For example, the grid shown in Figure 2 is Lagrangian in the vertical coordinate. Although this method is not applicable to flows undergoing large distortions, where meshes can be twisted into unacceptable shapes, but its advantage is the ease with which it handles free surfaces and interfaces, which makes it applicable to a wide variety of problems. The fluid boundaries always coincide with the grid boundaries and the fluid inside each cell of the grid always remains in that computational cell. In Lagrangian method, the flow field of the considered fluid is covered by a mesh moving with the fluid. For example, the collapse of a column of a fluid could be modeled in the Eulerian grid which is shown in Figure 1.Ī sample of Lagrangian grid in vertical direction. The main superiority of the Eulerian description is the possibility of modeling of complicated surfaces. In this case, using finer mesh could increase the portion of the number of the inner elements to the boundary elements, which in turn, increases the precision of the numerical solution. This is crucial when the portion of the area to the perimeter of a zone is low, for example on phase of a multiphase fluid. Therefore, when the free surface of a discontinuous region is modeled by this method, finer grid should be employed in order to achieve more precise results, specifically if this surface has large deflections. In the Eulerian method, it is not possible to decompose the equation on the boundaries with the same precision of inner region of fluid and accordingly, the finer mesh should be used near the boundaries. For example, when the portion of the perimeter to the area of a zone of fluid is large, the error of this method is increased. The Eulerian method has some limitations. Therefore, this method is not appropriate for formulation of basic equations of fluid movement. The fluid is studied while passing this volume and continuously replaced in time. It uses a fixed grid system which is not transformed during the solution procedure. A mesh remains fixed in the Eulerian method and fluid regions change in shape and location on the mesh. In this method, attention is paid to a special volume in the space. The first description is the Eulerian approach. In the continuum mechanics, there are two methods to express the motion in the environment. Simulations of free surface flows have progressed rapidly over the last decade, and it is now possible to simulate the motion of complicated waves and their interactions with structures considering even deformable bubbles in turbulent flows. Finally, two schemes of parametric study of interfaces are discussed. Moreover, surface tension modeling and its discretization as one of the most demanding phenomena in the nature are brought to the readers. Meanwhile, Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM), Higher Resolution Artificial Compressive (HiRAC), High Resolution Interface Capturing (HRIC), Switching Technique for Advection and Capturing of Surfaces (STACS), and some other newly proposed methods are introduced, and the accuracy and time calculation of each method are evaluated. Herein, the governing equations of fluid flow including Navier‐Stokes coupled with VOF equation are discussed and the most prominent VOF schemes hierarchically presented to the readers. Volume of fluid (VOF) is a powerful and the most prevailing method for modeling two immiscible incompressible fluid‐fluid interfaces. In this chapter, free surface simulation methods based on computational grid are presented. For these flows, temporal and spatial position of this moving free surface in unsteady or non‐uniform conditions is very complicated. Viscous flow with moving free surface is an important phenomenon in nature which has broad applications in engineering.
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