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求解二维浅水波方程的旋转混合格式

郑素佩 李霄 赵青宇 封建湖

郑素佩,李霄,赵青宇,封建湖. 求解二维浅水波方程的旋转混合格式 [J]. 应用数学和力学,2022,43(2):176-186 doi: 10.21656/1000-0887.420063
引用本文: 郑素佩,李霄,赵青宇,封建湖. 求解二维浅水波方程的旋转混合格式 [J]. 应用数学和力学,2022,43(2):176-186 doi: 10.21656/1000-0887.420063
ZHENG Supei, LI Xiao, ZHAO Qingyu, FENG Jianhu. A Rotated Mixed Scheme for Solving 2D Shallow Water Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 176-186. doi: 10.21656/1000-0887.420063
Citation: ZHENG Supei, LI Xiao, ZHAO Qingyu, FENG Jianhu. A Rotated Mixed Scheme for Solving 2D Shallow Water Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 176-186. doi: 10.21656/1000-0887.420063

求解二维浅水波方程的旋转混合格式

doi: 10.21656/1000-0887.420063
基金项目: 国家自然科学基金(面上项目) (11971075);陕西省自然科学基金(2020JQ-338;2019JM-243)
详细信息
    作者简介:

    郑素佩(1978—),女,副教授,博士,硕士生导师(E-mail:zsp2008@chd.edu.cn

    李霄(1998—),女,硕士生(通讯作者. E-mail:1012124794@qq.com

  • 中图分类号: O354

A Rotated Mixed Scheme for Solving 2D Shallow Water Equations

  • 摘要:

    针对二维浅水波方程数值求解问题,构造了一种旋转通量混合格式。空间方向上,该算法利用浅水波方程通量函数的旋转不变性,在单元界面法线方向及单元界面切线方向上采用可消除红斑现象的HLL与满足热力学第二定律的熵稳定加权混合数值通量函数,时间方向上采用三阶强稳定Runge-Kutta法。数值结果表明,该混合格式对于二维浅水波方程数值求解具有分辨率高的良好特性。

  • 图  1  圆柱溃坝模拟图

    Figure  1.  The simulation diagram for the cylindrical dam

    图  2  二维圆柱溃坝问题密度等值线图:(a) 非混合格式密度结果;(b) 混合格式密度结果

    Figure  2.  The density contour for the 2D cylindrical dam-break problem:(a) the non-mixed scheme density results; (b) the mixed scheme density results

    图  3  二维圆柱溃坝问题速度图:(a) 非混合格式x方向的速度u;(b) 混合格式x方向的速度u;(c) 非混合格式y方向的速度v;(d) 混合格式y方向的速度v

    Figure  3.  The velocity contour for the 2D cylindrical dam-break problem: (a) the non-mixed scheme x direction velocity u results; (b) the mixed scheme x direction velocity u results; (c) the non-mixed scheme y direction velocity v results; (d) the mixed scheme y direction velocity v results

    图  4  圆形溃坝模拟图

    Figure  4.  The simulation diagram for the circular dam break

    图  5  二维圆形溃坝问题密度等值线图:(a) 非混合格式密度结果; (b) 混合格式密度结果

    Figure  5.  The density contour for the 2D circular dam-break problem: (a) the non-mixed scheme density results; (b) the mixed scheme density results

    图  6  二维圆形溃坝问题速度图:(a) 非混合格式x方向的速度u;(b) 混合格式x方向的速度u;(c) 非混合格式y方向的速度v;(d) 混合格式y方向的速度v

    Figure  6.  The velocity contour for the 2D circular dam-break problem: (a) the non-mixed scheme x direction velocity u results; (b) the mixed scheme x direction velocity u results; (c) the non-mixed scheme y direction velocity v results; (d) the mixed scheme y direction velocity v results

    图  7  激波聚焦模拟图

    Figure  7.  The simulation diagram for the shock wave focusing problem

    图  8  二维激波聚焦问题密度等值线图:(a) 非混合格式密度结果; (b) 混合格式密度结果

    Figure  8.  The density contour for the 2D shock wave focusing problem: (a) the non-mixed scheme density results; (b) the mixed scheme density results

    图  9  二维激波聚焦问题速度图:(a) 非混合格式x方向的速度u; (b) 混合格式x方向的速度u;(c) 非混合格式y方向的速度v ; (d) 混合格式y方向的速度v

    Figure  9.  The velocity contour for the 2D shock wave focusing problem: (a) the non-mixed scheme x direction velocity u results; (b) the mixed scheme x direction velocity u results; (c) the non-mixed scheme y direction velocity v results; (d) the mixed scheme y direction velocity v results

    图  10  潮汐问题模拟图

    Figure  10.  The simulation diagram for the tidal problem

    图  11  二维潮汐问题密度等值线图:(a) 非混合格式密度结果;(b) 混合格式密度结果

    Figure  11.  The density contour map for the 2D tidal problem: (a) the non-mixed scheme density results; (b) the mixed scheme density results

    图  12  二维潮汐问题速度图:(a) 非混合格式x方向的速度u;(b) 混合格式x方向的速度u;(c) 非混合格式y方向的速度v;(d) 混合格式y方向的速度v

    Figure  12.  The velocity contour for the 2D tidal problem: (a) the non-mixed scheme x direction velocity u results; (b) the mixed scheme x direction velocity v results; (c) the non-mixed scheme y direction velocity v results; (d) the mixed scheme y=direction velocity v results

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出版历程
  • 收稿日期:  2021-03-08
  • 修回日期:  2021-09-27
  • 网络出版日期:  2022-01-07
  • 刊出日期:  2022-02-01

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