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

Part of: Incompressible viscous fluids Partial differential equations, boundary value problems

Published online by Cambridge University Press:  15 October 2015

Jitenjaya Pradhan ,
Amit ,
Bikash Mahato ,
Satish D. Dhandole  and
Yogesh G. Bhumkar
Jitenjaya Pradhan
Affiliation:
School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India, 751013
Amit
Affiliation:
School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India, 751013
Bikash Mahato
Affiliation:
School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India, 751013
Satish D. Dhandole
Affiliation:
School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India, 751013
Yogesh G. Bhumkar*
Affiliation:
School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India, 751013
*
*Corresponding author. Email addresses: jp10@iitbbs.ac.in (J. Pradhan), am17@iitbbs.ac.in (Amit), bm12@iitbbs.ac.in (B. Mahato), satish@iitbbs.ac.in (S. D. Dhandole), bhumkar@iitbbs.ac.in (Y. G. Bhumkar)
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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.

Keywords

Coupled compact difference schemeDRP propertyadaptive numerical diffusioncomputational acousticPML technique

MSC classification

Secondary: 65N06: Finite difference methods 65N35: Spectral, collocation and related methods 76D05: Navier-Stokes equations 76D17: Viscous vortex flows

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 4 , October 2015 , pp. 957 - 984
Copyright
Copyright © Global-Science Press 2015 

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