Finite Difference formulation of any lattice Boltzmann scheme

Lattice Boltzmann schemes rely on the enlargement of size target problem in order to solve PDEs a highly parallelizable and efficient kinetic-like fashion, split into collision stream phase. This structure, despite well-known advantages from computational standpoint, is not suitable construct rigorous notion consistency with respect equations provide precise stability. In alleviate these shortages introduce framework, we demonstrate that any lattice scheme can be rewritten as corresponding multi-step Finite Difference conserved variables. achieved by devising formalism based operators, commutative algebra polynomials. Therefore, allows invoke Lax-Richtmyer theorem case linear schemes. Moreover, show frequently-used von Neumann-like stability analysis for entirely corresponds Neumann their counterpart. More generally, usual tools are now readily available study Their relevance verified means numerical illustrations.