Stability analysis of the vectorial Lattice-Boltzmann method

We perform a stability analysis of the Vectorial Lattice-Boltzmann Method (VLBM). The VLBM has been introduced in [1–3, 9, 18]. It is a variant of the LBM with extended stability features: it allows handling compressible flows with shock waves, while the LBM is limited to low-Mach number regime. The stability analysis is based on the Legendre transform theory. We also propose a new tool: the equivalent system analysis, which we conjecture to contains both the stability and the consistency of the VLBM.