In physics, biology, chemistry and engineering many applications of simulation science involve Partial Differential Equations (PDEs) in complex and evolving geometries. These geometries often exhibit topological changes or strong deformations. Important examples are fluid-structure-interaction, flame propagation and two-phase flow problems. The accurate and efficient numerical solution of PDEs in these moving domains is a challenging task.
Different strategies exist to deal with evolving geometries, for instance Lagrangian methods where the computational mesh follows the motion of the geometry and Eulerian methods where the description of the geometry is separated from the computational mesh. In the last decade research on this topic has become a very active field. Especially methods using an Eulerian description – among them cut-cell methods and diffuse interface methods – have become very popular.
The minisymposium aims at presenting recent advancements in this field of numerical methods for PDEs in moving domains. Topics include the development of new numerical schemes, the application of such schemes to challenging engineering applications and their rigorous theoretical analysis.