Adaptive third order Adams-Bashforth time integration for extended Boussinesq equations

We develop the third-order adaptive Adams-Bashforth time integration 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. The newly added adaptive scheme significantly improves the robustness of the model while providing faster computational performance. 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.

本研究开发了适用于变时间步长的三阶自适应亚当姆斯-巴什福斯（Adams-Bashforth）时间积分格式与二阶有限差分方程。我们将上述两种格式集成至Celeris Advent软件中，用于离散求解二维扩展布辛内斯克（Boussinesq）方程。该软件采用混合有限体积-有限差分格式，并借助图形处理器（GPU）实现超实时求解与同步可视化。新增的自适应格式显著提升了模型的鲁棒性，同时优化了计算性能。本研究利用Celeris Advent的自适应时间步长格式开展多组基准测试模拟，验证了该软件在模拟波浪破碎、波浪爬高、不规则波浪及裂流等物理过程中的应用能力。