It is well-known that the standard level set advection equation does not preserve the signed distance property, which is a desirable property for the level set function representing a moving interface. Therefore, reinitialization or redistancing methods are frequently applied to restore the signed distance property while keeping the zero-contour fixed. As an alternative approach to these methods, we introduce a modified level set advection equation that intrinsically preserves the norm of the gradient at the interface, i.e. the local signed distance property. Mathematically, this is achieved by introducing a carefully chosen source term being proportional to the local rate of interfacial area generation. The introduction of the source term turns the problem into a non-linear one. However, we show that by discretizing the source term explicitly in time, it is sufficient to solve a linear equation in each time step. Notably, without further adjustment, the method works in the case of a moving contact line. This is a major advantage since redistancing is known to be an issue when contact lines are involved. We provide a first implementation of the method in a simple first-order upwind scheme in both two and three spatial dimensions.
翻译:众所周知,标准水平设定的平流方程式并不保存签名的远方属性,这是代表移动界面的平面设定函数的可取属性。因此,经常采用重新初始化或重写方法来恢复签名的远方属性,同时保持零反波固定。作为这些方法的替代方法,我们引入了修改的平面设定的平面方程式,在本质上保留了界面的梯度规范,即当地签名的距离属性。从数学角度讲,这是通过引入一个谨慎选择的源术语来实现的,该源术语与跨轴区域生成的本地速率成正比。引入源术语将问题变成非线性一。然而,我们表明,通过将源术语明确分解,可以解决每个时间步骤的线性方程式。值得注意的是,在不作进一步调整的情况下,该方法在移动接触线的情况下起作用。这是一个重要的优势,因为在涉及接触线时,人们知道再平衡是一个问题。我们在两个和三个空间层面的简单第一阶梯段中首次实施该方法。</s>