The aim of this study is to implement Newton-GMRES method into supersonic flows as an alternative to Newton method which is a reliable and efficient solver. The flow analysis is based on the three dimensional Euler equations. The objective of this study is compare the performances of Newton and Newton-GMRES methods in a 3-D nozzle design. The Jacobian matrix needed for Newton method is evaluated analytically. Newton-GMRES method is a matrix free solution technique hence it does not require the Jacobian matrix evaluation. A gradient based method is used for numerical optimization. Sensitivities are evaluated by using adjoint method. Design optimization is conducted by Newton's method.
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