A hybrid adjoint approach

The book explores adjoint-based techniques that efficiently assess the sensitivity of simulation objective functions to various parameters, requiring only an additional flow calculation. It discusses the existing discrete and continuous methods for deriving numerically discretized adjoint equations, highlighting their respective strengths and weaknesses in complexity and computational cost. A novel hybrid approach is introduced, merging elements from both methods to enhance the efficiency of mathematical derivation, reduce computational demands, and improve the overall quality of adjoint solutions.