波浪模式的变分多尺度方法模拟

刘小刚; 任睿超; 王震; 惠小健; 章培军

doi:10.3969/j.issn.0253-4193.2020.11.004

波浪模式的变分多尺度方法模拟

doi: 10.3969/j.issn.0253-4193.2020.11.004

1.
西京学院理学院，陕西西安 710123
2.
西北大学数学学院，陕西西安 710127

基金项目: 西京学院校科研基金项目（XJ180210）；陕西省自然科学基础研究计划项目（2020JM-646）；陕西省自然科学基础研究计划项目（2019-03-18）；陕西省创新能力支撑计划项目（2018GHJD-21）。

详细信息

作者简介:
刘小刚（1983-），男，陕西省延安市人，副教授，从事计算流体力学、数学建模方面研究。E-mail：sun8894@163.com

中图分类号: O241
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出版历程
- 收稿日期: 2018-10-09
- 修回日期: 2019-09-05
- 网络出版日期: 2020-12-23
- 刊出日期: 2020-11-25

Numerical simulation of wave pattern with variational multiscale method

1.
School of Science, Xijing University, Xi’an 710123, China
2.
School of Mathematics, Northwest University, Xi’an 710127, China

摘要

摘要: 针对波浪模式问题，将变分多尺度方法与自由面捕捉技术相结合；把波浪模式的各个物理量分解到“粗” “细”两种尺度上，引入消除数值伪振荡的稳定化结构；最后求解“粗” “细”两种尺度耦合的整体变分多尺度方程，模拟了水波自由晃动的1个周期和波浪的传播过程。模拟结果表明：采用变分多尺度方法模拟水波晃动和波浪传播不会引起数值伪振荡，得到精确的数值解，能够正确模拟水波自由晃动的周期性变化现象以及波浪的传播过程。
- 波浪模式 /
- 变分多尺度 /
- 稳定化方法 /
- 自由面
Abstract: For the wave model, we combine the variational multiscale method with the free surface captured technology, and decompose various physical quantities of the wave model into “coarse” scale and “fine” scale following the variational multiscale method, and introduce the stabilization structure to eliminate numerical pseudo oscillation. Finally, the total variational multiscale equation of coupling “coarse” scale and “fine” scale is solved to simulate the water wave oscillating freely in a cycle and wave propagation. The numerical results show that the numerical results is accurate, and the method eliminates the spurious oscillations, and simulate correctly the phenomenon of periodic changes of water waves oscillating freely and wave propagation.
- wave model /
- variational multiscale /
- stabilized methods /
- free surface

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图 1 初始时刻波浪的水平速度（u）、垂直速度（v）和压力

Fig. 1 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at the initial moment

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图 5 $T$时刻波浪的水平速度（ u ）、垂直速度（ v ）和压力

Fig. 5 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at the T moment

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图 2 ${T}/{4}$时刻波浪的水平速度（u）、垂直速度（v）和压力

Fig. 2 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at the T moment

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图 3 ${T}/{2}$时刻波浪的水平速度（u）、垂直速度（v）和压力

Fig. 3 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at the T/2 moment

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图 4 ${{3T}}/{4}$时刻波浪的水平速度（u）、垂直速度（v）和压力

Fig. 4 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at the 3T/4 moment

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图 6 初始时刻波浪的水平速度（u）、垂直速度（v）和压力

Fig. 6 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at the initial moment

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图 8 t=1.6 s时刻波浪的水平速度（u）、垂直速度（v）和压力

Fig. 8 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at t=1.6 s moment

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图 7 t=0.8 s时刻波浪的水平速度（u）、垂直速度（v）和压力

Fig. 7 The horizontal velocity (u), the vertical velocity (v), and the pressure of the wave at t=0.8 s moment

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