We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked using a volume fraction function. The volume fraction is advected using a method based on the minimization of a directional flux-based error. For stability, the advection terms are discretized using upwinding schemes. In the vicinity of the embedded geometries, the signed distance function is used to populate the surface of the geometries to generate a body-conforming point cloud. Consequently, the points on the boundaries participate directly in the discretization, unlike conventional immersed-boundary methods where they are either used to calculate momentum deficit (for example, continuous forcing) or conservation losses (for example, cut-cell methods). The boundary conditions are, therefore, directly imposed at these points on the embedded geometries, opening up the possibility for a discretization that is body-conforming and spatially varying in resolution, while retaining the consistency of the scheme. We present benchmark test cases that validate the method for two-phase flows, flows with embedded boundaries and a combination of both.

中文翻译：

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具有嵌入几何结构的两相流的欧拉无网格方法


我们提出了一种新颖的欧拉无网格方法，用于具有任意嵌入几何形状的两相流。使用无网格广义有限差分法 (GFDM) 计算空间导数。使用体积分数函数跟踪尖锐的相界面。使用基于方向通量误差最小化的方法来平流输送体积分数。为了稳定性，使用逆风方案对平流项进行离散化。在嵌入几何图形的附近，带符号的距离函数用于填充几何图形的表面以生成符合身体的点云。因此，边界上的点直接参与离散化，这与传统的浸入边界方法不同，传统的浸入边界方法用于计算动量赤字（例如，连续强迫）或守恒损失（例如，切割单元方法）。因此，边界条件直接施加在嵌入几何形状的这些点上，从而为身体一致且分辨率在空间上变化的离散化提供了可能性，同时保持了方案的一致性。我们提出了基准测试用例，用于验证两相流、具有嵌入边界的流以及两者的组合的方法。