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
Finite difference schemes for long-time integration
Journal of Computational Physics
A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
Journal of Computational Physics
Optimized compact-difference-based finite-volume schemes for linear wave phenomena
Journal of Computational Physics
Journal of Computational Physics
Compact implicit MacCormack-type schemes with high accuracy
Journal of Computational Physics
A Comparative Study of Time Advancement Methods for Solving Navier–Stokes Equations
Journal of Scientific Computing
High Accuracy Compact Schemes and Gibbs' Phenomenon
Journal of Scientific Computing
Navier-Stokes Solution by New Compact Scheme for Incompressible Flows
Journal of Scientific Computing
High Accuracy Schemes for DNS and Acoustics
Journal of Scientific Computing
Analysis of a new high resolution upwind compact scheme
Journal of Computational Physics
A new family of high-order compact upwind difference schemes with good spectral resolution
Journal of Computational Physics
Journal of Scientific Computing
A new combined stable and dispersion relation preserving compact scheme for non-periodic problems
Journal of Computational Physics
Design and analysis of a new filter for LES and DES
Computers and Structures
Journal of Computational Physics
Journal of Computational Physics
Optimal time advancing dispersion relation preserving schemes
Journal of Computational Physics
Curvilinear finite-volume schemes using high-order compact interpolation
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
A linear focusing mechanism for dispersive and non-dispersive wave problems
Journal of Computational Physics
Journal of Computational Physics
A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square
Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
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Central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space, numerical stability and dispersion relation preservation. A von Neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously. This allows one to evaluate various boundary closures and their effects on the domain interior. The same method can be used for stability analysis performed for the semi-discrete initial boundary value problems (IBVP). This analysis tells one about the stability for every resolved length scale. Some well-known compact schemes that were found to be G-K-S and time stable are shown here to be unstable for selective length scales by this analysis. This is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming. To demonstrate the asymptotic stability of the resultant schemes, numerical solution of the wave equation is compared with analytical solution. Furthermore, some of these schemes are used to solve two-dimensional Navier-Stokes equation and a computational acoustic problem to check their ability to solve problems for long time. It is found that those schemes, that were found unstable for the wave equation, are unsuitable for solving incompressible Navier-Stokes equation. In contrast, the proposed compact schemes with improved boundary closure and an explicit higher-order upwind scheme produced correct results. The numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite DRP property.