fenicsR13

Lambert Theisen, M. Torrilhon
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引用次数: 5

Abstract

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.
本文提出了非平衡气体动力学线性化正则化13矩方程的混合有限元求解方法。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的所需微分算子。所提出的求解器是在fenic中实现张量变分公式的一个例子,关于这方面的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层次允许底层数学和结果源代码之间几乎一对一的对应关系。测试用例使用精确解验证来支持所建议方法的正确性。为了证明扩展气体流动模型的使用是合理的,我们讨论了涉及稀薄效应的典型应用案例。我们公开提供文档化和验证的求解器。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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