constant ambient temperature of 294.14 K, and the initial properties of Air and SF6 at the constant temperature are listed in Table 1. The computation domain is discretised by applying a grid resolution of 1024 × 512 × 512 in spherical coordinates (r, θ, φ).