University of Wisconsin–Madison

Fluid-Solid Interaction

Studying fluid-solid interaction (FSI) problems involves several aspects of scientific computing. Perhaps the more remarkable aspect is that in our group we use a Lagrangian-Lagrangian framework to tackle FSI problems. In this area, our technical effort is focused along three research thrusts:

1- Numerical method aspects: The Smoothed Particles Hydrodynamics (SPH) is a meshless, Lagrangian numerical method in computational fluid dynamics (CFD) that closely matches the Lagrangian framework generally used in classical solid mechanics and multi-body dynamics. We are interested in improving the accuracy, robustness and efficiency of SPH. On the accuracy and robustness fronts, we are investigating (i) higher-order accurate discretization methods, (ii) higher-order accurate boundary condition enforcement, (iii) projection-based methods and higher-order fractional time-splitting approaches, (iv) variable resolution approaches; and, (v) incorporating fast linear-system solvers. These research areas pursue from different directions a unified solution. Their common denominator is achieving a better solver in terms of spatial/ temporal accuracy inside the domain as well as at the fluid-solid boundary. (Milad Rakhsha, Zubin Lal, Lijing Yang)

2- HPC aspects: We are investigating ways to increase the speed of the CFD solver by making use of advanced computing techniques such as MPI, multi/many-core parallelism, GPU computing. Ongoing research focuses on mapping the FSI problem onto multiple GPUs to be able to scale up the problem size. (Milad Rakhsha, Justin Williams)

3- Applications: We are currently investigating applications in biomechanics simulating the micro-structure of biological tissues such as articular cartilage. The challenges we are facing include (i) coupling the fluid solver to different types of flexible bodies such as 1D beam elements, 2D shell elements, 3D brick elements, and rigid-bodies with arbitrary shapes; and, (ii) implicit coupling between the fluid and solid as opposed to explicit force-displacement coupling. (Milad Rakhsha)

Contributors: Milad Rakhsha, Zubin Lal, Lijing Yang, Justin Williams, Radu Serban and Dan Negrut