Newton-Krylov Algorithm for Aerodynamic Design Using the Navier-Stokes Equations

By M. Nemec, David W. Zingg. 2002

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An adaptive geometry parametrization for aerodynamic shape optimization (2014, methodology): “For a two-dimensional airfoil, an efficient NewtonKrylov flow solver was developed by Nemec and Zingg (2002) to solve the Reynoldsaveraged Navier-Stokes equations with the Spalart-Allmaras turbulence model.”
Effective adjoint approaches for computational fluid dynamics (2019, methodology): “Four numerical algorithms are implemented to converge the residual equations including a Runge–Kutta (RK) algorithm, a diagonalized-diagonally-dominant alternating direction implicit (D3ADI) algorithm [143], an approximate Newton–Krylov (ANK) algorithm [144], and a full Newton–Krylov (NK) algorithm ”
Multimodality and Global Optimization in Aerodynamic Design (2013, methodology): “The discretized equations are solved using a Newton-Krylov approach [1].”
Jacobian-free Newton-Krylov methods: a survey of approaches and applications (2004, background): “Other JFNK applications in compressible flow include [9,63,80,134,147].”
Three-Dimensional Large-Scale Aerodynamic Shape Optimization Based on Shape Calculus (2013, background): “Although this approach is known to be applicable and well working, one is often forced into finite differencing for these terms [2,3].”