General mechanisms for stabilizing weakly compressible models

Many weakly compressible models with intrinsic mechanisms for stabilizing computation have been proposed to simulate incompressible flows. The present paper analyzes several weakly compressible models to establish general mechanisms that incorporate them into a unified and simple framework. It is found that all these models contain some identical numerical dissipation terms, mass diffusion terms in the continuity equation, and bulk viscosity terms in the momentum equation. They are proven to provide general mechanisms for stabilizing computation. Referring to the general mechanisms and the computational procedures of the lattice Boltzmann flux solver, two general weakly compressible solvers for isothermal flows and thermal flows are proposed. They can be directly derived from standard governing equations and implicitly introduce those numerical dissipation terms. Detailed numerical investigations demonstrate that the two general weakly compressible solvers have good numerical stability and accuracy for both isothermal and thermal flows, which validates the general mechanisms further and the general approach of constructing general weakly compressible solvers.