Abstract This work designs fluid structures that interact with steady Navier–Stokes flows under a Brinkman body force by setting the density at the control points of an NURBS mesh. It approximates the velocity using standard NURBS basis functions and the pressure with one order of accuracy lower. Such a so-called Taylor–Hood pair selection ensures inf-sup stability while providing a smooth, CAD-consistent geometry that enables seamless integration between design and fabrication models. The proposed method employs an optimality-criteria algorithm that utilizes adjoint-based sensitivities to update design variables, along with a bisection method to meet the volume constraint. Numerical benchmarks, including diffuser, dual-inlet/dual-outlet, flow-reversal, and a 3D bend-pipe, confirm that the proposed method exhibits robust convergence over a range of Reynolds numbers and consistently generates smooth, near-binary designs with sharp interfaces and reduced numerical artefacts, achieving lower objective values without artificially altering sensitivities through filtering. These findings demonstrate that NURBS-based isogeometric analysis is an effective method for fluid topology optimization and shows strong correlation with traditional finite-element techniques.
Li et al. (Wed,) studied this question.