The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 till 10:00 in the room K3. The talk will be given by Peter Kottman. Please see the details below.
Speaker: Peter Kottman
Title: On Pitfalls of Using Diffuse Interface Methods for Problems Involving Flow across an Interface
Abstract: Problems with mass flux across non-material interfaces (e.g. phase interfaces) occur in numerous applications of continuum mechanics, such as geophysics, material science, and biology. While from a physical point of view these problems are viewed as systems of governing equations solved on subdomains with jump conditions prescribed at the surface representing the interface, the numerical solutions of the problems usually treat the interface as a layer of finite thickness, where quantities change rapidly but smoothly, and solve the governing equations in the entire domain. This diffuse interface approach is effective and widely used. On the basis of heuristic results from the field of geodynamics, we demonstrate that these two points of view are inconsistent, provide a framework for a rigorous study of sharp limits the diffuse interface solutions in the form of the Colombeau algebra, and discuss the issues arising in efforts to generalize this idea for more complicated models.