NUMERICAL STUDIES OF SOLUTIONS OF THE KROOK EQUATION OF KINETIC THEORY,
ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB
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Because of the difficulty encountered in evaluating the collision integral in the Boltzmann equation, it has been proposed to solve the nonequilibrium rarefied gas flow problems by using a substitute equation, namely the Krook equation which replaces the collision integral by a statistical or relaxation model. Even though the need to evaluate the complicated collision integral is eliminated in solving the Krook equation, the equation collision integral is eliminated in solving the Krook equation, the equation is still-non-linear and is still quite difficult to solve numerically. Error studies on the solutions of the Krook equation will give information on the errors in the solution of the Boltzmann equation because the solution algorithms are identical except for the different means of calculation of the collision integral. Because solutions to the Krook equation take much less time to compute, the systematic errors in the numerical method can be more accurately investigated. Four errors are studied, namely, those due to 1 the effect of the number of stations, 2 the effect of the variable of integration, 3 the effect of appropriate boundary conditions for the shock wave, and 4 the effect of a modification of the integration formula.
- Physical Chemistry
- Numerical Mathematics