Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for High Order Methods

“…This might involve the use of more than one type of wavelet and filters (cf. Yee et al, Yee and Sjögreen, and Sjögreen and Yee [20,26,27] for some discussion). Regardless of the amount of information on the Lipschitz exponent used to design the wavelet sensor, the sensor is not really parameter free.…”

“…It is especially important for long-time integrations, and enables a norm estimate of the solution. It has been reported [20] that the onset of non-linear instability can be delayed for an order of magnitude in the time scale, by using entropy splitting. If entropy splitting is used, the base scheme is applied to the split form of the inviscid flux derivatives.…”

“…Developing the best suited wavelets that can characterize all of the flow features might involve the switching or blending of more than one mother wavelet k(x) and scaling function f(x), especially if one needs to distinguish turbulent fluctuations from shock/shear and/or spurious high frequency oscillations. See [20,26,27] for some discussion. The mother wavelet function used in [3] and described in detail in [14] meets some of our requirements.…”

“…In addition, this dual purpose adaptive method is scheme independent and can be a stand-alone option for a variety of schemes other than what is discussed here. A procedure which adapts the appropriate type of filters for the particular flow structures for long time integrations is proposed and studied in Yee and Sjögreen [26] and Sjögreen and Yee [20]. This adaptive detection/filter approach is able to distinguish shock/shear, turbulent fluctuation and spurious high frequency oscillation, and is valuable for high speed turbulence and combustion simulations.…”

“…This adaptive detection/filter approach is able to distinguish shock/shear, turbulent fluctuation and spurious high frequency oscillation, and is valuable for high speed turbulence and combustion simulations. For numerical experiments in [20], it appears that more than one type of filter is needed for this type of applications. Section 2 reviews the Yee et al [25] high order scheme employing ACM as a numerical dissipation sensor.…”