Adaptive artificial compression methods independently adapt time-step and ε, embed first- and second-order methods, and have computational complexity similar to the basic constant-parameter version.
Shen , On error estimates of the projection method for the Navier-S tokes equations: second- order schemes, Math
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Doubly-Adaptive Artificial Compression Methods for Incompressible Flow
Adaptive artificial compression methods independently adapt time-step and ε, embed first- and second-order methods, and have computational complexity similar to the basic constant-parameter version.