The mesh within the fluid flow domain is deformed to account for the movement of the interface between the two fluids. The software perturbs the mesh vertices so they conform with the moving interface 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 equations for the mesh displacements (a Laplace, Winslow, or hyperelastic smoothing equation). 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 of the form:

The original, undeformed, mesh is referred to as the material frame (or reference frame) whilst 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.