A Continuous Adjoint Method for Viscous Flows at All Speeds

초록

A preconditioned continuous adjoint approach for the Navier-Stokes equations is presented, and its convergence characteristics are assessed. To enhance the residual convergence rate of the adjoint equations at low Mach numbers, the Weiss and Smith’s preconditioning matrix is used. The preconditioned adjoint equations are derived, and directly discretized without any assumptions on the preconditioning matrix. The dissipation of the numerical flux is modified to scale the eigenvalues at the low Mach numbers. Flows of a Quasi 1-D nozzle, an NACA0012 airfoil, and a circular cylinder are considered to verify the accuracy and convergence characteristics of the preconditioned adjoint equations.