基于SPH方法的流体模拟的研究

发布时间：2018-03-19 21:03

本文选题：光滑粒子流体动力学　切入点：非对称核函数　出处：《合肥工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：流体模拟是计算机模拟中不可或缺的一部分。随着计算机硬件的发展,模拟出的结果已经越来越真实。但是,如何获得更快的、更真实的模拟结果一直是研究人员的目标所在。光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)是一种拉格朗日无网格方法,通常被用于液体模拟。该方法相对网格法来说计算相对简单,而且容易实现。SPH方法的关键在于核函数,核函数影响着SPH方法的精度。然而,SPH方法2个不足:(1)处理边界处的粒子时难以保证精度;(2)在模拟大场景时,需要更多的粒子,计算量大。本文针对上述问题进行了研究。核函数的特性之一是对称性,但是,在边界处,由于核函数的支持半径被边界截断,对称性无法满足,导致计算精度不高。对于此,本文提出了一种应用于边界处的非对称的核函数。该核函数能够有效地改善对称核函数在边界处产生的数值耗散。文中详细叙述了非对称核函数在一维情况下的构造方法,并举例验证了它的有效性。由于SPH方法处理边界处的粒子时难以保证精度,这会使得在边界处产生较大的数值耗散,进而影响粒子密度值及压强值的计算。这两者的计算结果的不准确影响着流体体积的错误变化,进而影响模拟效果。本文提出一个新的方法来解决这个问题,即SPH方法和物理碰撞相耦合的方法。对于非靠近边界的粒子,用SPH方法计算它们的各种属性;对于靠近边界处的粒子,赋予它们静止密度,使用纯粹的物理弹性碰撞来计算其速度和位置。在此过程中,本文给出了一种有效区分靠近边界的粒子和非靠近边界的粒子的方法;此外,本文还给出了使计算出的两种力的耦合方法,减少耦合过程中的误差,降低数值耗散。通过对比实验结果发现,本文方法可以准确地计算流体的密度及压强,使得流体体积更加接近精确值。表面重建是另外一个比较耗费时间的操作。传统的表面重建使用的是Marching Cubes方法,该方法对于没有粒子的空间区域也会进行遍历,浪费了大量的时间。本文给出一种新的表面重建的方法:将表面重建分为两部分,一部分是连续的流体表面,另一部分是溅起的水花。第一部分使用改进后的高度场方法进行模拟,将传统的高度场中使用等大单元格的网格变为不等大单元格的网格,可以有效减少网格数量;第二部分通过三阶Bézier曲线构造一种水滴状粒子,代替传统的粒子,能更好地模拟水花的真实形态。两部分都有效地减少了表面三角形的数量,进而减少了计算网格数据和绘制网格的时间,加快了模拟速度。除此之外,相比较传统的方法,本文只使用了一次迭代计算每个粒子的支持半径,就可使得粒子的密度变化平稳,从而用较少的计算量就能提高压强项的计算精度。
[Abstract]:Fluid simulation is an integral part of computer simulation. With the development of computer hardware, the simulation results have become more and more real. More realistic simulation results have been the goal of the researchers. Smooth particle hydrodynamics is a Lagrangian meshless method, which is usually used in liquid simulation. And the key to easy implementation of .SPH method is kernel function, which affects the accuracy of SPH method. However, it is difficult to guarantee the accuracy when dealing with particles at the boundary. One of the characteristics of kernel function is symmetry, but at the boundary, because the supporting radius of kernel function is truncated by boundary, symmetry can not be satisfied, so the calculation accuracy is not high. In this paper, an asymmetric kernel function applied to the boundary is proposed. The kernel function can effectively improve the numerical dissipation of the symmetric kernel function at the boundary. In this paper, the construction method of the asymmetric kernel function in one-dimensional case is described in detail. The effectiveness of the method is verified by an example. Because the SPH method is difficult to ensure the accuracy of the particles at the boundary, it will result in a large numerical dissipation at the boundary. This paper presents a new method to solve this problem, which affects the calculation of particle density and pressure. The inaccuracy of these two results affects the wrong change of fluid volume and further affects the simulation effect. That is, the SPH method is coupled with the physical collision method. For particles that are not near the boundary, the SPH method is used to calculate their properties; for the particles near the boundary, they are given a static density. The velocity and position of the particles are calculated by using pure physical elastic collisions. In this process, an effective method for distinguishing particles near and near the boundary from particles not near the boundary is presented. In this paper, the coupling method of two kinds of forces is given to reduce the error in the coupling process and to reduce the numerical dissipation. By comparing the experimental results, it is found that the method can accurately calculate the density and pressure of the fluid. Surface reconstruction is another time-consuming operation. Traditional surface reconstruction uses the Marching Cubes method, which also traverses the space without particles. This paper presents a new method of surface reconstruction: the surface reconstruction is divided into two parts, one of which is a continuous fluid surface. In the first part, using the improved height field method to simulate, the grid of the same size cells used in the traditional height field can be changed into the grid with unequal size cells, which can effectively reduce the number of meshes. In the second part, a kind of water droplet is constructed by the third-order B 茅 zier curve instead of the traditional particle, which can better simulate the true shape of the waterfall. Both parts effectively reduce the number of surface triangles. Furthermore, it reduces the time of computing grid data and drawing grid, and speeds up the simulation. In addition, compared with the traditional method, this paper uses only one iteration to calculate the support radius of each particle. The density of particles can change smoothly, and the calculation precision of pressure term can be improved with less calculation.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O35

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