Towards Lattice-boltzmann on Dynamically Adaptive Grids —minimally-invasive Grid Exchange in Espresso

We present the minimally-invasive exchange of the regular Cartesian grid in the lattice-Boltzmann solver of ESPResSo by a dynamically-adaptive octree grid. Octree grids are favoured by computer scientists over other grid types as they are very memory-efficient. In addition, they represent a natural generalisation of regular Cartesian grids, such that most discretisation details of a regular grid solver can be maintained. Optimised codes, however, require a special tree-oriented grid traversal, which typically conflicts with existing simulation codes using various iterators, some for only parts of the grid, e.g., boundaries. ESPResSo is a large software package developed for soft-matter simulations involving fluid flow, electrostatic, and electrokinetic effects, and molecular dynamics. The currently used regular Cartesian grid hinders the simulation of realistic domain sizes and significant time periods, a problem that can be solved using grid adaptivity. In a first step, we focus on the lattice-Boltzmann flow solver in ESPResSo. p4est is a grid framework, that already provides dynamically adaptive quadtree and octree grids together with high-level interfaces for flexible grid traversals with direct neighbour access in all grid components. In this paper, we first describe extensions of p4est that were necessary to fulfill certain application requirements. The second part of our work consists of the minimally-invasive changes in ESPResSo preserving the expertise accumulated in the software’s implementation over years. Our numerical results demonstrate physical correctness of the implementation, good parallel scalability and low overhead of the dynamical grid adaptivity. These are prerequisites to actually profit from grid adaptivity in terms of being able to simulate larger domains over longer time periods with limited computational resources. Thus, the current status forms a solid basis for further steps such as the development of refinement criteria, the setup of more realistic application scenarios, and a GPU implementation.