Gas-Kinetic Unified Algorithm for Re-Entering Complex Problems Covering Various Flow Regimes by Solving Boltzmann Model Equation

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

“…f and 1 f remain with probability density distribution and possess the property of exponential function exp(-c 2 ), then the DVOM and numerical quadrature formula from the GKUA [18,19,22] can be applied to discretize and remove the continuous dependency of the reduced VDF equation (3) …”

“…w n denotes the number density of molecules diffusing from the solid surface, which can be derived from the insulated condition of zero mass flux [19,22] normal to the wall surface. …”

“…The time-splitting technique can be employed to split the convective movement and the colliding relaxation terms so as to couple to solve them in the computation [19,22], and then the finite difference second-order scheme for solving the discretized and reduced VDFs are constructed as…”

“…By introducing f N and , the resultant Boltzmann model equation links the macroscopic flow variables, gas viscosity transport properties, thermodynamic effect, the flow state controlling parameter and molecular interaction rule with molecular models in unified expressions for the full spectrum of flow regimes. The GKUA has been successfully applied to the gas flows [19,21,22] covering the whole range of flow regimes from continuum to free-molecule flow around spacecrafts and microchannels from low to high Mach numbers. Recently, a unified gas-kinetic scheme has been developed [23,24] for the one-dimensional shock structures and two-dimensional jets of both continuum and rarefied flows from the combination of BGK-type schemes and above-mentioned DVOM on the GKUA.…”