Implementation aspects of 3D lattice-BGK: Boundaries, accuracy, and a new fast relaxation method

In many realistic fluid-dynamical simulations the specification of the boun dary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we stud y these issues in the case of the lattice-BGK model. The objective is to pr esent a comprehensive overview of some pitfalls and shortcomings of the lat tice-BGK method and to introduce some new ideas useful in practical simulat ions. We begin with an evaluation of the widely used bounce-back boundary c ondition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non-slip wall is assumed to be at the boundary nodes. Moreover, for a specific inclination angle of 45 degrees, the scheme is fou nd to be second-order accurate when the location of the non-slip velocity i s fitted halfway between the last fluid nodes and the first solid nodes. Th e error as a function of the relaxation parameter is in that case qualitati vely similar to that of flat walls. Next, a comparison of simulations of fl uid flow by means of pressure boundaries and by means of body force is pres ented. A good agreement between these two boundary conditions has been foun d in the creeping-flow regime. For higher Reynolds numbers differences have been found that are probably caused by problems associated with the pressu re boundaries. Furthermore, two widely used 3D models, namely D(3)Q(15) and D(3)Q(19), are analysed. It is shown that the D(3)Q(15) model may induce a rtificial checkerboard invariants due to the connectivity of the lattice. F inally, a new iterative method, which significantly reduces the saturation time, is presented and validated on different benchmark problems. (C) 1999 Academic Press.