Abstract
In this work, a double distribution function-based lattice Boltzmann flux solver (LBFS) is proposed for simulating compressible viscous flows. This approach utilizes the double distribution function compressible lattice Boltzmann model and employs Chapman–Enskog expansion analysis to connect the lattice Boltzmann equation (LBE) with the Navier–Stokes (N–S) equations. Unlike conventional computational fluid dynamics methods that compute inviscid and viscous fluxes separately, the present method simultaneously evaluates both types of fluxes at the cell interface by locally reconstructing the solution of the LBE. Recognizing the significance of considering the non-equilibrium part of distribution functions for viscous flows, a straightforward method is introduced to calculate this component. This facilitates the derivation of computational expressions for macroscopic conservative variables and fluxes in the N–S equations. To validate the accuracy and stability of the present numerical scheme, various benchmark problems, including shock tube problem, Couette flow, lid-driven cavity flow, and flow around the NACA0012 airfoil, are tested. The obtained numerical results are compared with analytical solutions or existing reference data, confirming the capability of the proposed LBFS to deliver accurate and stable numerical results for compressible flows. Moreover, this method demonstrates effectiveness in handling viscous flow problems on non-uniform grids and with curved boundaries.
Funder
National Natural Science Foundation of China
National Key Basic Research Projects
Natural Science Foundation of Jiangsu Province
Fundamental Research Funds for the Central Universities
Fund of Prospective Layout of Scientific Research for NUAA
Priority Academic Program Development of Jiangsu Higher Education Institutions