Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
A note on the effect of artificial viscosity on solutions of conservation
Applied Numerical Mathematics
Designing an efficient solution strategy for fluid flows
Journal of Computational Physics
Multiphase dynamics in arbitrary geometries on fixed Cartesian grids
Journal of Computational Physics
A 2D analysis of the influence of artificial viscosity terms on solutions of the Euler equations
Journal of Computational Physics
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Uniformly Accurate Finite Difference Schemes for p-Refinement
SIAM Journal on Scientific Computing
Conservative smoothing on an adaptive quadrilateral grid
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
A Cartesian grid finite-volume method for the advection-diffusion equation in irregular geometries
Journal of Computational Physics
A fixed-grid, sharp-interface method for bubble dynamics and phase change
Journal of Computational Physics
Journal of Computational Physics
Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity: 381
Journal of Computational Physics
On analogy and dissimilarity of dependence of stability on several parameters in flow simulations
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
Finite difference time domain dispersion reduction schemes
Journal of Computational Physics
Compact finite volume schemes on boundary-fitted grids
Journal of Computational Physics
Journal of Computational Physics
Curvilinear finite-volume schemes using high-order compact interpolation
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.