Steven Lind

Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves

The incompressible smoothed particle hydrodynamics (ISPH) method with projection-based pressure correction has been shown to be highly accurate and stable for internal flows and, importantly for many problems, the pressure field is virtually noise-free in contrast to the weakly compressible SPH approach (Xu et al., 2009 [31]). However for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels. A new algorithm is presented which remedies this issue, giving stable and accurate solutions to both internal and free-surface flows. Generalising the particle shifting approach of Xu et al. (2009) [31], the algorithm is based upon Ficks law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability. The algorithm is validated against analytical solutions for an internal flow at higher Reynolds numbers than previously, the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times. The method is then validated for progressive regular waves with paddle motion defined by linear theory. The accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels. The test cases are thought to provide a more thorough quantitative validation than previously undertaken.

Incompressible-compressible flows with a transient discontinuous interface using smoothed particle hydrodynamics (SPH)

A new two-phase incompressible-compressible Smoothed Particle Hydrodynamics (SPH) method has been developed where the interface is discontinuous in density. This is applied to water-air problems with a large density difference. The incompressible phase requires surface pressure from the compressible phase and the compressible phase requires surface velocity from the incompressible phase. Compressible SPH is used for the air phase (with the isothermal stiffened ideal gas equation of state for low Mach numbers) and divergence-free (projection based) incompressible SPH is used for the water phase, with the addition of Fickian shifting to produce sufficiently homogeneous particle distributions to enable stable, accurate, converged solutions without noise in the pressure field. Shifting is a purely numerical particle regularisation device. The interface remains a true material discontinuity at a high density ratio with continuous pressure and velocity at the interface. This approach with the physics of compressibility and incompressibility represented is novel within SPH and is validated against semi-analytical results for a two-phase elongating and oscillating water drop, analytical results for low amplitude inviscid standing waves, the Kelvin-Helmholtz instability, and a dam break problem with high interface distortion and impact on a vertical wall where experimental and other numerical results are available.

Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment

Tsunamis caused by landslides may result in significant destruction of the surroundings with both societal and industrial impact. The 1958 Lituya Bay landslide and tsunami is a recent and well-documented terrestrial landslide generating a tsunami with a run-up of 524 m. Although recent computational techniques have shown good performance in the estimation of the run-up height, they fail to capture all the physical processes, in particular, the landslide-entry profile and interaction with the water. Smoothed particle hydrodynamics (SPH) is a versatile numerical technique for describing free-surface and multi-phase flows, particularly those that exhibit highly nonlinear deformation in landslide-generated tsunamis. In the current work, the novel multi-phase incompressible SPH method with shifting is applied to the Lituya Bay tsunami and landslide and is the first methodology able to reproduce realistically both the run-up and landslide-entry as documented in a benchmark experiment. The method is the first paper to develop a realistic implementation of the physics that in addition to the non-Newtonian rheology of the landslide includes turbulence in the water phase and soil saturation. Sensitivity to the experimental initial conditions is also considered. This work demonstrates the ability of the proposed method in modelling challenging environmental multi-phase, non-Newtonian and turbulent flows.

High-order Eulerian incompressible smoothed particle hydrodynamics with transition to Lagrangian free-surface motion

The incompressible Smoothed Particle Hydrodynamics (ISPH) method is derived in Eulerian form with high-order smoothing kernels to provide increased accuracy for a range of steady and transient internal flows. Periodic transient flows, in particular, demonstrate high-order convergence and accuracies approaching, for example, spectral mesh-based methods. The improved accuracies are achieved through new high-order Gaussian kernels applied over regular particle distributions with time stepping formally up to 2nd order for transient flows. The Eulerian approach can be easily extended to model free surface flows by merging from Eulerian to Lagrangian regions in an Arbitrary-LagrangianEulerian (ALE) fashion, and a demonstration with periodic wave propagation is presented. In the long term, it is envisaged that the method will greatly increase the accuracy and efficiency of SPH methods, while retaining the flexibility of SPH in modelling free surface and multiphase flows.

Incompressible SPH (ISPH) with fast Poisson solver on a GPU

Abstract This paper presents a fast incompressible SPH (ISPH) solver implemented to run entirely on a graphics processing unit (GPU) capable of simulating several millions of particles in three dimensions on a single GPU. The ISPH algorithm is implemented by converting the highly optimised open-source weakly-compressible SPH (WCSPH) code DualSPHysics to run ISPH on the GPU, combining it with the open-source linear algebra library ViennaCL for fast solutions of the pressure Poisson equation (PPE). Several challenges are addressed with this research: constructing a PPE matrix every timestep on the GPU for moving particles, optimising the limited GPU memory, and exploiting fast matrix solvers. The ISPH pressure projection algorithm is implemented as 4 separate stages, each with a particle sweep, including an algorithm for the population of the PPE matrix suitable for the GPU, and mixed precision storage methods. An accurate and robust ISPH boundary condition ideal for parallel processing is also established by adapting an existing WCSPH boundary condition for ISPH. A variety of validation cases are presented: an impulsively started plate, incompressible flow around a moving square in a box, and dambreaks (2-D and 3-D) which demonstrate the accuracy, flexibility, and speed of the methodology. Fragmentation of the free surface is shown to influence the performance of matrix preconditioners and therefore the PPE matrix solution time. The Jacobi preconditioner demonstrates robustness and reliability in the presence of fragmented flows. For a dambreak simulation, GPU speed ups demonstrate up to 10–18 times and 1.1–4.5 times compared to single-threaded and 16-threaded CPU run times respectively.

New massively parallel scheme for Incompressible Smoothed Particle Hydrodynamics (ISPH) for highly nonlinear and distorted flow

Abstract 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.