Restoring the conservativity of characteristic-based segregated models: Application to the hybrid lattice Boltzmann method

A general methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum, and energy equations are solved by different methods. It especially designed here developing new discretizations of the total equation adapted a thermal coupling with lattice Boltzmann method (LBM). The proposed linear equivalence standard entropy equation, which, as characteristic variable Euler system, allows efficiently decoupling LBM. To this extent, any LBM scheme equivalently written under finite-volume formulation involving fluxes, which further included in corrections. viscous heat production implicitly considered thanks knowledge momentum flux. Three subsequently derived: first-order upwind, Lax–Wendroff, third-order Godunov-type schemes. They assessed academic test cases: Couette flow, spot vortex convections, Sod shock tube, several two-dimensional Riemann problems, shock–vortex interaction. key features then exhibited: (1) construction, recovering correct jump relations across waves; (2) stability accuracy modes can be explicitly controlled; (3) low dissipation isentropic phenomena preserved.