A Gas-Kinetic Unified Algorithm for Non-Equilibrium Polyatomic Gas Flows Covering Various Flow Regimes (Communications in Computational Physics, 2021)
In this paper, a gas-kinetic unified algorithm (GKUA) is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes. Basedon the ellipsoidal statistical model with rotational energy excitation, the computablemodelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function. By constructing thecorresponding conservative discrete velocity ordinate method for this model, the conservative properties during the collision procedure are preserved at the discrete levelby the numerical method, decreasing the computational storage and time. Explicitand implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solvethe discrete hyperbolic conservation equations directly. Applying the new GKUA,some numerical examples are simulated, including the Sod Riemann problem, homogeneous flow rotational relaxation, normal shock structure, Fourier and Couette flows,supersonic flows past a circular cylinder, and hypersonic flow around a plate placednormally. The results obtained by the analytic, experimental, direct simulation MonteCarlo method, and other measurements in references are compared with the GKUAresults, which are in good agreement, demonstrating the high accuracy of the presentalgorithm. Especially, some polyatomic gas non-equilibrium phenomena are observedand analysed by solving the Boltzmann-type velocity distribution function equationcovering various flow regimes.