声波方程数值模拟矩形网格有限差分系数确定法

发布时间：2018-03-04 23:30

本文选题：声波模拟　切入点：时间—空间域　出处：《石油地球物理勘探》2017年01期 　论文类型：期刊论文

【摘要】：压制数值频散是有限差分方法的关键问题之一。目前压制数值频散的方法大多假设不同方向空间偏导数的空间步长相同,导致算法精度低,计算效率低。为此,提出使用线性方法压制声波方程矩形网格有限差分算子的数值频散,并进行了稳定性分析、频散分析和数值模拟。通过频散分析和数值模拟,验证了本文方法能够有效压制矩形网格有限差分数值频散,相较于泰勒展开方法和最小二乘方法,线性方法计算有限差分系数的效率更高,可以替代传统的正方形有限差分网格和相应的系数用于声波方程数值延拓。
[Abstract]:The suppression of numerical dispersion is one of the key problems in finite difference methods. At present, most of the methods for suppressing numerical dispersion assume that the spatial step size of the partial derivatives in different directions is the same, which leads to the low accuracy and low efficiency of the algorithm. A linear method is proposed to suppress the numerical dispersion of finite difference operator with rectangular grid for acoustic equation, and the stability analysis, dispersion analysis and numerical simulation are carried out. It is proved that the proposed method can suppress the numerical dispersion of finite difference with rectangular grids effectively. Compared with the Taylor expansion method and the least square method, the linear method is more efficient than the Taylor expansion method and the least square method in calculating the finite difference coefficients. It can replace the traditional square finite difference grid and the corresponding coefficients for numerical continuation of acoustic equation.
【作者单位】：龙岩学院资源工程学院;中国科学院地质与地球物理研究所中国科学院油气资源研究重点实验室;
【基金】：国家自然科学基金项目(41325016,91630202) 福建省自然科学基金(2016J05104) 龙岩学院博士科研启动基金(LB2014010)资助
【分类号】：P631.4

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