CFC 2025

Reduced Order Modelling for Water Waves using Incompressible Navier-Stokes Simulation

  • Engsig-Karup, Allan (Technical University of Denmark)
  • Melander, Anders (Technical University of Denmark)

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A new incompressible Navier-Stokes equations (INSE) based tool [1] has been developed recently for simulating two-dimensional water wave motion in 2D using a high-order finite dif- ference scheme. We present new extensions of this work into a 3D high-fidelity simulation tool setup as a numerical wave tank, and validate it against benchmarks cases that incorpo- rate varying sea beds while accounting for nonlinear wave propagation. The robustness of these new free surface INSE-based simulation tools relies on a discrete mixed-stage pressure-velocity coupling that is incorporated into the numerical scheme to both preserve mass continuity and high-order convergence with boundary conditions imposed conveniently using ghost points . This pressure-velocity coupling step requires solving a Poisson problem for the pressure at ev- ery stage of the temporal integration, which is currently done using a low-storage explicit 4th order Runge-Kutta method. In the context of 3D free surface flow modelling of water waves, that is still considered computationally costly today for routine use in simulations of the evo- lution of regional sea states as well as for wave-structure interaction applications. Due to the large degrees of freedom counted as total number of grid points in the fluid volume, there is a significant potential for speeding up computations with data-driven dimensionality reduction techniques such as reduced basis methods [2] that is based on snapshot data of temporal state information. With this new tool, we analyse numerically the speedup potential to enable quicker engineering analysis via benchmarking of the new INSE models and compare these with previous results that demonstrated acceleration of more than two orders of magnitude achieved using fully nonlinear potential flow (FNPF) modelling [3,4] for wave propagation and wave-structure interaction applications.