Abstract
In this article, we develop a general formulation of the continuous sensitivity equation method that accounts for a complex parameter dependence in both flow variables and physical fluid properties (such as viscosity, thermal conductivity, etc.). This formulation unifies the treatment of shape sensitivities and value sensitivities. The result leads to the development of software that is suitable for a wide range of problems. In addition to details of an implementation within an existing adaptive finite-element program, we perform a careful verification study as well as demonstrate the flexibility of the software by computing cost function gradients for an optimization algorithm.
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