A simple algorithm to implement jump boundary conditions within the lattice Boltzmann method

An algorithm is proposed to implement unsteady jump boundary conditions, presenting discontinuity in physical quantities, within the lattice Boltzmann method (LBM). This is useful to tackle problems involving mass or heat transfer through interfaces or membranes that exhibit resistance to transport. The algorithm is simple to implement within an existing LBM based code that computes diffusion and advection of a scalar field, either temperature or solute concentration. Analytical solutions are recovered numerically with acceptable accuracy for the limiting case of a planar membrane. The algorithm is adapted for moving-free boundaries and adopting arbitrary geometries when combined with the immersed boundary method. This is demonstrated by simulating controlled release of a solute from a stationary rigid particle and from a moving deformable particle.