Coupling of particle simulation and lattice Boltzmann background flow on adaptive grids

Abstract

The lattice-Boltzmann method as well as classical molecular dynamics are established and widely used methods for the simulation and research of soft matter. Molecular dynamics is a computer simulation technique on microscopic scales solving the multi-body kinetic equations of the involved particles. The lattice-Boltzmann method describes the hydrodynamic interactions of fluids, gases, or other soft matter on a coarser scale. Many applications, however, are multi-scale problems and they require a coupling of both methods. A basic concept for short ranged interactions in molecular dynamics is the linked cells algorithm that is in O(N) for homogeneously distributed particles. Spatial adaptive methods for the lattice-Boltzmann scheme are used in order to reduce costly scaling effects on the runtime and memory for large-scale simulations. As basis for this work the highly flexible simulation software ESPResSo is used and extended. The adaptive lattice-Boltzmann scheme, that is implemented in ESPResSo, uses a domain decomposition with tree-based grids along the space-filling Morton curve using the p4est software library. However, coupling the regular particle simulation with the adaptive lattice-Boltzmann method for highly parallel computer architectures is a challenging issue that raises several problems. In this work, an approach for the domain decomposition of the linked cells algorithm based on space-filling curves and the p4est library is presented. In general, the grids for molecular dynamics and fluid simulations are not equal. Thus, strategies to distribute differently refined grids on parallel processes are explained, including a parallel algorithm to construct the finest common tree using p4est. Furthermore, a method for interpolation and extrapolation, that is needed for the viscous coupling of particles with the fluid, on adaptively refined grids are discussed. The ESPResSo simulation software is augmented by the developed methods for particle-fluid coupling as well as the Morton curve based domain decompositions in a minimally invasive manner. The original ESPResSo implementation for regular particle and fluid simulations is used as reference for the developed algorithms.