Numerical discretization errors of fluid-structure interaction model in pressurized pipeline systems

Abstract

The fluid-structure interaction (FSI) effects in pressurized pipeline systems may induce pipe vibrations, leading to more severe water hammer incidents. Therefore, establishing an FSI model for liquid-filled pipelines and developing efficient and accurate numerical simulation methods are crucial. These advancements enable precise prediction of FSI water hammer phenomena, which is essential for the design and protection of pressurized pipeline systems. When using the FSI four-equation axial model for water hammer calculations, techniques such as space-line interpolation (SLI), time-line interpolation (TLI), or wave speed adjustment (WSA) are commonly employed for grid processing. However, these techniques inevitably introduce additional numerical discretization errors. Existing literatures have primarily conducted quantitative analyses by comparing numerical results of different grid processing techniques with exact solutions or experimental data, lacking a theoretical analysis. To address this gap, this study establishes an equivalent hyperbolic differential equations (EHDE) approach for numerical discretization error analysis of the FSI four-equation axial model. EHDEs for SLI, TLI, and WSA are specifically derived to analyze how these techniques generate numerical discretization errors and the factors influencing these errors during the solution process. Theoretical findings are validated through numerical case studies. The results indicate that SLI introduces non-physical numerical dissipation terms into the fluid equations of the FSI four-equation axial model. TLI transforms a single fluid pressure wave into a superposition of two pressure waves with different wave speeds, causing additional numerical dissipation and dispersion due to this non-physical superposition. WSA introduces numerical errors when adjusting wave speeds artificially. Among the three grid processing techniques, SLI exhibits the highest sensitivity to grid resolution, followed by TLI, while WSA shows the least sensitivity. Under the identical spatial grid conditions, SLI yields the lowest computational accuracy, with the largest mean absolute error (MAE) compared to the recursive exact solution. TLI follows next, whereas the WSA demonstrates the smallest MAE. These findings enhance the theoretical analysis of numerical discretization errors in the FSI four-equation axial model, providing theoretical support for selecting grid processing techniques during the solution process.