The evolution of Optimum Shape Design has gone through many phases and currently is in the process of transition from baseline and intuitive designs to the combination of computer modeling and applied optimization algorithms, which in turn require automated and more robust CFD solvers. In this work the use of Brinkman Volume Penalization is explored for shape and topology optimization. As the implementation is conceptually the same for both optimization methods, with considerably more degrees of freedom during topology optimization, this work elaborates on shape optimization. While the feasibility of Brinkman Volume Penalization with shape optimization is shown only for incompressible cases, the use of this method is also intended for compressible flows. Furthermore, the efficient implementation of Brinkman Volume Penalization necessitates the addition of a mesh refinement technique, which is incorporated through the Adaptive Wavelet Collocation Method. Both compressible and incompressible regimes are investigated, however due to special issues that arise with wave reflections in compressible flows, the use of Multidimensional Navier-Stokes Characteristic Boundary Conditions are explored as well.
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