A DISCRETE ORDINATE TECHNIQUE FOR THE NON-LINEAR BOLTZMANN EQUATION WITH APPLICATION TO PSEUDO-SHOCK RELAXATION.
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GENERAL ELECTRIC CO PHILADELPHIA PA MISSILE AND SPACE DIV
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A numerical method for the solution of the non-linear Boltzmann equation for hard sphere molecules is developed, in which approximations are made only in the sense of numerical truncations. This is an extension of the work on the linearized Boltzmann equation previously reported in AD-604 749. The distribution function is evaluated at a three-dimensional grid of distinct velocity points. A five fold Gaussian quadrature is performed to evaluate the derivatives at these points. The distribution function is then evaluated at t sub o delta t by solving a system of first order ordinary differential equations. In the non-linear case the grid is no longer closed, and the procedure to circumvent the difficulty is described. In the present paper, this technique is applied to the problem of non-linear, homogeneous, pseudo-shock relaxation. Author
- Fluid Mechanics