Numerical Simulations of Unsteady Flows from Rarefied Transition to Continuum Using Gas-Kinetic Unified Algorithm (Advances in Applied Mathematics and Mechanics, 2018)
Numerical simulations of unsteady gas flows are studied on the basis ofGas-Kinetic Unified Algorithm (GKUA) from rarefied transition to continuum flowregimes. Several typical examples are adopted. An unsteady flow solver is developedby solving the Boltzmann model equations, including the Shakhov model andthe Rykov model etc. The Rykov kinetic equation involving the effect of rotationalenergy can be transformed into two kinetic governing equations with inelastic andelastic collisions by integrating the molecular velocity distribution function with theweight factor on the energy of rotational motion. Then, the reduced velocity distributionfunctions are devised to further simplify the governing equation for one- and two-dimensionalflows. The simultaneous equations are numerically solved by the discretevelocity ordinate (DVO) method in velocity space and the finite-difference schemes inphysical space. The time-explicit operator-splitting scheme is constructed, and numericalstability conditions to ascertain the time step are discussed. As the applicationof the newly developed GKUA, several unsteady varying processes of one- and two-dimensionalflows with different Knudsen number are simulated, and the unsteadytransport phenomena and rarefied effects are revealed and analyzed. It is validatedthat the GKUA solver is competent for simulations of unsteady gas dynamics coveringvarious flow regimes.