Optimisation using smoothed particle hydrodynamics with volume-based geometry control

Abstract

This work explores how smoothed particle hydrodynamics (SPH) may be applied for fluids optimisation problems. To achieve this, a newly developed volume of solid geometric parameterisation is applied that implicitly allows large geometric changes as well as topological changes. The meshless nature of SPH has long been an advantage, but when combined with the parameterisation presented here, optimisation calculations are able to make unlimited changes in the geometry without user intervention. To demonstrate the benefits this pairing of techniques affords for free-surface problems, three model optimisations and objective functions are considered: improvement of discharge coefficient through a nozzle, maximisation of damping in a pivoting tank and minimisation of wave overtopping for a simplified coastal defence. For the wave problem, varying constraints are explored and a time-recorded particle boundary condition is applied to accelerate the optimisation process. In each of the cases the optimisation finds a significant improvement in the objective function and shows how constraint selection influences the performance of the final design.

Parametric Surfaces with Volume of Solid Control for Optimisation of Three Dimensional Aerodynamic Topologies

“…Some progress towards a topologically flexible external aerodynamic parametrisation has been achieved by Hall et al [25,26]. This method relies on material distribution, or volume of solid (VOS), to generate the external geometry of an aerodynamic body.…”

“…The 2D-RSVS builds upon the volumetric aerodynamic parameterisation by Hall et al [25,26] which was the first topologically flexible parameterisation for external aerodynamics. Like the parameterisation of Hall et al, the RSVS uses volume of solid (VOS) design variables to control profile shape and topology, these were kept as they provide intuitive handling of topology change.…”

Fluid initialization and dynamic window for smoothed-particle hydrodynamics simulation

“…As such, the number of iterations is much lower than in a damped simulation or in a particle packing process. Before explaining our selection process, we must note one additional difference with Hall et al's 21 approach. Since we compute the particles density, we must load additional particles around the volume of fluid we are trying to initialize.…”

“…Due to the objective of doing repeated initialization for an optimization, Hall et al 21 noted that, even if the particle packing approach is faster than a damped simulation (i.e., simulating a non-negligible number of steps for the fluid to stabilize and remove the local high- and low-pressure regions), its iterative nature is still too slow for its application. As such, instead of starting with the usual Cartesian or triangular initial particle distribution, they decided to initialize the fluid with particles already in a rest-state distribution (see Figure 10 in the work by Hall et al 21 ). To obtain the rest-state distribution of the particles, a volume of fluid enclosing all the volumes of fluid they aim to initialize during their optimizations is simply pre-simulated and stored.…”

“…Our algorithm follows Hall et al’s 21 idea of precomputing and saving a larger simulation space with the fluid at rest and then loading only the particles inside the simulation area at execution time. However, instead of not loading any particle within the smoothing length of the boundaries, we use a condition based on the density to select the particles that will be loaded (see Section 3.1 and Section 3.2).…”