Continuous Adjoint Sensitivities for Optimization with General Cost Functionals on Unstructured Meshes

摘要: A continuous adjoint approach is developed to obtain the sensitivity derivatives for Euler equations. The completederivationofthecostateequations andtheirtransversality (boundary)conditionsarepresented. Both state and costate equations are second-order e nite volume discretized unstructured meshes, they coupled with a constrained optimization algorithm. Also integrated into overall methodology geometry parameterization method shape optimization, dynamic mesh evolution consequent adaptations. For proof of concept, three transonic airfoil problems presented. This accepts general cost functionals, which not necessarily functions pressure only. It also shown that switch natural coordinate system in conjunction reduction governing equation control surface results integrals only function tangential derivativesof variables. Thisapproach eliminates need fornormal derivativecomputations can be erroneous.