direct design of 3-d ducts, using the euler equations

in this work, a direct design approach for designing a surface shape (inverse design problem) has been developed, in which both the target surface pressure and the unknown nodal coordinates appear explicitly in the formulations. the final discretized form of the governing equations (unified formulation) can be used for both analysis and shape design problems. in this work, shape design problems in the context of steady, in viscid, and compressible flow, based on the three-dimensional euler equations, were directly solved to achieve a prescribed pressure along solid boundaries. the ausm+ scheme, in which the in viscid flux is split into convective and pressure components, was used to discretize the flux terms in the euler equations. conversion of the ausm+ formulations into a novel implicit form was performed in this study. the approaches for robustness, especially in the cases where there exist shock waves in the flow, were validated. two different models for the design of three-dimensional ducts were used and both of them worked properly. our test cases are applied in convergent-divergent nozzles in wind tunnels and s-shaped diffusers in the airplane inlet engines.