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首页> 外文期刊>Journal of Computational Physics >Numerical simulations of two-dimensional foam by the immersed boundary method
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Numerical simulations of two-dimensional foam by the immersed boundary method

机译：二维边界法的二维泡沫数值模拟

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In this paper, we present an immersed boundary (IB) method to simulate a dry foam, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquid-film internal boundaries that partition the gas into discrete cells or bubbles. The liquid-film boundaries are flexible, contract under the influence of surface tension, and are permeable to the gas, which moves across them by diffusion at a rate proportional to the local pressure difference across the boundary. Such problems are conventionally studied by assuming that the pressure is uniform within each bubble. Here, we introduce instead an IB method that takes into account the non-equilibrium fluid mechanics of the gas. To model gas diffusion across the internal liquid-film boundaries, we allow normal slip between the boundary and the gas at a velocity proportional to the (normal) force generated by the boundary surface tension. We implement this method in the two-dimensional case, and test it by verifying the von Neumann relation, which governs the coarsening of a two-dimensional dry foam. The method is further validated by a convergence study, which confirms its first-order accuracy.
机译：在本文中，我们提出了一种浸入边界（IB）方法来模拟干燥泡沫，即其中大部分体积归因于其气相的泡沫。干泡沫动力学涉及气体与一系列薄的液膜内部边界之间的相互作用，这些内部边界将气体分隔为离散的气泡或气泡。液膜边界是柔性的，在表面张力的作用下会收缩，并且对气体是可渗透的，气体通过扩散以与边界上的局部压差成比例的速率在膜上移动。通常通过假设每个气泡内的压力均匀来研究这些问题。在这里，我们引入一种IB方法，该方法考虑了气体的非平衡流体力学。为了模拟气体在内部液膜边界上的扩散，我们允许边界和气体之间的法向滑动以与边界表面张力产生的（法向）力成比例的速度进行。我们在二维情况下实施此方法，并通过验证控制二维干泡沫粗化的冯·诺伊曼关系进行测试。收敛性研究进一步验证了该方法，证实了其一阶准确性。

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