An efficient discrete velocity method with inner iteration for steady flows in all flow regimes

Abstract

An efficient improved discrete velocity method (IDVM) with inner iteration is presented to simulate the steady flows in all flow regimes in this work. It is an extension of our previous implicit IDVM to achieve a faster convergence rate. In the previous method, both the discrete velocity Boltzmann equation (DVBE) and the corresponding macroscopic governing equations are solved synchronously, where the computational discrete cost is dominated by the calculation of the DVBE since the number of distribution functions is far larger than that of macroscopic conservative variables. Furthermore, the convergence rate of the calculation of the DVBE is affected by the predicted equilibrium state obtained from the solution of macroscopic governing equations. To provide a more accurate predicted equilibrium state for the fully implicit discretization of the DVBE, an inner iteration is introduced into the solution of macroscopic governing equations, and the flux Jacobian of these equations is evaluated by the difference of numerical fluxes of Navier–Stokes equations rather than the Euler equation-based flux splitting method used in the previous implicit IDVM. This more accurate prediction procedure endows the developed method to accelerate the computation greatly, especially in the continuum flow regime. Numerical results indicate that, in the continuum flow regime, the present method is about one order of magnitude faster than the previous implicit IDVM and one to two orders of magnitude faster than the conventional semi-implicit DVM.