Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> I. INTRODUCTION <s> A finite-size particle scheme for the numerical solution of two- and three-dimensional gas dynamical problems of astronomical interest is described and tested. The scheme is then applied to the fission problem for optically thick protostars. Results are given, showing the evolution of one such protostar from an initial state as a single, rotating star to a final state as a triple system whose components contain 60% of the original mass. The decisiveness of this numerical test of the fission hypothesis and its relevance to observed binaries are briefly discussed. <s> BIB001 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> I. INTRODUCTION <s> This paper introduces particle systems--a method for modeling fuzzy objects such as fire, clouds, and water. Particle systems model an object as a cloud of primitive particles that define its volume. Over a period of time, particles are generated into the system, move and change form within the system, and die from the system. The resulting model is able to represent motion, changes of form, and dynamics that are not possible with classical surface-based representations. The particles can easily be motion blurred, and therefore do not exhibit temporal aliasing or strobing. Stochastic processes are used to generate and control the many particles within a particle system. The application of particle systems to the wall of fire element from the Genesis Demo sequence of the film Star Trek H: The Wrath of Khan [10] is presented. <s> BIB002 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> I. INTRODUCTION <s> Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks. <s> BIB003
As a common phenomenon in nature, objects with ''blurred'' shape, such as flame, cloud, spray, smoke and cloud, have no fixed shape and regular geometric shape. More importantly, their appearance changes uncertainly with time. There is a basic law in physics, ''Objects are made up of elementary particles'' Based on this idea, Reeves BIB002 proposed the particle system in 1983, and it is recognized as the most successful method of graphics generation for simulating irregular blurred objects. The particle system defines tens of thousands of irregular and randomly distributed particles moving continuously and transforming to form the overall shape, characteristics and dynamic changes of the scenery. Water, smoke and other fluids have always been representative objects in realistic visual scenes. Because of their The associate editor coordinating the review of this manuscript and approving it for publication was Shuhan Shen. large degree of freedom, many factors affecting motion and complex physical equations, traditional grid-based methods confine all simulations to fixed grids in advance, and their computations are complex. Compared with the traditional mesh or grid-based numerical modeling methods, the meshfree simulation methods have some special advantages BIB003 for computer animation. The main idea of the meshfree methods is to provide accurate and stable numerical solutions to integral equations or all types of possible boundary conditions using a set of arbitrarily distributed nodes or particles. Smoothed particle hydrodynamics (SPH)  is a ''truly'' meshfree, particle method was used for continuous scale applications, and SPH may be regarded as the oldest modern meshfree particle method. SPH was developed by Gingold and Monaghan  and Lucy BIB001 initially for astrophysical problems in 1977. However, it is a meshfree Lagrangian method, in which the coordinates move with the fluid, and the application of the method can be easily adjusted with VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ respect to variables such as density, velocity, acceleration, and energy. SPH has been used in many research fields, such as astrophysics, ballistics, volcanology, and oceanography. Here, we focus on SPH simulation and the particle system that could be used for computer animation and geometric modeling. In Section 1, the background of particle techniques is introduced. In Sections 2, 3, 4, and 5, the invention, theoretical process features, boundary processing and computational efficiency of SPH are described. In Section 6, the applications of the SPH method are discussed. In Sections 7, 8, and 9, the concepts, ideas and model of the particle system are explained. In Section 10, the applications of particle modeling are discussed. In Section 11, the advantages and main attributes of SPH simulation and the particle system are discussed. In Section 12, the advice and concluding remarks are presented.