<p>This study presents a physics-informed neural network (PINN) framework to simulate axisymmetric submerged jet grout flow using high-fidelity data generated from ANSYS Fluent simulations. The CFD model solves the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$k - \varepsilon$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>-</mo> <mi>ε</mi> </mrow> </math></EquationSource> </InlineEquation> turbulence closure model, converted into axisymmetric form to reflect jet grouting. The PINN incorporates continuity, RANS equations, and turbulence closure equations into the loss function, enabling it to learn turbulent flow physics without requiring mesh generation. Separate neural networks were used for each flow variables—axial velocity (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$U$</EquationSource> <EquationSource Format="MATHML"><math> <mi>U</mi> </math></EquationSource> </InlineEquation>), radial velocity (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$V$</EquationSource> <EquationSource Format="MATHML"><math> <mi>V</mi> </math></EquationSource> </InlineEquation>), pressure (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$P$</EquationSource> <EquationSource Format="MATHML"><math> <mi>P</mi> </math></EquationSource> </InlineEquation>), turbulent kinetic energy (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$k$</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>), and dissipation rate (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\varepsilon$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>). The model was trained using a curriculum learning strategy to enhance stability and avoid gradient explosion and the predicted results closely matched the CFD outputs. This study demonstrates that PINNs can serve as efficient and accurate surrogate models for complex, high-gradient flow systems like jet grouting, offering a promising tool for understanding submerged jet flow behavior and reducing computational demands in geotechnical engineering.</p>

Physics-informed neural network for the simulation of turbulent jet grout flow

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2026年3月17日

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Rakam Lama Tamang,
Yichuan Zhu,
Joseph Coe

摘要

This study presents a physics-informed neural network (PINN) framework to simulate axisymmetric submerged jet grout flow using high-fidelity data generated from ANSYS Fluent simulations. The CFD model solves the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the $k - \varepsilon$ $k - ε$ turbulence closure model, converted into axisymmetric form to reflect jet grouting. The PINN incorporates continuity, RANS equations, and turbulence closure equations into the loss function, enabling it to learn turbulent flow physics without requiring mesh generation. Separate neural networks were used for each flow variables—axial velocity ( $U$ $U$ ), radial velocity ( $V$ $V$ ), pressure ( $P$ $P$ ), turbulent kinetic energy ( $k$ $k$ ), and dissipation rate ( $\varepsilon$ $ε$ ). The model was trained using a curriculum learning strategy to enhance stability and avoid gradient explosion and the predicted results closely matched the CFD outputs. This study demonstrates that PINNs can serve as efficient and accurate surrogate models for complex, high-gradient flow systems like jet grouting, offering a promising tool for understanding submerged jet flow behavior and reducing computational demands in geotechnical engineering.