Volume 24, Issue 2
Joint Optimization of the Spatial and the Temporal Discretization Scheme for Accurate Computation of Acoustic Problems.

Jitenjaya Pradhan, Saksham Jindal, Bikash Mahato & Yogesh G. Bhumkar

Commun. Comput. Phys., 24 (2018), pp. 408-434.

Published online: 2018-08

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  • Abstract

Here, a physical dispersion relation preserving (DRP) scheme has been developed by combined optimization of the spatial and the multi-stage temporal discretization scheme to solve acoustics problems accurately. The coupled compact difference scheme (CCS) has been spectrally optimized (OCCS) for accurate evaluation of the spatial derivative terms. Next, the combination of the OCCS scheme and the five stage Runge-Kutta time integration (ORK5) scheme has been optimized to reduce numerical diffusion and dispersion error significantly. Proposed OCCS−ORK5 scheme provides accurate solutions at considerably higher CFL number. In addition, ORK5 time integration scheme consists of low storage formulation and requires less memory as compared to the traditional Runge-Kutta schemes. Solutions of the model problems involving propagation, reflection and diffraction of acoustic waves have been obtained to demonstrate the accuracy of the developed scheme and its applicability to solve complex problems.

  • Keywords

DRP scheme, compact difference scheme, computational acoustics, barrier, wave propagation.

  • AMS Subject Headings

65N06, 65N35, 76D05, 35L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-408, author = {}, title = {Joint Optimization of the Spatial and the Temporal Discretization Scheme for Accurate Computation of Acoustic Problems.}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {2}, pages = {408--434}, abstract = {

Here, a physical dispersion relation preserving (DRP) scheme has been developed by combined optimization of the spatial and the multi-stage temporal discretization scheme to solve acoustics problems accurately. The coupled compact difference scheme (CCS) has been spectrally optimized (OCCS) for accurate evaluation of the spatial derivative terms. Next, the combination of the OCCS scheme and the five stage Runge-Kutta time integration (ORK5) scheme has been optimized to reduce numerical diffusion and dispersion error significantly. Proposed OCCS−ORK5 scheme provides accurate solutions at considerably higher CFL number. In addition, ORK5 time integration scheme consists of low storage formulation and requires less memory as compared to the traditional Runge-Kutta schemes. Solutions of the model problems involving propagation, reflection and diffraction of acoustic waves have been obtained to demonstrate the accuracy of the developed scheme and its applicability to solve complex problems.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0191}, url = {http://global-sci.org/intro/article_detail/cicp/12246.html} }
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