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The purpose of this paper is to present applications of the topological optimization method dealing with fluid dynamic problems in two- and three dimensions. The main goal is to develop a tool package able to optimize topology in realistic devices (e.g. inlet manifolds) considering the non-linear terms on Navier–Stokes equations.

Using an in-house Fortran code, a Galerkin stabilized finite element is implemented method to solve the three equation systems necessary for the topological optimization method: the direct problem, adjoint problem and topological derivative. The authors address the non-linearity in the equations using an iterative method. Different techniques to create holes into a two-dimensional discrete domain are analyzed.

One technique to create holes produces more accurate and robust results. The authors present several examples of applications in two- and three-dimensional components, which highlight the potential of this method in the optimization of fluid components.

The authors contribute to the methodology and design in engineering.

Engineering fluid flow systems are used in many different industrial applications, e.g. oil flow in pipes; air flow around an airplane wing; sailing submarines; blood flow in synthetic arteries; and thermal and fissure spreading problems. The aim of this work is to create an effective design tool for obtaining efficient engineering structures and devices.

The authors contribute by creating an application of the method to design a tridimensional realistic device, which can be essayed experimentally. Particularly, the authors apply the design tool to an inlet manifold.