Velocity Projection with Upwind Scheme Based on the Discontinuous Galerkin Methods for the Two Phase Flow Problem

Jiangyong Hou, Wenjing Yan, Jie Chen
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Abstract

The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.
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基于不连续Galerkin方法的两相流迎风速度投影
逆风格式在对流主导问题、两相流问题等问题的数值逼近中起着重要的作用。对于两相流问题的分流公式,通常采用罚不连续伽辽金(PDG)法结合迎风格式来求解相压力方程。在这种情况下,除非在速度重建中考虑逆风方案,否则局部质量平衡不能准确保持。本文给出了一种完全考虑逆风格式的H(div)空间速度重建方案。此外,计算非线性系数的不同方法可能会产生不同而显著的影响,一些作者已经对此进行了研究。在考虑逆风格式的情况下,我们提出了一种新的算法来获得更有效和稳定的系数近似。
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