The fixed-mesh ALE approach for the numerical approximation of flows in moving domains
In this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization, and therefore the formulation to be presented falls within the category of fixed-grid methods. Even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed-grid method, our approach can be applied together with any technique to impose approximately boundary conditions, although we also describe the one we actually favor. Our main concern is to properly account for the advection of information as the domain boundary evolves. To achieve this, we use an arbitrary LagrangianEulerian framework, the distinctive feature being that at each time step results are projected onto a fixed, background mesh, that is where the problem is actually solved.
ale approximate boundary conditions immersed boundary methods transmission conditions level set