| 求解波动方程的准粒子离散修正辛算法 |
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| 引用本文： | 苏波,刘知贵,庹先国,李怀良.求解波动方程的准粒子离散修正辛算法[J].声学学报,2018,43(5):843-849. |
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| 作者姓名： | 苏波 刘知贵 庹先国 李怀良 |
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| 作者单位： | 1. 中国工程物理研究院研究生院 绵阳 621900; |
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| 基金项目： | 国家自然科学基金面上项目(41774118)资助国家重大科研仪器设备研制专项(41227802) |
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| 摘 要： | 针对波动方程求解,在Hamilton体系下建立了对空间离散的准粒子体系,该准粒子体系实现简单,物理意义明确;在时间离散方面,构造了一种适合高效声波模拟的修正辛格式,该格式是在常规的二阶Partitioned Runge-Kutta(PRK)基础之上构造而成,其具有三阶时间精度,从理论上分析了修正辛格式的数值稳定性和频散性能.数值结果表明,本文提出的方法在计算时间,计算精度和计算存储量等各方面性能都有相应改善。
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| 关 键 词： | 波动方程方程求解空间离散HAMILTON体系辛算法准粒子计算时间数值稳定性 |
| 收稿时间： | 2017-04-20 |
Modified symplectic quasi-particles discrete methods for simulation of wave propogation |
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| Affiliation: | 1. Graduate School, China Academy of Engineering Physics Mianyang 621900;2. School of Computer Science and Technology, Southwest University of Science and Technology Mianyang 621010;3. Sichuan University of science and Engineering Zigong 643002;4. Fundamental Science on Nuclear Wastes and Environmental Safety Laboratory Mianyang 621010 |
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| Abstract: | Hamiltonian system with quasi-particles for spatial discrete of acoustic wave propogation is presented. A modified symplectic scheme for temporal discretization of wave equation is proposed. First, we transformed the wave equation into a Hamilton system. An explicit symplecitc Partitioned Runge-Kutta (PRK) scheme is used to solve the Hamilton system. Then, the additional spatial discretization term is added into the symplectic PRK scheme. Theoretical analytic shows the new scheme has lower dispersion and long-term calculation ability than that of the conventional symplectic schemes. Numerical results indicate that the present method is effective and feasible, such as the low numerical dispersion, high stability and long-time performance of the new scheme. |
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