The Reference Map Technique: A Fully Eulerian Numerical Method for Fluid-structure Interactions
Yuexia Lin, Harvard University
Conventional computational methods often create a dilemma for fluid-structure interaction (FSI) problems. Typically, solids are simulated using a Lagrangian approach with a grid that moves with the material, whereas fluids are simulated using an Eulerian approach on a fixed spatial grid. This difference in the choice of methods is in part due to the differences in the stress responses in solids and fluids. In general, solid stress arises from the total deformation, whereas fluid stress is related to the deformation rate. FSI methods that use both Lagrangian and Eulerian approaches require some type of interfacial coupling between the two perspectives, quickly increasing the complexity of the methods.
We present a fully Eulerian method by introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid. Using the reference map technique, the interfacial coupling problem is highly simplified. The method is particularly well-suited for simulating soft, highly deformable materials and many-body contact problems. We demonstrate the method by using a three-dimensional, parallel implementation to simulate immersed flexible objects.
Abstract Author(s): Yuexia Lin, Nicholas Derr, Ken Kamrin, Chris Rycroft