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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (2): 316-326.doi: 10.3969/j.issn.1005-3085.2026.02.008cstr: 32411.14.cjem.CN61-1269/O1.2026.02.008

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三维耗散波有限差分PCFD数值模拟

罗志强   

  1. 浙江传媒学院媒体工程学院，杭州 310018
  • 收稿日期:2024-11-04 接受日期:2025-11-09 出版日期:2026-04-15 发布日期:2026-06-15
  • 基金资助:
    浙江省高等教育“十四五”研究生教改项目 (JGGC2024031).

The Three-dimensional Numerical Simulation of Dissipative Standing Wave Based on PCFD Method

LUO Zhiqiang   

  1. School of Media Engineering, Communication University of Zhejiang, Hangzhou 310018
  • Received:2024-11-04 Accepted:2025-11-09 Online:2026-04-15 Published:2026-06-15
  • Supported by:
    The Teaching Reform Project for Postgraduates in the Tenth Five-Year Plan of Higher Education in Zhejiang Province (JGGC2024031).

摘要：

能量耗散存在于许多动力学实际问题中，但带能量耗散的耗散性晃荡问题的研究相对较少。为些，采用一种复杂的预测校正有限差分法(Predictor-Corrector Finite Difference, PCFD)对耗散性驻波进行数值模拟。PCFD方法用于求解三维耗散势流方程，并通过数值计算揭示了自由表面耗散驻波的运动变化。计算域采用交错网格系统，以精确捕捉流场变量。通过$\sigma$坐标变换将不规则水槽映射至立方体水槽，并应用PCFD方法对势流方程、泊松方程及边界条件进行离散化求解。实验过程表明，当前研究结果与既有文献高度吻合。通过不同实验参数呈现了能量耗散驻波的特征，并在实验过程中详细展示了自由表面波高的变化规律。研究证明：在能量耗散条件下，自由表面仍能良好保持驻波的特性。

关键词: 能量耗散波, PCFD方法, 交错网格, 有限差分法, 驻波波高

Abstract:

Energy dissipation exists in many practical problems of dynamics, yet research on the oscillation problems with energy dissipation remains relatively scarce. Thus, the novel energy dissipative standing wave is simulated with a complex prediction-correction finite difference method (PCFD). The PCFD is used to solve the three dimensional energy dissipation potential flow equation and is applied to numerically simulate the dynamic evolution of dissipative standing wave in free surface. The computational domain is arranged with a staggered mesh-grid system and it is used to capture the flow field variables correctly. An irregular tank is mapped onto a square cubic tank through $\sigma$ coordinate transformation. The PCFD is applied to discrete the potential flow equations, Poisson equation and boundary conditions. From the experimental process, we can conclude that the present results are good agree with previous article. The energy dissipation standing wave is presented with different experimental parameters and the different wave elevation of free surface is detailed displayed in experimental process. The free surface maintains the characteristics of the standing wave well under energy dissipation.

Key words: energy dissipative wave, PCFD method, staggered grid, finite difference method, standing wave elevation

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