Time dependent boundary conditions for hyperbolic systems
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
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Optimized compact-difference-based finite-volume schemes for linear wave phenomena
Journal of Computational Physics
Prefactored small-stencil compact schemes
Journal of Computational Physics
The spatial resolution properties of composite compact finite differencing
Journal of Computational Physics
Optimised boundary compact finite difference schemes for computational aeroacoustics
Journal of Computational Physics
Finite difference approximations of first derivatives for three-dimensional grid singularities
Journal of Computational Physics
Multidimensional optimization of finite difference schemes for Computational Aeroacoustics
Journal of Computational Physics
A family of dynamic finite difference schemes for large-eddy simulation
Journal of Computational Physics
Curvilinear finite-volume schemes using high-order compact interpolation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Optimized explicit finite-difference schemes for spatial derivatives using maximum norm
Journal of Computational Physics
Hi-index | 31.51 |
The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and dissipation errors. In this paper we describe a strategy for developing high-order accurate prefactored compact schemes, requiring very small stencil support. These schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes. The prefactorization strategy splits the central implicit schemes into forward and backward biased operators. Using Fourier analysis, we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components. This ensures that when the forward and backward stencils are added, the original central compact scheme is recovered. To extend the resolution characteristic of the schemes, an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh. The resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth- and eighth-order compact schemes making them more suitable for high-resolution numerical simulations in gas dynamics and computational aeroacoustics. The efficiency, accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems.