用于模拟微波加热流动的不连续Petrov-Galerkin有限元框架

中文摘要 AI 辅助

我们提出了一种用于模拟微波加热流动的高阶多物理场求解器。该求解器将用于时谐麦克斯韦方程的不连续Petrov-Galerkin（DPG）有限元方法，与用于热传导方程和不可压缩纳维-斯托克斯方程的连续Galerkin有限元方法耦合。我们针对多个基准问题验证了电磁求解器：矩形波导中的波传播、具有奇异解的腔体问题，以及微波加热障碍物问题，将我们的结果与文献中的数值和实验数据进行了比较。结果证实了实现的有效性，并展示了其利用DPG方法内置误差估计器进行自适应网格细化的能力。研究的最后部分通过对具有奇异几何特征的障碍物周围微波加热流动的模拟，展示了该多物理场框架的能力。这些结果凸显了所提出框架在微波辅助化学过程的模拟与优化方面的潜力。最后，所开发的高阶多物理场求解器具有低内存占用，因为电磁求解器依赖于共轭梯度（CG）迭代求解器，而流体求解器以无矩阵方式实现，使得整体方法具有可扩展性，非常适合大规模并行模拟。

英文摘要

We present a high-order multiphysics solver for the simulation of microwave-heated flows. The solver couples a discontinuous Petrov-Galerkin (DPG) finite element method for the time-harmonic Maxwell equations with continuous Galerkin finite element methods for the heat equation and the incompressible Navier-Stokes equations. We validate the electromagnetic solver against multiple benchmark problems: wave propagation in a rectangular waveguide, a cavity problem with a singular solution, and a microwave-heated obstacle problem, comparing our results against numerical and experimental data from the literature. The results confirm the validity of the implementation and demonstrate its ability to perform adaptive mesh refinement using the DPG method's built-in error estimator. The final part of the study showcases the capabilities of the multiphysics framework through simulations of microwave-heated flow around obstacles with singular geometric features. These results highlight the potential of the proposed framework for the simulation and optimization of microwave-assisted chemical processes. Finally, the developed high-order multiphysics solver has a low memory footprint, since the electromagnetic solver relies on a Conjugate Gradient (CG) iterative solver and the fluid solver is implemented in a matrix-free fashion, making the overall approach scalable and well-suited for large-scale parallel simulations.

发表机构

• Polytechnique Montreal（蒙特利尔理工大学）
• Texas A&M University（德克萨斯农工大学）

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