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The Numerical Simulation of Discontinuous Phenomena Using SPH

Author: SongJunHao
Tutor: ZhangChaoYing
School: Guangxi Normal University
Course: Computer Software and Theory
Keywords: Intermittent phenomenon SPH Particle inconsistent
CLC: O35
Type: Master's thesis
Year: 2010
Downloads: 64
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Abstract


With the rapid development of computer hardware and software level in recent years, numerical simulation has been becoming an important way to analyze and solve complex system phenomena. Compared with the traditional method of experimental, numerical simulation without expensive, time-consuming and dangerous experiment in the laboratory, can also difficult observation to provide more specific and complete information, and can provide the theoretical data basis, explain, and even found a new phenomenon. Now commonly used numerical simulation methods are mainly divided into two types based on the grid method and meshless method. Grid-based numerical simulation method for intermittent phenomena (such as dynamic crack propagation, material damage and failure, corrosion and penetration, as well as large deformation, etc.) there are inherent defects, numerical unstable phenomenon, without grid method has incomparable advantages in dealing with these issues. Series of Lagrangian nature arbitrary distribution of particles as meshless particle method smoothed particle hydrodynamics (SPH), to solve all kinds of the value of the function, and the integral equation with various boundary conditions or partial differential equations, has become an effective numerical method is widely used in computational fluid dynamics neighborhood. Particle approximation of the integral form of nuclear approximation method and discrete form the basis of the SPH method, integral and discrete forms of consistency is the key to the regeneration of the SPH approximation method. Integral consistency condition both for the structural analysis of smoothing kernel function provides a generalized method of, and plays an important role in the form of the SPH formula. Discrete consistency condition for the particle inconsistency defects in the traditional SPH method provides repair methods, and promote corrected smoothed particle method (CSPM) and restore the Smoothed Particle Hydrodynamics (RSPH) development. Traditional SPH method for intermittent problems of inconsistency defects, this paper draw on the idea deduced DCSPM method, based on the the RSPH methods proposed the new SPH method (DRSPH), one for analog intermittent phenomenon. DRSPH method on both sides of the discontinuity at the location of the Taylor expansion, rather than in the entire support domain extension RSPH method. The main part of the function and its derivatives the final nuclear approximate and particle approximate formula RSPH same additional term is obtained by processing the physical phenomenon of intermittent. DRSPH additional items appear to ensure the coordination of intermittent field function kernel approximation. DRSPH method does not need to modify the kernel function, Fixed boundary defects, and repair a break in a nearby area consistency. Different and Liu 2003 DCSPM methods, DRSPH method without regularization, approximate the function and the first derivative is calculated by solving the matrix to improve the numerical stability of the SPH method with two first-order approximation accuracy. Intermittent near region consistency definition DRSPH method DCSPM method can more effectively restore the consistency of the particles in discontinuity at the region near the approximated function can be achieved when (1) order particle consistency. The method of DRSPH need for an efficient algorithm to determine the position of the discontinuity at the basis of the current time step, the discrete function values. If coupled with an effective discontinuity detection algorithm at then DRSPH methods on a physical problem in the analog discontinuity is very useful.

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CLC: > Mathematical sciences and chemical > Mechanics > Fluid Mechanics
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