Continuous Space-Time Finite Element Simulations for Biomedical Flows with Large Boundary Motion and Time-Periodicity

Abstract

We present an axisymmetric continuous simplex space-time finite element method for incompressible fluid flow. Compared to conventional time-stepping methods, the space-time approach has several advantages. First, the motion of the domain is incorporated into the space-time geometry, allowing for large boundary motion without remeshing or projection of the solution. Second, the method allows for time-periodic solutions to be computed directly, without the need to simulate multiple cycles. Third, the space-time mesh can be partitioned in time as well as in space, which enables parallelism in time. The method is demonstrated on an intra-aortic balloon pump (IABP) in a rigid tube. The balloon inflation is modelled based on measured data, and includes a travelling wave along the balloon. The method is able to resolve complex flow features such as jets and recirculation zones. A refinement study shows convergence under temporal, spatial and combined space-time refinement. In weak scaling tests up to 960 ranks, the cost per solver iteration remains approximately constant, and partitioning the mesh into time slabs improves the convergence of the linear solver compared to partitions that cut through both space and time.