Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computations
Björn Sjögreen, H. C. Yee · NASA Technical Reports Server (NASA) · 2001
The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham and Djomehri (1999) aimed at minimizing nu- merical dissipations for high speed compressible viscous ows containing shocks, shears and turbulence. To detect non smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artifcial compression method (ACM) of Harten (1978) but utilize it in an entirely diferent context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem depen- dence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch off the extranumerical dissipation outside shock lay- ers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability atall parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet (Mallat & Zhong 1992 ) used by Gerritsen and Olsson (1996) in an adaptive mesh refinement method, to determine regions where refinement should be done. The other is the modification of the multiresolution method of Harten (1995) by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent ofacho- sen physical quantity (or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these sensors are scheme inde- pendent and can be stand alone options for numerical algorithm other than the Yee et al. scheme.