Adaptive Third Order Adams-Bashforth Time Stepping for Extended Boussinesq Equations

TL;DR

This paper introduces an adaptive third-order Adams-Bashforth time stepping method integrated into a GPU-accelerated software for efficiently solving and visualizing complex 2D extended Boussinesq equations, enhancing robustness and speed.

Contribution

The paper develops a novel third-order adaptive Adams-Bashforth scheme with variable time steps and incorporates it into the Celeris Advent software for advanced wave modeling.

Findings

Improved robustness of wave simulations with adaptive time stepping.

Faster computational performance using GPU acceleration.

Successful modeling of complex wave phenomena like wave-breaking and rip currents.

Abstract

We develop the third-order adaptive Adams-Bashforth time stepping and the second-order finite difference equation for variable time steps. We incorporate these schemes in the Celeris Advent software to discretize and solve the 2D extended Boussinesq equations. This software uses a hybrid finite volume - finite difference scheme and leverages the GPU to solve the equations faster than real-time while concurrently visualizing them. We simulate several benchmarks using the adaptive time stepping scheme of Celeris Advent and demonstrate the capability of the software in modeling wave-breaking, wave runup, irregular waves, and rip currents. The adaptive scheme significantly improves the robustness of the model while providing faster computational performance.