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We present an immersed boundary projection method formulated in a body-fixedframe of reference for flow-structure interaction (FSI) problems involvingrigid bodies with complex geometries. The body-fixed formulation is aimed atmaximizing the accuracy of surface stresses on the FSI body (the target) onduring spatial and temporal discretization. The incompressible vorticityequations and Newton's equations of motion are coupled implicitly so that themethod remains stable for low solid-to-fluid mass ratios. The influence offictitious fluid inside the rigid bodies is considered and the spuriousoscillations in surface stresses are filtered to impose physically correctrigid body dynamics. Similar to many predecessors of the immersed boundaryprojection method, the resulting discrete system is solved efficiently using ablock-LU decomposition. We then validate the method with two-dimensional testproblems of a neutrally buoyant cylinder migrating in a planar Couette flow anda freely falling or rising cylindrical rigid body.

A target-fixed immersed-boundary formulation for rigid bodies interacting with fluid flow