Principal Investigator Kenneth Kamrin
The finite-difference algorithm previously described for solid deformation bears a number of similarities to an explicit Navier-Stokes algorithm. Exploiting the likeness of these methods, one can write a simple code on a single fixed grid, where both fluid and solid phases coexist and interact. The interface between phases is described by a level-set function. Under a smeared treatment, the properties of the material change smoothly but rapidly from fluid to solid near the zero level-set. In the fluid phase, the material stress is derived from the finite-difference velocity gradient, and in the solid phase the reference map is used to compute the stress. Incompressibility of both phases can be upheld using an Eulerian splitting method (i.e. the projection method). Current work is underway to sharpen the treatment of the interface by employing an analogue of the Ghost Fluid Method for fluid/fluid interaction. Under this approach, a subgrid routine would be used to apply the appropriate jump conditions at the interface.