The adjoint method is a powerful tool in high-fidelity aerodynamic shape optimization, providing an efficient means to compute derivatives of a target function with respect to various design variables. This paper delves into the discrete adjoint method. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables, specifically applied to a subsonic NACA0012 airfoil. The study conducts a qualitative evaluation using a designated test case, considering specified Mach number and Reynolds number values of 0.297 and 6,667 million, respectively. The Spalart-Allmaras turbulence model is employed to enhance computational cost efficiency. The results affirm the efficacy of the introduced tool, DAFoam, showcasing its ability to generate optimal geometries. The achieved performance optimization is evidenced by minimizing the drag coefficient value (C _D ) to an impressive 0.0131. While this research does not delve into the post-processing of sensitivity calculations, it acknowledges the potential for future investigations. The primary objective and novelty of this study is to provide the elementary background of the state of the art test case (NACA0012) within the subsonic regime, introducing the pioneer discrete adjoint aerodynamic optimization methodology (DAFoam) with the potential to explore its higher order capabilities in other aerodynamic related studies. Furthermore, it caters the educational needs of both graduate students and engineers in this exciting field. By presenting this cutting-edge methodology, it contributes to future advancements for the aerodynamicists in terms of optimal solutions.

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Respiratory infections such as COVID-19 can be spread by respiratory droplets with a diameter larger than 5–10 \(\upmu {\text{m}}\) or by droplet nuclei with a diameter smaller than 5 \(\upmu {\text{m}}\). Besides wearing masks, fresh air should be supplied frequently in closed rooms to avoid infections. Constructing and operating new isolation rooms require time, money, and maintenance cost, which are scarce in the current pandemic and in many communities. Displacement ventilation may be a feasible and secure option in temporary hospitals and other buildings to control the disease. This paper investigates using CFD simulations how displacement ventilation systems can deliver high air quality, and thermal comfort and minimize the risk of COVID-19 infection in enclosed spaces.