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In the present study, the shock-disturbances interaction in hypersonic inviscid flows with real gas effects is studied by applying a high-order accurate numerical method with the shock capturing technique. To consider real gas effects, the equilibrium air model is utilized here. The strong conservative form of the unsteady compressible Euler equations in the 2D generalized curvilinear coordinates is formulated and the resulting system of equations for the equilibrium air model is discretized by using the fifth-order finite-difference WENO scheme in space and the explicit third-order TVD Runge–Kutta scheme in time to provide a highly accurate and robust equilibrium airflow solver. The... 

In the present study, shock-disturbances interaction in high-speed compressible inviscid flow is simulated utilizing the weighted essentially non-oscillatory (WENO) scheme by employing the shock-capturing technique. For this aim, the two-dimensional Euler equations in strong conservative form are discretized by using the explicit third-order TVD Runge–Kutta scheme in time and the fifth-order WENO finite difference scheme in space. The main advantage of using the WENO scheme is its capability for properly solving the discontinuities in the domain without needing any artificial viscosity, limiter function or filter. Hence, this scheme is stable, and thus, it is suitable for simulating very... 

This paper investigates implementation of upwind compact implicit and explicit high-order finite difference schemes for solution of the level set equation. The upwind compact implicit and explicit high-order finite difference schemes are well-known techniques to descritize spatial derivatives for convection term in hyperbolic equations. Applying of upwind high-order schemes on the level set equation leads to less error and CPU time reduction compared to essential non-oscillatory (ENO), weighted essential non-oscillatory schemes (WENO), and even different particle level set methods. The results indicate the error based on area loss decreases drastically with applying high-order upwind,...