Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Higher order Godunov methods for general systems of hyperbolic conservation laws
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Compact high-order accurate nonlinear schemes
Journal of Computational Physics
Low-dissipative high-order shock-capturing methods using characteristic-based filters
Journal of Computational Physics
A spectral vanishing viscosity method for large-eddy simulations
Journal of Computational Physics
Developing high-order weighted compact nonlinear schemes
Journal of Computational Physics
Low-storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations
Low-storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations
Journal of Computational Physics
An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes
Journal of Computational Physics
Journal of Computational Physics
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
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.50 |
A spectral-like viscosity is proposed for centered differencing schemes to help stabilize numerical solutions and reduce oscillations near discontinuities. Errors introduced by the added dissipation can be made arbitrarily small by adjusting the power of the derivative in the viscosity term. The high-wavenumber viscosity is combined with a 10th- order compact scheme to produce an accurate and efficient shock-capturing method. The new scheme compares favorably with other shock-capturing algorithms.