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 epsilon, k algorithms are negligibly greater than that of the simplest, first-order, constant epsilon, constant k artificial compression method.