A Multiple Temperature Kinetic Model and Its Application to Near Continuum Flows (Communications in Computational Physics, 2008)
In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)]. Basedon this model, the stress strain relationship in the Navier-Stokes (NS) equations is replaced by the translational temperature relaxation terms. The kinetic model has beensuccessfully used in both continuum and near continuum flow computations. In thispaper, we will further validate the multiple translational temperature kinetic model toflow problems in multiple dimensions. First, a generalized boundary condition incorporating the physics of Knudsen layer will be introduced into the model. Second, thedirect particle collision with the wall will be considered as well for the further modification of particle collision time, subsequently a new effective viscosity coefficient willbe defined. In order to apply the kinetic model to near continuum flow computations,the gas-kinetic scheme will be constructed. The first example is the pressure-drivenPoiseuille flow at Knudsen number 0.1, where the anomalous phenomena betweenthe results of the NS equations and the Direct Simulation Monte Carlo (DSMC) methodwill be resolved through the multiple temperature model. The so-called Burnett-ordereffects can be captured as well by algebraic temperature relaxation terms. Another testcase is the force-driven Poiseuille flow at various Knudsen numbers. With the effective viscosity approach and the generalized second-order slip boundary condition, theKnudsen minimum can be accurately obtained. The current study indicates that it isuseful to use multiple temperature concept to model the non-equilibrium state in nearcontinuum flow limit. In the continuum flow regime, the multiple temperature modelwill automatically recover the single temperature NS equations due to the efficientenergy exchange in different directions.