I am developing code on Compressible LBM . I have followed many articles but unable to do so. Can anyone guide me through this regarding which method is most promising for flows upto 4 Mach and beyond. I am currently using Entropic LBM and am struck on Lagrange multipliers.
Thanks and regards
Umer
To efficiently simulate the subsonic to supersonic compressible 3D flows with shocks, an extended hybrid lattice Boltzmann method has been proposed in the literature. The mass and momentum conservation equations are solved using an extended lattice Boltzmann model with a hybrid recursive regularization collision operator on the D3Q19 lattice stencil. The optimised form of the collision kernel, Hermite basis and the correction terms have been proposed. The energy conservation law is implemented by solving the entropy conservation equation written in the non-conservative form to minimize the influence of high-order errors on mass conservation stemming from LBM on a finite volume framework. The total number of degrees of freedom per cell is 20, which is among the most efficient existing LB methods for high-speed compressible flows. The isotropic feature is well preserved by the revised equilibrium distribution function on the D3Q19 lattice. Numerical tests show that this extended hybrid method can accurately and efficiently simulate the compressible flow problems with shock waves including the shock-capturing, the reflection and interaction of shock waves, shock-vortex interaction and the problem of the supersonic laminar boundary layer. The proposed method is well suited for supersonic flows without strong non-equilibrium effects, for which the imposed Q19 lattice would not be accurate enough. To handle rarefied gas dynamics, hypersonic flows or reactive plasma flows higher-order lattices of non-LB methods with an optimized selection of discrete velocities should certainly be considered. The theoretical demonstration of the convergence of this method toward the Navier-Stokes solutions in the presence of shock waves remains an open issue. The answer to this question is quite tricky. In the view of conventional fluid dynamics, a non-conservative formulation of the hyperbolic system and getting the correct solution has been a longstanding debate. In the view of the kinetic theory, the Navier–Stokes equations derived from the Boltzmann equation are not hyperbolic and do not allow discontinuous shocks, where the use of artificial viscosity can be considered as a regularization of Chapman-Enskog expansion.
Regards
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