An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Ten lectures on wavelets
Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
High order centered difference methods for the compressible Navier-Stokes equations
Journal of Computational Physics
Numerical experiments with the multiresolution scheme for the compressible Euler equations
Journal of Computational Physics
Summation by parts, projections, and stability. I
Mathematics of Computation
Numerical simulation of shock-cylinder interactions I.: resolution
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
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Spectral Simulation of Supersonic Reactive Flows
SIAM Journal on Numerical Analysis
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
Entropy splitting for high-order numerical simulation of compressible turbulence
Journal of Computational Physics
Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows
Journal of Computational Physics
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for High Order Methods
Journal of Scientific Computing
Journal of Computational Physics
Non-Linear Filtering and Limiting in High Order Methods for Ideal and Non-Ideal MHD
Journal of Scientific Computing
Singularity detection and processing with wavelets
IEEE Transactions on Information Theory - Part 2
Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation
Journal of Computational Physics
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Journal of Scientific Computing
Journal of Computational Physics
A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
Applied Numerical Mathematics
E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
Recent progress in the development of a class of low dissipative high order (fourth-order or higher) filter schemes for multiscale Navier-Stokes, and ideal and non-ideal magnetohydrodynamics (MHD) systems is described. The four main features of this class of schemes are: (a) multiresolution wavelet decomposition of the computed flow data as sensors for adaptive numerical dissipative control, (b) multistep filter to accommodate efficient application of different numerical dissipation models and different spatial high order base schemes, (c) a unique idea in solving the ideal conservative MHD system (a non-strictly hyperbolic conservation law) without having to deal with an incomplete eigensystem set while at the same time ensuring that correct shock speeds and locations are computed, and (d) minimization of the divergence of the magnetic field (@?.B) numerical error. By design, the flow sensors, different choice of high order base schemes and numerical dissipation models are stand-alone modules. A whole class of low dissipative high order schemes can be derived at ease, making the resulting computer software very flexible with widely applicable. Performance of multiscale and multiphysics test cases are illustrated with many levels of grid refinement and comparison with commonly used schemes in the literature.