Water wave reconstruction of full hydrodynamic models via data assimilation

TL;DR

This work tackles the problem of reconstructing the full hydrodynamic water-wave field from limited surface observations by coupling a finite-volume Navier–Stokes solver with ensemble Kalman filter data assimilation. It introduces a POD‑based reduced-order approach built on ensemble snapshots, and evaluates three free-surface representations (VOF, level set, curve) to enable accurate, physics‑constrained reconstruction and propagation, effectively forming a digital twin wave tank. Key contributions include a physics‑constrained ensemble generation strategy, a novel ensemble‑based POD workflow tailored to wave problems, and a systematic comparison of interface representations under regular, irregular, and plunging wave regimes, highlighting level set as the most robust for reconstruction. The results demonstrate substantial reconstruction accuracy for surface and low‑order velocity fields, with sequential assimilation helping maintain consistency as waves propagate toward the test section, enabling improved coupling between experiments and simulations in practical coastal/ocean engineering contexts.

Abstract

A strategy for reconstructing the water wave field using a data assimilation method is proposed in the present study. Special treatments are introduced to address the ensemble diversity and the discontinuous free surface with hydrodynamic constraints when implementing the EnKF approach. Additionally, the POD method is employed for dimensionality reduction, but from an ensemble point of view. The main purpose of this study is to achieve satisfactory consistency between the water waves computed by the numerical solver, particularly by the VOF method, and those observed in the laboratory wave flume within the test section of interest. To validate the proposed framework, three representative conditions are tested: regular waves, irregular waves, and plunging waves. The effects of observation noise, modal truncation, and other factors are also examined. From a practical perspective, this work provides a promising way to realize the coupling between experiments and numerical simulations, and establishes a prototype of a ``digital twin wave tank''.

Figures (36)

• Figure 1: Sketch of the numerical wave flume where the test section is the focus of this study.
• Figure 2: Flow chart of the model advancing and DA strategy. The ensemble is used throughout the whole simulation process to keep the diversity of members, and DA is carried out only when the reconstruction is needed. The reconstructed wave field will not be used to update the original simulation.
• Figure 3: Flow chart for the assimilation procedure to reconstruct the wave field at a time.
• Figure 4: The variance spectrum and modal structure of the dataset that consists of the flow fields from an ensemble of waves at the same time.
• Figure 5: The variance spectrum and modal structure of the dataset that consists of multi-time flow fields from a single case.