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
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Nonlinearly stable compact schemes for shock calculations
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
Journal of Computational Physics
Compact high-order accurate nonlinear schemes
Journal of Computational Physics
Journal of Computational Physics
A family of high order finite difference schemes with good spectral resolution
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Developing high-order weighted compact nonlinear schemes
Journal of Computational Physics
Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity: 381
Journal of Computational Physics
Conservative hybrid compact-WENO schemes for shock-turbulence interaction
Journal of Computational Physics
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces
Journal of Scientific Computing
A robust high-order compact method for large eddy simulation
Journal of Computational Physics
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
A staggered compact finite difference formulation for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Scientific Computing
Short Note: Effects of difference scheme type in high-order weighted compact nonlinear schemes
Journal of Computational Physics
A weighted-integral based scheme
Journal of Computational Physics
Journal of Computational Physics
A Speed-Up Strategy for Finite Volume WENO Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Generalized finite compact difference scheme for shock/complex flowfield interaction
Journal of Computational Physics
A balanced-force algorithm for two-phase flows
Journal of Computational Physics
Hi-index | 31.48 |
In this paper, we design a class of high order accurate nonlinear weighted compact schemes that are higher order extensions of the nonlinear weighted compact schemes proposed by Deng and Zhang [X. Deng, H. Zhang, Developing high-order weighted compact nonlinear schemes, J. Comput. Phys. 165 (2000) 22-44] and the weighted essentially non-oscillatory schemes of Jiang and Shu [G.-S. Jiang, C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228] and Balsara and Shu [D.S. Balsara, C.-W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys. 160 (2000) 405-452]. These nonlinear weighted compact schemes are proposed based on the cell-centered compact scheme of Lele [S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42]. Instead of performing the nonlinear interpolation on the conservative variables as in Deng and Zhang (2000), we propose to directly interpolate the flux on its stencil. Using the Lax-Friedrichs flux splitting and characteristic-wise projection, the resulted interpolation formulae are similar to those of the regular WENO schemes. Hence, the detailed analysis and even many pieces of the code can be directly copied from those of the regular WENO schemes. Through systematic test and comparison with the regular WENO schemes, we observe that the nonlinear weighted compact schemes have the same ability to capture strong discontinuities, while the resolution of short waves is improved and numerical dissipation is reduced.