fenicsR13：基于FEniCS计算平台的线性R13方程张量混合有限元求解器
fenicsR13: A Tensorial Mixed Finite Element Solver for the Linear R13 Equations Using the FEniCS Computing Platform
摘要：
我们提出了非平衡气体动力学线性化R13方程的混合有限元求解器。Python实现建立在FeNiCS计算平台提供的软件工具之上。我们描述了一种新的张量的方法，利用FEniCS的统一形式语言（UFL）的扩展功能，以定义所需的微分算子张量以上的二度。所提出的求解器作为一个例子，实现张量变分公式FEniCS，其中的文件和文献似乎是非常稀疏。使用UFL提供的软件抽象级别，可以在底层数学和结果源代码之间实现几乎一对一的对应。测试用例支持所提出的方法的正确性，使用精确解验证。为了证明扩展的气体流动模型的使用，我们讨论了涉及稀疏效应的典型应用案例。我们公开提供文档化和有效的解决方案。
英文摘要：
We present a mixed finite element solver for the linearized R13 equations of non-equilibrium gas dynamics. The Python implementation builds upon the software tools provided by the FEniCS computing platform. We describe a new tensorial approach utilizing the extension capabilities of FEniCS's Unified Form Language (UFL) to define required differential operators for tensors above second degree. The presented solver serves as an example for implementing tensorial variational formulations in FEniCS, for which the documentation and literature seem to be very sparse. Using the software abstraction levels provided by the UFL allows an almost one-to-one correspondence between the underlying mathematics and the resulting source code. Test cases support the correctness of the proposed method using validation with exact solutions. To justify the usage of extended gas flow models, we discuss typical application cases involving rarefaction effects. We provide the documented and validated solver publicly.
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