Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition

Abstract

We present a methodology to concurrently couple particle-based methods via a domain decomposition (DD) technique for simulating viscous flows. In particular, we select two resolutions of the smoothed particle hydrodynamics (SPH) method as demonstration. Within the DD framework, a simulation domain is decomposed into two (or more) overlapping sub-domains, each of which has an individual particle scale determined by the local flow physics. Consistency of the two sub-domains is achieved in the overlap region by matching the two independent simulations based on Lagrangian interpolation of state variables and fluxes. The domain decomposition based SPH method (DD-SPH) employs different spatial and temporal resolutions, and hence, each sub-domain has its own smoothing length and time step. As a consequence, particle refinement and de-refinement are performed asynchronously according to individual time advancement of each sub-domain. The proposed strategy avoids SPH force interactions between different resolutions on purpose, so that coupling, in principle, can go beyond SPH–SPH, and may allow SPH to be coupled with other mesoscopic or microscopic particle methods.The DD-SPH method is validated first for a transient Couette flow, where simulation results based on proper coupling of spatial–temporal scales agree well with analytical solutions. In particular, we find that the size of the overlap region should be at least rc,1+2rc,2, where rc,1 and rc,2 are cut off radii in the two sub-domains with rc,1≤rc,2. Subsequently, a perturbation wave is considered traveling either parallel or perpendicular to the hybrid interface. Compressibility is significant if transient behavior at short sonic-time-scale is relevant, while the fluid can be treated as quasi-incompressible at sufficiently long time scale. To this end, we propose a coupling of density fields from the two sub-domains. Finally, a steady Wannier flow is simulated, where a rotating cylinder is placed next to a wall. Lubrication effects are prominent in the gap between the cylinder and the bottom wall, rendering a high resolution necessary, whereas in the rest of the domain the flow can be simulated at much lower resolution. DD-SPH simulation results with both spatial and temporal resolution ratios up to 16 agree well with the results of a single high resolution simulation, but with the former two-orders of magnitude faster in the region away from the cylinder.