Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
High order filtering methods for approximating hyperbolic systems of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Family of spectral filters for discontinuous problems
Journal of Scientific Computing
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Uniform high-order spectral methods for one- and two-dimensional Euler equations
Journal of Computational Physics
Numerical study of pseudospectral methods in shock wave applications
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Uniformly high order accurate essentially non-oscillatory schemes, III
Journal of Computational Physics
Spectral Simulation of Supersonic Reactive Flows
SIAM Journal on Numerical Analysis
On the use of shock-capturing schemes for large-eddy simulation
Journal of Computational Physics
High-Order Central Schemes for Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing
Spectral methods in MatLab
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A class of approximate Riemann solvers and their relation to relaxation schemes
Journal of Computational Physics
Journal of Computational Physics
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Conjugate filter approach for solving Burgers' equation
Journal of Computational and Applied Mathematics
Journal of Computational Physics
High resolution conjugate filters for the simulation of flows
Journal of Computational Physics
Local spectral time splitting method for first- and second-order partial differential equations
Journal of Computational Physics
Mode Decomposition Evolution Equations
Journal of Scientific Computing
Hi-index | 31.45 |
A class of local spectral wavelet filters, discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC lowpass filters are adaptively implemented directly in the Fourier domain (i.e., windowed Fourier pseudospectral method), while a physical domain algorithm is also given to enable the treatment of some special boundary conditions. By adjusting the effective wavenumber region of the DSC filter, Gibbs oscillations can be removed effectively while the high resolution feature of the spectral method can be retained for a wide class of problems with various boundary conditions. The utility and effectiveness of the present approach are validated by extensive numerical experiments. The proposed method could operate at a resolution as high as only five points per wavelength (PPW) for the interaction of shocks and physical high frequency waves, which is some of the best for this class of problems. This high resolution, together with the low complexity of the fast Fourier transform (FFT), endows the proposed method considerable potential for solving large scale problems in hyperbolic conservation laws.