Adaptive third order Adams-Bashforth time integration for extended Boussinesq equations
Adaptive third order Adams-Bashforth time integration for extended Boussinesq equations
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DOI：
10.1016/j.cpc.2021.108006
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发表时间：
2021-04
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影响因子：
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通讯作者：
S. Tavakkol;S. Son;P. Lynett
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作者：
S. Tavakkol;S. Son;P. Lynett
我们发展了三阶自适应Adams-Bashforth时间积分和二阶变时间步长有限差分方程。我们将这些计划中的AdmisAdvent软件离散和解决二维扩展Boussinesq方程。该软件使用混合有限体积-有限差分方案，并利用GPU以比实时更快的速度求解方程，同时将其可视化。新增加的自适应方案显着提高了模型的鲁棒性，同时提供更快的计算性能。我们模拟了几个基准使用的自适应时间步进计划的Adjuis Advent和演示的能力，该软件在建模破波，波浪爬高，不规则波，和裂流。节目摘要节目标题：耶稣基督降临（v. 1.3。4)CPC Library链接到程序文件：https：//doi。org/10.17632/Lossjdsgz89。1许可证条款：GNU通用公共许可证3编程语言：C++，HLSL问题的性质：埃里斯降临在近岸波浪模拟中开创了一个新的范例，使研究人员和工程师能够在交互式环境中运行比实时更快的Boussinesq类型模型。为了简单起见，我们在第一次实现耶稣降临节时假设了一个固定的时间步长。这个固定的时间步长通常需要保守地选择，使得模型可以在实验期间解决最极端的情况。在实际模拟中，例如模拟海岸场，边界和初始条件的叠加可能会导致罕见但极端的条件，需要非常小的时间步长，在大多数模拟过程中过于保守。解决方法：我们开发了自适应三阶Adams-Bashforth时间积分，让Adamis Advent用可变的时间步长求解扩展的Boussinesq方程，允许它只在必要时减小时间步长。自适应方程以通用格式给出，因此也可用于求解其他方程。包括限制和不寻常功能在内的其他评论：具有自适应时间积分的新版本的Coriis Advent运行速度比标准圆锥岛基准快1.3倍，允许Coriis Advent在200× 200网格上模拟此基准，比消费级游戏笔记本电脑上的实时快一个数量级。对于一个现场模拟基准测试，对于罕见但极端的事件，新版本的运行速度快了250倍。
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× 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.