Nonlinear structural mechanics and free surface fluid mechanical phenomena are usually described by means of PDEs on unknown domains. Analytical methods such as asymptotic or stability analysis rely on perturbation techniques including the geometry. We have developed a method to carry out this cumbersome and tedious task in a systematic and universal manner, which overcomes the drawbacks of existing methods.
If you want to learn more about this method, you can find more details in our manuscript. A revised version is in progress. For an application of this method, go to the section on inertial migration.