Non-body-fitted fluid-structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation

摘要: Abstract Immersed boundary (IB) methods deal with incompressible visco-elastic solids interacting viscous fluids. A long-standing issue of IB is the challenge accurately imposing incompressibility constraint at discrete level. We present divergence-conforming immersed (DCIB) method to tackle this issue. The DCIB leads completely negligible errors Eulerian level and various orders magnitude increased accuracy Lagrangian compared other methods. Furthermore, second-order convergence error obtained as discretization refined. In method, velocity–pressure pair discretized using B-splines, leading inf–sup stable pointwise divergence-free solutions. displacement non-uniform rational which enables robustly handle large mesh distortions. data transfer needed between descriptions performed quadrature same spline basis functions that define computational meshes. This conduces a fully variational formulation, sharp treatment fluid–solid interface, 0.5 increase in rate velocity measured L 2 norm comparison Dirac delta for transfer. By combining generalized-α block-iterative solution strategy, results fully-implicit discretization, take larger time steps. Various two- three-dimensional problems are solved show all aforementioned properties along mesh-independence studies, verification numerical by literature, measurement rates.