Review of smoothed particle hydrodynamics Lind, Steven J.; Rogers, Benedict D.; Stansby, Peter K.
Proceedings - Royal Society. Mathematical, physical and engineering sciences,
09/2020, Letnik:
476, Številka:
2241
Journal Article
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This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with ...interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave–structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.
•We conduct truly incompressible SPH simulations for free-surface flows.•We further develop a stabilising particle shifting algorithm.•An improved free-surface boundary treatment is ...presented.•Slamming cases, and a novel, efficient wave–structure interaction technique are presented.•Accuracy is good, pressures are virtually noise free.
Incompressible smoothed particle hydrodynamics generally requires particle distribution smoothing to give stable and accurate simulations with noise-free pressures. The diffusion-based smoothing algorithm of Lind et al. (J. Comp. Phys. 231 (2012) 1499–1523) has proved effective for a range of impulsive flows and propagating waves. Here we apply this to body–water slam and wave–body impact problems and discover that temporal pressure noise can occur for these applications (while spatial noise is effectively eliminated). This is due to the free-surface treatment as a discontinuous boundary. Treating this as a continuous very thin boundary within the pressure solver is shown to effectively cure this problem. The particle smoothing algorithm is further generalised so that a non-dimensional diffusion coefficient is applied which suits a given time step and particle spacing.
We model the particular problems of cylinder and wedge slam into still water. We also model wave-body impact by setting up undisturbed wave propagation within a periodic domain several wavelengths long and inserting the body. In this case, the loads become cyclic after one wave period and are in good agreement with experiment. This approach is more efficient than the conventional wave flume approach with a wavemaker which requires many wavelengths and a beach absorber.
Results are accurate and virtually noise-free, spatially and temporally. Convergence is demonstrated. Although these test cases are two-dimensional with simple geometries, the approach is quite general and may be readily extended to three dimensions.
In India, there are plans for 5 GW of installed capacity of wind power by 2022. This study establishes that the wind resource along the west coast of Gujarat is sufficient for offshore wind farms of ...between 500 MW to 2 GW rated power to be operated with capacity factors of 40% to 54%. For the majority of sites, a levelized cost of energy (LCOE) in the range 68 to 86 £/MWh can be achieved with installation on floating support structures. The LCOE is up to 3.2 £/MWh greater for installation on bed‐fixed structures closer to shore. The wind resource and energy yield are predicted using Weather Research and Forecasting (WRF). Wind speed occurrence is predicted to within 1.3% for multiple sites simultaneously, and this provides wind turbine energy yield to within 3.4%. Wind speeds occurring due to sea breeze are accurately predicted and contribute 6.2% of annual energy generation at the nearshore locations and 3.8% at the deeper water offshore sites. While these events improve the viability of nearshore locations, floating installations offer lower LCOE for most locations along the Gujarat coast.
A numerical inconsistency has emerged for multi-phase smoothed particle hydrodynamics simulations when using very high resolution, made possible by graphical processing units. In violent flows ...unphysical voids and phase separation occur ultimately leading to numerical instability. New Fickian-based particle shifting algorithms with a selectively activated free-surface correction are developed for air-water simulations to prevent the creation of unnatural voids and maintain numerical stability through nearly uniform distributions. Using the shifting algorithm without surface correction in the air phase is recommended, with marginal improvements if the shifting algorithm is not applied in water. However, maintaining shifting in water would avoid possible void occurrence. The improvement is demonstrated using a dry-bed dam break and a sloshing tank case. A 3D case involving the impact of the water flow on an obstacle is compared with experimental data. The multi-phase SPH scheme gives closer agreement with experiment than a single-phase simulation.
Tidal stream turbines operate in the harsh marine environment, subjected to turbulence, wave action and wakes from upstream devices when deployed in arrays. Turbines may be mounted on the sea bed or ...on floating platforms. Numerical models are invaluable to study individual and array performance and their interaction with environmental flows. To date, shallow water models and three-dimensional Reynolds averaged Navier-Stokes (RANS) simulations predominate the simulation of turbine arrays, while large-eddy simulation (LES) is becoming more widely used due to availability of high-performance computing resources. The accuracy of turbine performance and load prediction depends on the ability to represent turbulence in the tidal flow and unsteady wake effects. Inclusion of waves increases the modelling complexity and is particularly significant for floating platforms. In this Vision Paper, we provide a perspective on the numerical approaches currently used for modelling tidal flows and marine turbines, suggesting future challenges envisaged in this field.
A new massively parallel scheme is developed to simulate free-surface flows with the meshless method incompressible smoothed particle hydrodynamics (ISPH) for simulations involving more than 100 ...million particles. As a pressure-projection method, ISPH requires the solution of a sparse matrix for the pressure Poisson equation (PPE) which is non trivial for large problems where the particles are moving with continuously evolving sparsity. The new scheme uses a Hilbert space filling curve with a cell-linked list to map the entire domain so that domain decomposition and load balancing can be achieved easily to take advantage of geometric locality in order to reduce latency in memory cache access. The computational domain can be subdivided into more than 12,000 partitions using the message passing interface (MPI) for communication between partitions. Load balancing is achieved using the open-source Zoltan library using a new particle weighting system. To solve the PPE for large problems using tens of thousands of partitions, the open-source PETSc library is used which requires the HYPRE BoomerAMG preconditioner to ensure rapid convergence for ISPH. The performance of the code is benchmarked on the U.K. National Supercomputer ARCHER. The results show that domain decomposition with a space filling curve can efficiently treat irregularly distributed particles creating a well-balanced scheme demonstrating that the approach is well matched to the highly irregular subdomains and non-uniform distribution of ISPH free-surface simulations. The benchmark results show that massively parallel ISPH code can achieve over 90% efficiency for the solution of the PPE, but the efficiency of computing matrix coefficients decreases when using more than 12000 partitions giving overall efficiencies in excess of 43% up to 6144 MPI partitions, highlighting future improvements required. The work demonstrates that the Zoltan and PETSc libraries can be effectively combined with ISPH to offer the capability of developing a massively parallel ISPH toolkit.
This paper presents the acceleration of multi-phase smoothed particle hydrodynamics (SPH) using a graphics processing unit (GPU) enabling large numbers of particles (10–20 million) to be simulated on ...just a single GPU card. With novel hardware architectures such as a GPU, the optimum approach to implement a multi-phase scheme presents some new challenges. Many more particles must be included in the calculation and there are very different speeds of sound in each phase with the largest speed of sound determining the time step. This requires efficient computation. To take full advantage of the hardware acceleration provided by a single GPU for a multi-phase simulation, four different algorithms are investigated: conditional statements, binary operators, separate particle lists and an intermediate global function. Runtime results show that the optimum approach needs to employ separate cell and neighbour lists for each phase. The profiler shows that this approach leads to a reduction in both memory transactions and arithmetic operations giving significant runtime gains. The four different algorithms are compared to the efficiency of the optimised single-phase GPU code, DualSPHysics, for 2-D and 3-D simulations which indicate that the multi-phase functionality has a significant computational overhead. A comparison with an optimised CPU code shows a speed up of an order of magnitude over an OpenMP simulation with 8 threads and two orders of magnitude over a single thread simulation. A demonstration of the multi-phase SPH GPU code is provided by a 3-D dam break case impacting an obstacle. This shows better agreement with experimental results than an equivalent single-phase code. The multi-phase GPU code enables a convergence study to be undertaken on a single GPU with a large number of particles that otherwise would have required large high performance computing resources.
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