Volume 18, Issue 4
Construction, Analysis and Application of Coupled Compact Difference Scheme in Computational Acoustics and Fluid Flow Problems

Jitenjaya Pradhan, Amit, Bikash Mahato, Satish D. Dhandole & Yogesh G. Bhumkar

Commun. Comput. Phys., 18 (2015), pp. 957-984.

Published online: 2018-04

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  • Abstract

In the present work, a new type of coupled compact difference scheme has been proposed for the solution of computational acoustics and flow problems. The proposed scheme evaluates the first, the second and the fourth derivative terms simultaneously. Derived compact difference scheme has a significant spectral resolution and a physical dispersion relation preserving (DRP) ability over a considerable wavenumber range when a fourth order four stage Runge-Kutta scheme is used for the time integration. Central stencil has been used for the present numerical scheme to evaluate spatial derivative terms. Derived scheme has the capability of adding numerical diffusion adaptively to attenuate spurious high wavenumber oscillations responsible for numerical instabilities. The DRP nature of the proposed scheme across a wider wavenumber range provides accurate results for the model wave equations as well as computational acoustic problems. In addition to the attractive feature of adaptive diffusion, present scheme also helps to control spurious reflections from the domain boundaries and is projected as an alternative to the perfectly matched layer (PML) technique.

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@Article{CiCP-18-957, author = {}, title = {Construction, Analysis and Application of Coupled Compact Difference Scheme in Computational Acoustics and Fluid Flow Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {4}, pages = {957--984}, abstract = {

In the present work, a new type of coupled compact difference scheme has been proposed for the solution of computational acoustics and flow problems. The proposed scheme evaluates the first, the second and the fourth derivative terms simultaneously. Derived compact difference scheme has a significant spectral resolution and a physical dispersion relation preserving (DRP) ability over a considerable wavenumber range when a fourth order four stage Runge-Kutta scheme is used for the time integration. Central stencil has been used for the present numerical scheme to evaluate spatial derivative terms. Derived scheme has the capability of adding numerical diffusion adaptively to attenuate spurious high wavenumber oscillations responsible for numerical instabilities. The DRP nature of the proposed scheme across a wider wavenumber range provides accurate results for the model wave equations as well as computational acoustic problems. In addition to the attractive feature of adaptive diffusion, present scheme also helps to control spurious reflections from the domain boundaries and is projected as an alternative to the perfectly matched layer (PML) technique.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.101214.250515s}, url = {http://global-sci.org/intro/article_detail/cicp/11057.html} }
TY - JOUR T1 - Construction, Analysis and Application of Coupled Compact Difference Scheme in Computational Acoustics and Fluid Flow Problems JO - Communications in Computational Physics VL - 4 SP - 957 EP - 984 PY - 2018 DA - 2018/04 SN - 18 DO - http://dor.org/10.4208/cicp.101214.250515s UR - https://global-sci.org/intro/article_detail/cicp/11057.html KW - AB -

In the present work, a new type of coupled compact difference scheme has been proposed for the solution of computational acoustics and flow problems. The proposed scheme evaluates the first, the second and the fourth derivative terms simultaneously. Derived compact difference scheme has a significant spectral resolution and a physical dispersion relation preserving (DRP) ability over a considerable wavenumber range when a fourth order four stage Runge-Kutta scheme is used for the time integration. Central stencil has been used for the present numerical scheme to evaluate spatial derivative terms. Derived scheme has the capability of adding numerical diffusion adaptively to attenuate spurious high wavenumber oscillations responsible for numerical instabilities. The DRP nature of the proposed scheme across a wider wavenumber range provides accurate results for the model wave equations as well as computational acoustic problems. In addition to the attractive feature of adaptive diffusion, present scheme also helps to control spurious reflections from the domain boundaries and is projected as an alternative to the perfectly matched layer (PML) technique.

Jitenjaya Pradhan, Amit, Bikash Mahato, Satish D. Dhandole & Yogesh G. Bhumkar. (2020). Construction, Analysis and Application of Coupled Compact Difference Scheme in Computational Acoustics and Fluid Flow Problems. Communications in Computational Physics. 18 (4). 957-984. doi:10.4208/cicp.101214.250515s
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