We apply moment methods to obtaining an approximate analytical solution to Knudsen layers. Based on the hyperbolic regularized moment system for the Boltzmann equation with the Shakhov collision model, we derive a linearized hyperbolic moment system to model the scenario with the Knudsen layer vicinity to a solid wall with Maxwell boundary condition. We find that the reduced system is in an even-odd parity form that the reduced system proves to be well-posed under all accommodation coefficients. We show that the system may capture the temperature jump coefficient and the thermal Knudsen layer well with only a few moments. With the increasing number of moments used, qualitative convergence of the approximate solution is observed.
Download