Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Finite-difference schemes on regular triangular grids
Journal of Computational Physics
Journal of Computational Physics
Several new numerical methods for compressible shear-layer simulations
Applied Numerical Mathematics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Journal of Computational Physics
A family of high order finite difference schemes with good spectral resolution
Journal of Computational Physics
Compact implicit MacCormack-type schemes with high accuracy
Journal of Computational Physics
Prefactored small-stencil compact schemes
Journal of Computational Physics
Optimized prefactored compact schemes
Journal of Computational Physics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Journal of Computational Physics
Comparison of Taylor finite difference and window finite difference and their application in FDTD
Journal of Computational and Applied Mathematics
Analysis of a new high resolution upwind compact scheme
Journal of Computational Physics
Conditionally Stable Multidimensional Schemes for Advective Equations
Journal of Scientific Computing
Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods
Journal of Computational Physics
Spectral properties of high-order residual-based compact schemes for unsteady compressible flows
Journal of Computational Physics
Hi-index | 31.46 |
Because of the long propagation distances, Computational Aeroacoustics schemes must propagate the waves at the correct wave speeds and lower the isotropy error as much as possible. The spatial differencing schemes are most frequently analyzed and optimized for one-dimensional test cases. Therefore, in multidimensional problems such optimized schemes may not have isotropic behavior. In this work, optimized finite difference schemes for multidimensional Computational Aeroacoustics are derived which are designed to have improved isotropy compared to existing schemes. The derivation is performed based on both Taylor series expansion and Fourier analysis. Various explicit centered finite difference schemes and the associated boundary stencils have been derived and analyzed. The isotropy corrector factor, a parameter of the schemes, can be determined by minimizing the integrated error between the phase or group velocities on different spatial directions. The order of accuracy of the optimized schemes is the same as that of the classical schemes, the advantage being in reducing the isotropy error. The present schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates. The optimized schemes are tested by solving various multidimensional problems of Aeroacoustics.