An accurate and versatile lattice closure scheme for lattice Boltzmann equation fluids under external forces

We derive and demonstrate a practical, analytic, versatile and accurate algorithm designed to impose Dirichlet boundary conditions (specified boundary velocity) on the edge nodes of a lattice Boltzmann fluid simulation space, valid for situations in which the fluid at the boundary is subject to a force. The current algorithm models the lattice fluid on boundary and bulk nodes to the same accuracy and in a demonstrably equivalent manner. Whilst the new method presented here applies to rectangular geometries, it adds to our previous method [I. Halliday, L.A. Hammond, C.M. Care, A. Stevens, J. Phys. A: Math. Gen. 35 (2002) 157]: (i) the condition of mass-conservation, (ii) the ability to subject boundary fluid to a force and (iii) the ability to treat a range of complicated geometries with unimpaired accuracy.