A finite volume method for undercompressive shock waves in two space dimensions
A finite volume method for undercompressive shock waves in two space dimensions
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DOI：
10.1051/m2an/2017027
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发表时间：
2017-09
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影响因子：
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通讯作者：
C. Chalons;C. Rohde;Maria Wiebe
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文献类型：
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作者：
C. Chalons;C. Rohde;Maria Wiebe
欠压冲击波出现在许多涉及多个阶段的物理过程中。我们提出了二维空间有限体积方法来近似包含欠压冲击波的双曲或双曲椭圆守恒定律系统的弱解。该方法可以被视为[C.中空间一维和标量方法的推广。 Chalons、P. Engel 和 C. Rohde，SIAM J. Numer。肛门。 52（2014）554–579]。它依赖于移动网格模拟，使欠压波表示为清晰的界面，而无需任何人工涂抹。证明该方法具有局部保守性，能够准确地恢复平面行波解。为了证明新方案的效率和可靠性，我们在标量模型问题上对其进行了测试，并将其作为二维空间可压缩液蒸气流的应用。
Undercompressive shock waves arise in many physical processes which involve multiple phases. We propose a Finite Volume method in two space dimensions to approximate weak solutions of systems of hyperbolic or hyperbolic-elliptic conservation laws that contain undercompressive shock waves. The method can be seen as a generalization of the spatially one-dimensional and scalar approach in [C. Chalons, P. Engel and C. Rohde, SIAM J. Numer. Anal. 52 (2014) 554–579]. It relies on a moving mesh ansatz such that the undercompressive wave is represented as a sharp interface without any artificial smearing. It is proven that the method is locally conservative and recovers planar traveling wave solutions exactly. To demonstrate the efficiency and reliability of the new scheme we test it on scalar model problems and as an application on compressible liquid-vapour flow in two space dimensions.