Steady-state two-relaxation-time lattice Boltzmann formulation for transport and flow, closed with the compact multi-reflection boundary and interface-conjugate schemes

•The steady-state two-relaxation-time LBM is introduced for flow and transport equations.•The method is stable for highly discontinuous transport coefficients and sources.•The system is closed with the compact multi-reaction MR boundary and interface-conjugate.•The parabolic solutions are exact with the developed Dirichlet, Neumann and Robin MR rules.•Two-phase Stokes flow and heterogeneous linear ADE exemplify the method in grid-rotated slabs.