The mesh within the free surface domain is deformed to account for the movement of the free surface. This mesh movement is accomplished using a moving mesh approach. The software perturbs the mesh nodes so that they conform with the free surface and with other moving or stationary boundaries in the model. The boundary displacement is propagated throughout the domain to obtain a smooth mesh deformation everywhere. This is done by solving PDEs for the mesh displacements, using the movement of the free surface as boundary condition. Taking two dimensions as an example, a location in the deformed mesh with coordinates (x, y) can be related to its coordinates in the original undeformed mesh (X, Y) by a function on the form:

The original, undeformed, mesh is referred to as the material frame (or reference frame), while the deformed mesh is called the spatial frame. COMSOL Multiphysics also defines geometry and mesh frames, which are coincident with the material frame for this physics interface.