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A new compact scheme for parallel computing using domain decomposition

A new compact scheme for parallel computing using domain decomposition
A new compact scheme for parallel computing using domain decomposition
Direct numerical simulation (DNS) of complex flows require solving the problem on parallel machines using high accuracy schemes. Compact schemes provide very high spectral resolution, while satisfying the physical dispersion relation numerically. However, as shown here, compact schemes also display bias in the direction of convection – often producing numerical instability near the inflow and severely damping the solution, always near the outflow. This does not allow its use for parallel computing using domain decomposition and solving the problem in parallel in different sub-domains. To avoid this, in all reported parallel computations with compact schemes the full domain is treated integrally, while using parallel Thomas algorithm (PTA) or parallel diagonal dominant (PDD) algorithm in different processors with resultant latencies and inefficiencies. For domain decomposition methods using compact scheme in each sub-domain independently, a new class of compact schemes is proposed and specific strategies are developed to remove remaining problems of parallel computing. This is calibrated here for parallel computing by solving one-dimensional wave equation by domain decomposition method. We also provide the error norm with respect to the wavelength of the propagated wave-packet. Next, the advantage of the new compact scheme, on a parallel framework, has been shown by solving three-dimensional unsteady Navier–Stokes equations for flow past a cone-cylinder configuration at a Mach number of 4.

Additionally, a test case is conducted on the advection of a vortex for a subsonic case to provide an estimate for the error and parallel efficiency of the method using the proposed compact scheme in multiple processors.
compact schemes, domain decomposition method, parallel computing, DNS
0021-9991
654-677
Sengupta, T.K.
4e56c603-19be-4896-9671-2ea547b26e56
Dipankar, A.
e48e77dd-1bde-40ba-972b-741a8d54b36c
Kameswara Rao, A.
e5663e1e-5bed-426d-83df-1a5d9329d8c4
Sengupta, T.K.
4e56c603-19be-4896-9671-2ea547b26e56
Dipankar, A.
e48e77dd-1bde-40ba-972b-741a8d54b36c
Kameswara Rao, A.
e5663e1e-5bed-426d-83df-1a5d9329d8c4

Sengupta, T.K., Dipankar, A. and Kameswara Rao, A. (2007) A new compact scheme for parallel computing using domain decomposition. Journal of Computational Physics, 220 (2), 654-677. (doi:10.1016/j.jcp.2006.05.018).

Record type: Article

Abstract

Direct numerical simulation (DNS) of complex flows require solving the problem on parallel machines using high accuracy schemes. Compact schemes provide very high spectral resolution, while satisfying the physical dispersion relation numerically. However, as shown here, compact schemes also display bias in the direction of convection – often producing numerical instability near the inflow and severely damping the solution, always near the outflow. This does not allow its use for parallel computing using domain decomposition and solving the problem in parallel in different sub-domains. To avoid this, in all reported parallel computations with compact schemes the full domain is treated integrally, while using parallel Thomas algorithm (PTA) or parallel diagonal dominant (PDD) algorithm in different processors with resultant latencies and inefficiencies. For domain decomposition methods using compact scheme in each sub-domain independently, a new class of compact schemes is proposed and specific strategies are developed to remove remaining problems of parallel computing. This is calibrated here for parallel computing by solving one-dimensional wave equation by domain decomposition method. We also provide the error norm with respect to the wavelength of the propagated wave-packet. Next, the advantage of the new compact scheme, on a parallel framework, has been shown by solving three-dimensional unsteady Navier–Stokes equations for flow past a cone-cylinder configuration at a Mach number of 4.

Additionally, a test case is conducted on the advection of a vortex for a subsonic case to provide an estimate for the error and parallel efficiency of the method using the proposed compact scheme in multiple processors.

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More information

e-pub ahead of print date: 18 July 2006
Published date: 10 January 2007
Keywords: compact schemes, domain decomposition method, parallel computing, DNS
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 363619
URI: http://eprints.soton.ac.uk/id/eprint/363619
ISSN: 0021-9991
PURE UUID: fb11cb0d-33ef-4f57-b744-985148e41097

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Date deposited: 27 Mar 2014 16:29
Last modified: 14 Mar 2024 16:26

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Contributors

Author: T.K. Sengupta
Author: A. Dipankar
Author: A. Kameswara Rao

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