Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Accurate upwind methods for the Euler equations
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
Uniformly Accurate Finite Difference Schemes for p-Refinement
SIAM Journal on Scientific Computing
Journal of Computational Physics
Conservative hybrid compact-WENO schemes for shock-turbulence interaction
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
Hi-index | 31.45 |
A systematic Fourier accuracy analysis is performed to examine the numerical diffusion inherent in a Godunov-type reconstruction, including both the reconstruction of the solution within each cell and the computation of the derivative terms of the reconstruction. It is found that compared with the more popular fifth-order polynomial fit of the interface values, a piecewise quadratic reconstruction of the solution with more accurate slope and curvature, especially those computed by compact difference schemes, is much less dissipative. Therefore, further given in the paper is a general framework to make a piecewise quadratic reconstruction free of numerical oscillations around the shocks. The improved accuracy and robustness of the resulting Godunov-type schemes for simulation of vortex-dominated flows are demonstrated with the numerical results of several carefully selected cases, including vortex convection and shock-vortex interaction.