Dissipation-based continuation (DBC) is a form of globalization suitable for inexact-Newton flow solvers and a robust alternative to pseudo-transient continuation. DBC uses a sequence of modified equations, each one a perturbation of the previous one. The modified equations are obtained by adding numerical dissipation to the discrete governing equations, with a continuation parameter controlling the magnitude of the dissipation. DBC begins with significant numerical dissipation, which increases the basin of attraction for Newton's method to converge using the free-stream as the initial iterate. The continuation parameter is then reduced, and the next modified equation in the sequence is inexactly solved using the previous solution as the initial iterate. The process is repeated until the dissipation is removed, the original equations are recovered, and the desired solution is obtained. We describe DBC in detail and its implementation in a multi-block finite-difference discretization. DBC is benchmarked against pseudo-transient continuation on a number of numerical experiments to quantify its robustness and efficiency, and it is shown to be generally superior.
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