The linearized Boltzmann equation with Cercignani–Lampis boundary conditions: Basic flow problems in a plane channel

A polynomial expansion procedure and the ADO (analytical discrete-ordinates) method are used to solve a collection of basic flow problems based on the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani–Lampis boundary conditions with a free choice of the accommodation coefficients at each boundary. In particular, three classical problems defined by flow in a plane-parallel channel (Poiseuille, thermal-creep, and Couette flow) are solved (essentially) analytically and evaluated to a very high numerical standard. Some comparisons with known kinetic models are also reported.