A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A study of numerical methods for hyperbolic conservation laws with stiff source terms
Journal of Computational Physics
Ten lectures on wavelets
Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Wavelet analysis of 2D turbulent fields
Physica D
Numerical experiments with the multiresolution scheme for the compressible Euler equations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Designing an efficient solution strategy for fluid flows
Journal of Computational Physics
Low-dissipative high-order shock-capturing methods using characteristic-based filters
Journal of Computational Physics
Entropy splitting and numerical dissipation
Journal of Computational Physics
Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-Capturing Methods
Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence
Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence
Non-Linear Filtering and Limiting in High Order Methods for Ideal and Non-Ideal MHD
Journal of Scientific Computing
On the adaptive control of a class of SISO dynamic hybrid systems
Applied Numerical Mathematics
Journal of Computational Physics
Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
Journal of Computational Physics
A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows
Journal of Computational Physics
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Journal of Scientific Computing
On the adaptive control of a class of SISO dynamic hybrid systems
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
A shock-detecting sensor for filtering of high-order compact finite difference schemes
Journal of Computational Physics
High Order Finite Difference and Finite Volume Methods for Advection on the Sphere
Journal of Scientific Computing
Journal of Scientific Computing
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The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham, and Djomehri [25] aimed at minimizing numerical dissipations for high speed compressible viscous flows 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 artificial compression method (ACM) of Harten [4] but utilize it in an entirely different 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 dependence, 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 extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all 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 and Zhong [14]) used by Gerritsen and Olsson [3] 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 [5] by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen 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 independent and can be stand-alone options for numerical algorithms other than the Yee et al. scheme.