Stability and Convergence of a Regularized Immersed Boundary Method under Dynamic Cartesian Refinement. Part III: Fluid-Driven Rigid-Body Motion
We study a conforming regularized immersed boundary discretization of the two-dimensional Eulerian Stokes–Newton system for one freely moving rigid body. Regularized interior moments complete the surface constraints used for prescribed motion. Positive excess mass and inertia define a fixed fluid–body kinetic inner product. A skew inertial correction is derived from the fictitious rigid interior; it has zero power but is necessary for the physical translational momentum equation. The method advances the body configuration with the preceding computed rigid velocity and then solves a linear…
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