论文标题
用于完全欧拉流体结构相互作用的界面和几何形状保存相位方法
An interface and geometry preserving phase-field method for fully Eulerian fluid-structure interaction
论文作者
论文摘要
我们提出了一种界面和几何形状（IGP）方法，用于通过相处公式进行完全欧拉的流体结构相互作用进行建模。虽然双曲线切线界面曲线由时间依赖性迁移率模型保留，但该方法通过减少体积保守的平均曲率流量来维持固体流体界面的几何形状。为了实现曲率流的降低，我们构建了一个梯度最小化速度场（GMV），以使其对流参数的对流。构造的速度场可以保留实心域中的实心速度，同时在整个弥漫性界面区域沿正常方向延伸速度。通过这种处理，GMV降低了顺序参数的水平集的正常速度差异，该水平集减轻了由于对流而导致的弥漫界面区域的不需要的增厚或变薄。在此过程中，依赖时间的迁移系数大大降低，并且曲率流量较小。 GMV确保弥漫界面区域以实体体积移动，从而使流体固体界面符合固体的几何形状。使用统一动量方程和相关插值，我们将IGP方法基于不可压缩的粘性流体和新霍克亚固体将IGP方法集成到完全欧拉的FSI求解器中。我们首先证明了基于相位场的IGP方法具有规定速度场的圆形和方形界面对流的能力。然后检查具有IGP方法的变异FSI框架，以通过在通道域中的固定可变形块的流量进行流。最后，采用了经受传入流的固定圆柱体后面附着的板的振动来评估较大纵横比和锋利角的完全欧拉框架。
We present an interface and geometry preserving (IGP) method for the modeling of fully Eulerian fluid-structure interaction via phase-field formulation. While the hyperbolic tangent interface profile is preserved by the time-dependent mobility model, the proposed method maintains the geometry of the solid-fluid interface by reducing the volume-conserved mean curvature flow. To achieve the reduction in the curvature flow, we construct a gradient-minimizing velocity field (GMV) for the convection of the order parameter. The constructed velocity field enables the preservation of the solid velocity in the solid domain while extending the velocity in the normal direction throughout the diffuse interface region. With this treatment, the GMV reduces the normal velocity difference of the level sets of the order parameter which alleviates the undesired thickening or thinning of the diffuse interface region due to the convection. During this process, the time-dependent mobility coefficient is substantially reduced and there is a lesser curvature flow. The GMV ensures that the diffuse interface region moves with the solid bulk such that the fluid-solid interface conforms to the geometry of the solid. Using the unified momentum equation and the phase-dependent interpolation, we integrate the IGP method into a fully Eulerian variational FSI solver based on the incompressible viscous fluid and the neo-Hookean solid. We first demonstrate the ability of the phase-field-based IGP method for the convection of circular and square interfaces with a prescribed velocity field. The variational FSI framework with the IGP method is then examined for the flow passing a fixed deformable block in a channel domain. Finally, the vibration of a plate attached behind a stationary cylinder subjected to incoming flow is employed to assess the fully Eulerian framework for a large aspect ratio and sharp corners.
