A numerical solution of inviscid transonic flow using the Boltzmann equation.

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  • ボルツマン方程式による非粘性遷音速流れの数値計算
  • ボルツマン ホウテイシキ ニ ヨル ヒ ネンセイ センオンソク ナガレ ノ ス

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An efficient numerical method of the Boltzmann equation has been developed for inviscid transonic flow. In this method, the convective terms in the Boltzmann equation are approximated by the second order upwind finite difference with limiter: The rational Runge-Kutta scheme is used for the corresponding time integration. The residual averaging technique is incorporated into the method so that the rate of convergence is improved to a steady-state solution. The solution of the collision integral is obtained as thermodynamic equilibrium states. The number of grid points in molecular velocity space is reduced to 4 for each direction to shorten the CPU time in the present approach. As an example, the one-dimensional unsteady shock-tube problem is solved and the results are compared with the exact solution. The feasibility of the present method is demonstrated for the two-dimensional transonic flow in a channel, and over the NACA0012 airfoil and the RAE2822 airfoil. Those results are compared with the results of the Euler equations.

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