Abstract
A truly three-dimensional (3D) gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work. By local reconstruction of continuous Boltzmann equation, the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver. Different from conventional gas-kinetic scheme, in the present work, the distribution function at cell interface is computed in a straightforward way. As an extension of our previous work (Sun et al., Journal of Computational Physics, 300 (2015) 492–519), the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points. As a result, the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly. To validate the proposed flux solver, several incompressible and compressible viscous flows are simulated. Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows.
Highlights
In the last few decades, the gas-kinetic scheme has been developed in both continuum [1,2,3,4,5,6,7,8] and rarefied flow regimes [9,10,11,12]
Another difference is that the non-equilibrium distribution function is approximated by the difference of equilibrium distribution functions on the cell interface and its surrounding streaming nodes in gas-kinetic flux solver (GKFS) (see Eq (27)), while in the gas-kinetic BGK scheme, the non-equilibrium distribution function is included in the initial distribution function around the cell interface
5 Conclusions This paper presents a three-dimensional GKFS for simulation of incompressible and compressible viscous flows
Summary
In the last few decades, the gas-kinetic scheme has been developed in both continuum [1,2,3,4,5,6,7,8] and rarefied flow regimes [9,10,11,12]. Unlike the traditional Riemann solver [13,14,15], the gas-kinetic scheme reconstructs the solution for the continuous Boltzmann equation at local cell interface. It is usually more complicated and inefficient than conventional computational fluid dynamics (CFD) schemes This is because in the gas-kinetic BGK scheme, a number of coefficients related to the physical space should be calculated to evaluate the distribution function at each interface and each time step. To the best of our knowledge, there is still no work of the gas-kinetic BGK scheme which can give explicit formulations for evaluating the conservative variables and numerical fluxes. The non-equilibrium distribution function at cell interface can be calculated and the explicit formulations for computing the conservative flow variables and fluxes can be derived.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
