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.

Program Summary

Program title: Celeris Advent (v.1.3.4)

CPC Library link to program files: https://doi.org/10.17632/pwsjdsgz89.1

Licensing provisions: GNU General Public License 3

Programming language: C++, HLSL

Nature of problem: Celeris Advent started a new paradigm in nearshore wave simulations and enabled researchers and engineers to run a Boussinesq-type model, faster than real-time and in an interactive environment. For simplicity, we assumed a fixed time step in our first implementation of Celeris Advent. This fixed time step often needs to be chosen conservatively such that the model can resolve the most extreme cases during the experiment. In practical simulations, such as simulating coastal fields, the superposition of boundary and initial conditions may cause rare but extreme conditions, requiring a very small time step that is too conservative during most of the simulation.

Solution method: We developed adaptive third order Adams-Bashforth time integration to let Celeris Advent solve the extended Boussinesq equations with a variable time step, allowing it to decrease the time step only when necessary. The adaptive equations are presented in a generic format and therefore can be used for solving other equations as well.

Additional comments including restrictions and unusual features: The new version of the Celeris Advent with the adaptive time integration runs ∼3 times faster for the standard conical island benchmark, allowing Celeris Advent simulate this benchmark on a $200\times 200$ grid an order of magnitude faster than real-time on a consumer-level gaming laptop. For a field simulation benchmark, with rare but extreme events, the new version runs ∼25 times faster.

中文翻译：

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扩展的Boussinesq方程的自适应三阶Adams-Bashforth时间积分

我们开发了可变时间步长的三阶自适应Adams-Bashforth时间积分和二阶有限差分方程。我们将这些方案整合到Celeris Advent软件中，离散化和求解二维扩展Boussinesq方程。该软件使用混合有限体积-有限差分方案，并利用GPU来以比实时更快的速度求解方程式，同时可视化它们。新添加的自适应方案显着提高了模型的鲁棒性，同时提供了更快的计算性能。我们使用Celeris Advent的自适应时间步长方案模拟了多个基准，并演示了该软件在模拟波浪破碎，波浪加速，不规则波浪和裂隙电流方面的能力。

计划摘要

程序标题： Celeris Advent（v.1.3.4）

CPC库链接到程序文件： https : //doi.org/10.17632/pwsjdsgz89.1

许可条款：GNU通用公共许可3

编程语言： C ++，HLSL

问题的本质： Celeris Advent在近岸波浪模拟中启动了新的范例，使研究人员和工程师能够在实时和交互式环境中以更快的速度运行Boussinesq型模型。为简单起见，我们在Celeris Advent的第一个实现中假定了固定的时间步长。通常需要保守地选择此固定时间步长，以便模型可以解决实验过程中最极端的情况。在实际的模拟中，例如模拟沿海地区，边界条件和初始条件的叠加可能会导致罕见但极端的条件，这需要非常小的时间步长，而这在大多数模拟过程中都过于保守。

解决方法：我们开发了自适应三阶Adams-Bashforth时间积分，让Celeris Advent用可变的时间步长求解扩展的Boussinesq方程，从而仅在必要时才减小时间步长。自适应方程式以通用格式表示，因此也可以用于求解其他方程式。

其他注释包括限制和异常功能：具有自适应时间积分功能的Celeris Advent的新版本在标准圆锥形岛基准测试中的运行速度提高了约3倍，从而使Celeris Advent可以在$200\times 200$在消费者级别的游戏笔记本电脑上，网格速度比实时速度快了一个数量级。对于现场模拟基准，发生罕见但极端的事件，新版本的运行速度快约25倍。