Doubly-Adaptive Artificial Compression Methods for Incompressible Flow

This report presents adaptive artificial compression methods in which the time-step and artificial compression parameter $\epsilon$ are independently adapted. The resulting algorithms are supported by analysis and numerical tests. The first and second-order methods are embedded. As a result, the computational, cognitive and space complexities of the adaptive $% \varepsilon ,k$ algorithms are negligibly greater than that of the simplest, first-order, constant $\epsilon ,$ constant $k$ artificial compression method.