Sjögreen and Yee construct an adaptive numerical dissipation control that is an improvement over Yee et al.’s artificial compression method (ACM) sensor.

The new sensors, with improved detection properties, are derived from a multi-resolution wavelet-based analysis, and require a slightly higher operation count than the ACM sensor. There are a variety of wavelets to choose from, depending on the flow feature. Developing the best suited adaptive numerical dissipation/filter control for a particular flow speed and flow structure might involve the switching on and off, and/or blending, of different filters, by automatic sensors. This method, however, is superior to the tuning of parameters and the use of the same filter, and especially to using the same amount of numerical dissipation throughout the entire domain.

The authors consider two types of nonorthogonal wavelet basis functions for their two-dimensional compressible Euler and Navier-Stokes numerical experiments. The first is similar to the B-spline wavelet, and the second is a modification of the multi-resolution method of Harten as a redundant multi-resolution wavelet. The B-spline wavelet sensor requires slightly more arithmetic operations than the redundant form of Harten wavelet sensor, and a wider grid stencil.

From their numerical experiments, it appears that the redundant form of the Harten wavelet sensor exhibits slightly more accurate results than the B-spline wavelet sensor.