Search

Abstract In this paper, we develop an optimal particle setup method for initial condition with Centroidal Voronoi Particle (CVP) dynamics, which combines the Centroidal Voronoi Tessellation (CVT) and Voronoi Particle (VP) concept. CVT optimizes the energy function in terms of compactness and consequently ensures the isotropy of particle distribution. The CVT configuration is computed by Lloyd's algorithm, which decreases the energy function monotonically. A physics-motivated model equation with tailored equation of state (EOS) is employed to relax the Voronoi particle system such that the convergent equilibrium matches the target configuration. The resulting particle distribution approximates the given analytical profiles of spatially adaptive density, smoothing-length and mass distribution with high interpolation accuracy. The level-set method is introduced to describe arbitrarily complex geometries. A set of Smoothed Particle Hydrodynamics (SPH) simulations is computed to demonstrate the performances of the proposed method. Without parameter tuning, good performance is obtained for presented benchmarks implying its promising potential. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we develop a numerical method for the N-dimensional sine-Gordon equation using differentiation matrices, in the theoretical frame of matrix differential equations. Our method avoids calculating exponential matrices, is very intuitive and easy to express, and can be implemented without toil in any number of spatial dimensions. Although there is currently a vast literature on the numerical treatment of the one-dimensional sine-Gordon equation, the references for the two-dimensional case are much sparser, and virtually nonexistent for higher dimensions. We apply it to a battery of two-dimensional problems taken from the literature, showing that it largely outperforms the previously existing algorithms; while for three-dimensional problems, the results seem very promising. [Copyright &y& Elsevier]

Abstract: Event-driven algorithms are a powerful and efficient simulation method that can be used to numerically study the behavior of particulate systems, such as granular materials or powders. Its superior efficiency originates from only considering analytically calculable points in time, where physically relevant events occur. This, however, is only possible for pairs of trajectories whose relative distance can be expressed as a polynomial of order less than or equal to four. For more complex trajectories, like a sinusoidal motion of a wall, the collision times have to be calculated numerically, which dramatically reduces the efficiency. In this paper we present a tabulation method implemented in an event-driven algorithm, which is able to efficiently handle the one-dimensional motion of a periodically moving wall. By demonstrating this for a sinusoidally moving wall, we enhance the comparability of simulations with (usually sinusoidally driven) experiments. Because granular materials or powders are systems which are easily accessible through both experiments and simulations, our work enhances the growing field of statistical physics far from equilibrium. [Copyright &y& Elsevier]

Abstract: The paper presents numerical simulations of the discharge and the near-outlet regions of the hybrid-stabilized argon–water electric arc. Two different numerical methods for solving the set of conservative equations for the continuity, momentum and energy have been applied. The major difference between the results using the two methods occurs in the temperature distribution in arc fringes within the discharge chamber. This fact influences the potential drop, overpressure, reabsorption of radiation and arc efficiency. It is shown that the radial profiles of temperature at the exit nozzle are less influenced by different temperature distribution within the discharge chamber. Comparison with chosen experimental temperature profiles shows very good agreement. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the numerical simulation of highly relativistic beams. We developed a particle-in-cell code for highly relativistic beams, based on the paraxial Vlasov–Maxwell formulation of Laval et al. This formulation follows the beam in a speed-of-light frame. It is fourth order accurate in the small characteristic velocity of the beam. The formulation is simpler than standard particle-in-cell codes in the lab frame or in the beam frame and gives a fast and easy to implement algorithm. Numerical examples illustrate the accuracy of the method. [Copyright &y& Elsevier]

Abstract: This paper presents a new contact algorithm to analyze an elasto-plastic contact problem using the SPH (Smoothed Particle Hydrodynamics) method. This algorithm is available to both contact types, which are the particle-to-particle contact and the surface-to-particle one. It is employed to determine the actual boundary normal vector and apply the reproducing condition in the cylindrical coordinate. The variational equation based on the virtual work principle is derived and its solution is obtained by the penalty method, which includes both a penetration and a penetration rate. Numerical simulations are presented to show that the proposed algorithm can be applied to the elasto-plastic contact problem for the case that either both bodies are deformable or one is a rigid wall and the other is deformable. Two colliding bodies can be separated with the expected rebound velocity and the total contact force acting on between them similar to theoretical value. Results of the rod impact analysis are shown to be in agreement with the ones obtained by other solution and experiment. [Copyright &y& Elsevier]