We present the first formulation of topology optimisation for transient compressible flow. We discretise the equations with a discontinuous Galerkin method, due to its similarity to the popular finite volume method, and its capacity to model discontinuities in the flow. The discretised topology optimisation problem is solved through an integer linear programming algorithm. We present numerical examples that optimise the shape of a nozzle and a pipe joint in the presence of a time-varying inflow.
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Alonso et al. (2025) studied this question.
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