Аннотация:A new conservative discrete ordinate method for nonlinear model kinetic equations is proposed. The conservation property with
respect to the collision integral is achieved by satisfying at the discrete level approximation conditions used in deriving the model collision
integrals. Additionally to the conservation property, the method ensures the correct approximation of the heat fluxes. Numerical examples of flows with large gradients are provided for the Shakhov and Rykov model kinetic equatio