We present a mixed finite element solver for the linearized regularized 13-moment 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’ Unified Form Language 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 Unified Form Language 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.

中文翻译：

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fenicsR13

我们提出了一种混合有限元求解器，用于非平衡气体动力学的线性化正则化 13 矩方程。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方法，利用 FEniCS 的统一形式语言的扩展能力来定义二阶以上张量所需的微分算子。所提出的求解器作为在 FEniCS 中实现张量变分公式的示例，其文档和文献似乎非常稀少。使用统一形式语言提供的软件抽象级别允许在底层数学和生成的源代码之间几乎一一对应。测试用例使用精确解决方案的验证来支持所提出方法的正确性。为了证明使用扩展气流模型的合理性，我们讨论了涉及稀疏效应的典型应用案例。我们公开提供记录和验证的求解器。