论文标题
FenicsR13：使用Fenics Computing平台的线性R13方程的紧张混合有限元求解器
fenicsR13: A Tensorial Mixed Finite Element Solver for the Linear R13 Equations Using the FEniCS Computing Platform
论文作者
论文摘要
我们为非平衡气体动力学的线性化R13方程提供了一个混合有限元求解器。 Python实现建立在Fenics Computing平台提供的软件工具上。我们描述了一种使用Fenics统一形式语言（UFL）的扩展功能来定义张量高于二级张量所需的差分操作员的新调整方法。提出的求解器是实施fenics中的张力变异表述的示例，文档和文献似乎非常稀疏。使用UFL提供的软件抽象级别，可以在基础数学和结果源代码之间几乎一对一的对应关系。使用精确解决方案验证的测试用例支持所提出的方法的正确性。为了证明扩展气流模型的使用是合理的，我们讨论了涉及稀疏效果的典型应用程序案例。我们公开提供已记录和验证的求解器。
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.
