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Abstract: We propose a new interpolation technique for the CIP method applied to curvilinear coordinates. The CIP method can hardly maintain third-order accuracy on curvilinear coordinates. The reason for the degeneracy in accuracies has not been discussed in detail. This paper reveals the problems of the CIP method on curvilinear coordinates and presents an improved CIP method to solve the advection equation accurately. The features of the presented method are: (1) the metric computation on the upwind stencil is defined in the same manner as in the advection phase of the CIP method; and (2) gradient values in the physical domain in the computation on the curvilinear coordinates are used. Various test problems show that the improved CIP method has approximate third-order accuracy. [Copyright &y& Elsevier]

Monatomic molecular recombination is formulated using the Boltzmann kinetic equation. The recombination is coupled to the diatomic molecular vibrational states using the truncated harmonic oscillator model. The obtained recombination rate is equal to the modified Arrhenius rate, which is independent of the dissociation (activation) energy, when the temperature defined in the gain term on the basis of the intermediate’s collisions is much lower than that of the dissociation. The formulated model is numerically analyzed by solving the hypersonic shock layer problem with dissociation-recombination reactions. The obtained numerical results indicate that dissociated monatomic molecules behind a shock wave recombine into diatomic molecules owing to the decrease in the temperature near the wall. [ABSTRACT FROM AUTHOR]

Abstract: The relativistic shock layer problem was numerically analyzed by using two relativistic Boltzmann–kinetic equations. One is Marle model, and the other is Anderson–Witting model. As with Marle model, the temperature of the gain term was determined from its relation with the dynamic pressure in the framework of 14-moments theory. From numerical results of the relativistic shock layer problem, behaviors of projected moments in the nonequilibrium region were clarified. Profiles of the heat flux given by Marle and Anderson–Witting models were similar to the profile approximated by Navier–Stokes–Fourier law. On the other hand, profiles of the dynamic pressure given by Marle and Anderson–Witting models were quite opposite to the profile of the dynamic pressure approximated by Navier–Stokes–Fourier law. Additionally, we discuss the differences between Anderson–Witting model and Marle model by focusing on the fact that the relaxational rate of the distribution function depends on both flow velocity and molecular velocity for Anderson–Witting model, while it depends only on the molecular velocity for Marle model. [Copyright &y& Elsevier]

The direct description of chemical reactions by the Boltzmann equation still involves some difficulties in the kinetic theory. In this paper, we describe diatomic molecular dissociation due to transitions of vibrational quantum states resulting from inelastic collisions. These can be described by the Wang Chang-Uhlenbeck (WCU) equation. To avoid direct evaluation of the strong nonlinear collision kernel of the WCU equation, we used a kinetic equation. For accurate description of the dissociation process, we describe improvements we made to the conventional inelastic collision model (the so-called Morse model). Combining this inelastic collision model with the gas mixture model by Oguchi, we formulated a model for representing diatomic molecular dissociations. We validated this model by simulating a hypersonic shock layer with diatomic molecular dissociation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the local time step method is applied to the lattice Boltzmann method (LBM) on non-uniform grid (generalized form of interpolation supplemented LBM: GILBM) for steady flow simulations. The local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non-uniform grid. First, code validation for global time step method is performed by solving flow around a cylinder at low Reynolds numbers. Our results show good agreement with previous studies. Two-dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions. The pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement. They are also consistent with the previous studies. At the same time, CPU time required to obtain the steady-state solutions using the local time step are reduced by 70–80% compared with that using global time step. [Copyright &y& Elsevier]