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A mathematical model of liquid oscillations in two storage tanks connected to a pipe branch is presented. In its basic form, the model consists of three ordinary 1st-order differential equations (ODEs) and one algebraic equation, which are mutually coupled. Based on a prediction-correction procedure, the algorithm for its solution is explained and demonstrated on a simplified example. The oscillations calculated in the considered case reflect plausible behavior of the liquid. The presented solution of the ODE-model is in quite good agreement with the results of computational fluid dynamics (CFD) simulation with free-surface model and Volume-of-Fluid approach. The ODE solution is achieved in considerably shorter time. The model and algorithm can be easily extended to multiple tanks.

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Numerical Solution of Liquid Oscillations in Storage Tanks Connected to a Pipe Branch

  • 会议论文

  • 发表日期：

    2026年

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  • Muris Torlak,
  • Adis Bubalo,
  • Safet Isić

摘要

A mathematical model of liquid oscillations in two storage tanks connected to a pipe branch is presented. In its basic form, the model consists of three ordinary 1st-order differential equations (ODEs) and one algebraic equation, which are mutually coupled. Based on a prediction-correction procedure, the algorithm for its solution is explained and demonstrated on a simplified example. The oscillations calculated in the considered case reflect plausible behavior of the liquid. The presented solution of the ODE-model is in quite good agreement with the results of computational fluid dynamics (CFD) simulation with free-surface model and Volume-of-Fluid approach. The ODE solution is achieved in considerably shorter time. The model and algorithm can be easily extended to multiple tanks.