In the current work, for the first time, we extend the application of a second order slip/jump equations introduced by Karniadakis et al. for the simulation of high speed, high Knudsen (Kn) number flows over flat plate and cylinder. The NS equations subject to a second order slip/jump boundary conditions are solved using the Petrov-Galerkin Finite Element discritization. We compare our numerical solution for flow and thermal field with the solution of the DSMC and Generalized Hydrodynamic (GH) techniques, as well as a recently developed slip/jump boundary condition, i.e., Paterson equation. Current results demonstrate the suitable accuracy of the employed boundary conditions for different set of test cases. Our numerical solutions are obtained with much less numerical costs compared to alternative boundary conditions.

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