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It is quite straightforward to extend the problem by applying a force to the bar and actually computing the displacement of the bar due to the counterforces applied by the fluid.

In the example problem, we prescribe the displacement of the little rectangular bar on the surface. Fluid-Structure Interaction and Free Surfaces We can see that the elements to the right of the little rectangular bar are stretched out before remeshing, but look more isotropic after remeshing. The mesh before remeshing is triggered (left) and after remeshing (right). In other words, the free surface in the moving mesh case does not have to displace air and can use this energy to create slightly higher waves and a more undulated surface. The air domain is not present in the moving mesh case and the surface only “sees” a constant air pressure on top of the fluid surface. The air domain above the free surface in the phase field case has a small damping effect on the surface in the phase field method. We can see that the agreement between the two methods is decent and both the shape of the free surface and the streamlines of the velocity field are similar. The figures below show the free surface computed using moving mesh, as compared with the results computed using the phase field method. Comparing Moving Mesh with Phase Field Results The resulting differences are discussed in the next section. Neglecting the influence of the air domain is motivated in this case by the large ratios in density and dynamic viscosity between water and air. Not solving for the fluid flow in the air domain above the free surface results in a substantial improvement in performance, since the number of degrees of freedom for the Navier-Stokes system are reduced to roughly half of that used by the field-based methods.

The modeling of free surfaces is, in a way, cleaner using moving mesh compared to the level set and phase field methods, since we can apply surface tension and other surface forces directly as boundary conditions, as mentioned above. (This can, of course, be changed by manually adding a second fluid flow interface or by using the Fluid-Fluid Interface feature available in the Two-Phase Flow, Moving Mesh interface in the Microfluidics Module.) Furthermore, the moving mesh implementation in COMSOL Multiphysics is not able to treat topology changes of the free surface, such as breaking waves. Therefore, it is not possible to obtain the flow field in the gas phase with the current implementation. With this approach, the liquid is modeled while the flow field in the gas domain above the free surface is not treated other than through surface tension and pressure effects.

The Navier-Stokes equations are in turn formulated on a moving coordinate system where the movement is obtained from the moving mesh equations that are solved simultaneously. The solution of the moving mesh equations smoothly displaces the mesh nodes inside the bulk of the fluid. Using the Free-Surface feature, the displacement velocity of the free surface is obtained as the fluid’s velocity at the surface at any given time. Surface tension and other surface forces are directly applied as boundary conditions at the free surface. With the moving mesh approach, the free surface is modeled as a geometrical surface separating two domains.

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The moving mesh free surface modeling feature in the COMSOL Multiphysics® software is a completely different approach for the same problem, compared to the level set and phase field methods discussed previously.

The slip length is equal to the size of the element length. In order to compare the results from the moving mesh method with the phase field and level set methods, we use Navier slip conditions for the walls. We account for gravity in the model by adding a source in the momentum equations. The moving mesh method for the free surface prescribes the displacement of the rectangular bar and keeps track of the displacement of the water surface. Geometry and definition of the example problem. Note that the moving mesh functionality is actually also used to prescribe the movement of the little rectangular bar back and forth on the surface in the level set and phase field methods, as well as the moving mesh method. The model is of a solid bar that is partially immersed in water in a small channel. To demonstrate the moving mesh functionality, we will use the same problem as we did in the previous blog post on the phase field and level set methods.

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In this blog post, we will demonstrate how to use the moving mesh method for modeling free surfaces and compare the results with field-based methods. Another option, moving mesh, can handle free liquid surfaces that do not undergo topology changes. In a previous blog post, we discussed using field-based methods (level set and phase field) for modeling free surfaces.

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