Work

Subspace Acceleration for Efficient Nonlinear Water Wave Simulation

Year: 2026

Type: article

Abstract: ABSTRACT Efficient simulation of nonlinear and dispersive free‐surface flows governed by the incompressible Navier–Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a time‐dependent discretized Poisson problem at every time step to enforce divergence free flow. This is crucial to ensure conservation of mass and requires solving long sequences of time‐dependent linear systems typically using iterative methods, such as preconditioned Krylov subspace methods. In this work, we investigate new subspace acceleration techniques for improving initial guesses to reduce the number of iterations required by iterative solvers, with a focus on nonlinear wave propagation problems. We extend the original subspace acceleration method by incorporating the complete history of previous solutions through an exponentially weighted formulation. This approach eliminates the need for repeated sketching and orthonormalization, resulting in a more efficient and scalable strategy to generate better initial guesses. Our method is implemented within a high‐order finite‐difference framework using a method‐of‐lines formulation and a low‐storage Runge–Kutta time integration scheme. We demonstrate that subspace acceleration significantly reduces the number of GMRES iterations when solving the Poisson equation in nonlinear water wave simulations. Performance is evaluated on two benchmark problems: nonlinear stream function wave propagation and harmonic wave generation over a submerged bar. In both cases, the new approach achieves substantial improvements in computational efficiency without compromising accuracy. Although demonstrated using high‐order finite difference methods, the technique is discretization independent and broadly applicable to incompressible free‐surface flow solvers.

Source: International Journal for Numerical Methods in Fluids

DOI: 10.1002/fld.70087

Authors: Rasmus Kleist Hørlyck Sørensen, Margherita Guido, Allan Peter Engsig‐Karup, Daniel Kressner

Institutions: Technical University of Denmark, École Polytechnique Fédérale de Lausanne

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,220

Funders: COWIfonden, EUROfusion