Construction, Analysis and Application of Coupled Compact Difference Scheme in Computational Acoustics and Fluid Flow Problems (Communications in Computational Physics, 2020)
In the present work, a new type of coupled compact difference scheme hasbeen proposed for the solution of computational acoustics and flow problems. Theproposed scheme evaluates the first, the second and the fourth derivative terms simultaneously.Derived compact difference scheme has a significant spectral resolution anda physical dispersion relation preserving (DRP) ability over a considerable wavenumberrange when a fourth order four stage Runge-Kutta scheme is used for the timeintegration. Central stencil has been used for the present numerical scheme to evaluatespatial derivative terms. Derived scheme has the capability of adding numericaldiffusion adaptively to attenuate spurious high wavenumber oscillations responsiblefor numerical instabilities. The DRP nature of the proposed scheme across a widerwavenumber range provides accurate results for the model wave equations as wellas computational acoustic problems. In addition to the attractive feature of adaptivediffusion, present scheme also helps to control spurious reflections from the domainboundaries and is projected as an alternative to the perfectly matched layer (PML)technique.