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

TL;DR

This paper introduces a straightforward algorithm for implementing jump boundary conditions in the lattice Boltzmann method, enabling accurate simulation of transport across interfaces with resistance, adaptable to complex geometries and moving boundaries.

Contribution

The paper presents a simple, easily integrable algorithm for jump boundary conditions in LBM, applicable to static and dynamic interfaces with resistance, including complex geometries.

Findings

Accurately recovers analytical solutions for planar membranes.

Effectively simulates solute release from stationary and moving particles.

Compatible with existing LBM codes and immersed boundary methods.

Abstract

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.