In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Hydrodynamic model simulations of a steady-state electron shock wave in a 1-pm Si semiconductor device at 77 K are compared with a Monte Carlo simulation of the Boltzmann equation using the DAMOCLES program. Excellent agreement between the two different methods for simulating the electron shock wave can be obtained by adjusting the amount of heat conduction in the hydrodynamic model.

where u — u(x, t) in some domain and v is a parameter. The occurrence of the first derivative in t and the second in x clearly indicates the equation is parabolic, similar to the heat equation, while the interesting additional feature is the occurrence of the non-linear term u du/dx. The equation thus shows a structure roughly similar to that of the Navier-Stokes equations and has actually appe...

in the present work, an engineering method is developed to predict laminar and turbulent heating-rate solutions for blunt reentry spacecraft at hypersonic conditions. the calculation of aerodynamic heating around blunt bodies requires alternative solution of inviscid flow field around the hypersonic bodies. in this paper, the procedure is of an inverse nature, that is, a shock wave is assumed a...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect, it ’ s state equation remains always valid, except, it was called by gas calorically imperfect or gas at high temperatures. The purpose of this work is to develop a mathematical model for a normal shock wave normal at high temperature when the stagna...

An approach based on a discontinuous Galerkin discretization is proposed for the Bhatnagar-Gross-Krook model kinetic equation. This approach allows for a high order polynomial approximation of molecular velocity distribution function both in spatial and velocity variables. It is applied to model normal shock wave and heat transfer problems. Convergence of solutions with respect to the number of...

In this paper, the non-Fourier heat conduction in a semi-infinite body was examined. The heat wave non-Fourier heat conduction model was used for thermal analysis. Thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The heat source was also considered temperature-dependent which resulted in a non-homogeneous equation. The Mac-Cormack predictor-correct...

We model strong shock-wave propagation, both in the ideal gas and in the dense Lennard-Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic-temperature components on the hot, compressed side of the shock front. The ...