Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Finite difference schemes for long-time integration
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
Journal of Computational Physics
Conservative hybrid compact-WENO schemes for shock-turbulence interaction
Journal of Computational Physics
Analysis of central and upwind compact schemes
Journal of Computational Physics
Navier-Stokes Solution by New Compact Scheme for Incompressible Flows
Journal of Scientific Computing
A new family of high-order compact upwind difference schemes with good spectral resolution
Journal of Computational Physics
Large Eddy Simulation of Combustion on Massively Parallel Machines
High Performance Computing for Computational Science - VECPAR 2008
Optimal time advancing dispersion relation preserving schemes
Journal of Computational Physics
A hybrid numerical simulation of isotropic compressible turbulence
Journal of Computational Physics
Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods
Journal of Computational Physics
Numerical and Physical Instabilities in Massively Parallel LES of Reacting Flows
Journal of Scientific Computing
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Compact difference schemes have been investigated for their ability to capture discontinuities. A new proposed scheme (Sengupta, Ganerwal and De (2003). J. Comp. Phys. 192(2), 677.) is compared with another from the literature Zhong (1998). J. Comp. Phys. 144, 622 that was developed for hypersonic transitional flows for their property related to spectral resolution and numerical stability. Solution of the linear convection equation is obtained that requires capturing discontinuities. We have also studied the performance of the new scheme in capturing discontinuous solution for the Burgers equation. A very simple but an effective method is proposed here in early diagnosis for evanescent discontinuities. At the discontinuity, we switch to a third order one-sided stencil, thereby retaining the high accuracy of solution. This produces solution with vastly reduced Gibbs' phenomenon of the solution. The essential causes behind Gibbs' phenomenon is also explained.