Scalable Nonlinear Compact Schemes

Ghosh, Debojyoti; Constantinescu, Emil M.; Brown, Jed

doi:10.2172/1171189

Cited by 4 publications

(5 citation statements)

References 66 publications

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“…The modified procedure to compute the flux derivative is applied to both the x and y dimensions; in the absence of gravitational forces along a particular dimension, for example g 0 ⇒ ϱy φy 1, it reduces to the standard flux computation given by Eqs. (47)(48)(49)(50). Three examples of the steady state [Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Equation (33) results in a tridiagonal system of equations that must be solved at each timeintegration step or stage; however, the additional expense is justified by the higher accuracy and spectral resolution of the compact scheme [31,33,34]. An efficient and scalable implementation of the CRWENO5 scheme was recently proposed in [35,50] and is used in this study.…”

Section: A Reconstructionmentioning

confidence: 99%

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Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

Ghosh

Constantinescu

2016

AIAA Journal

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Section: Discussionmentioning

confidence: 99%

Section: A Reconstructionmentioning

confidence: 99%

Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

Ghosh

Constantinescu

2016

AIAA Journal

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“…Equation (25) results in a tridiagonal system of equations that must be solved at each time-integration step or stage. An efficient and scalable implementation of the CRWENO5 scheme is proposed in 32,44 and used in this study. The solution of a hyperbolic system is composed of waves propagating at their characteristic speeds along their characteristic directions.…”

Section: A Reconstructionmentioning

confidence: 99%

Well-Balanced Formulation of Gravitational Source Terms for Conservative Finite-Difference Atmospheric Flow Solvers

Ghosh

Constantinescu

2015

7th AIAA Atmospheric and Space Environments Conference

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Numerical simulation of atmospheric flows requires high-resolution, nonoscillatory algorithms to accurately capture all length scales. In this paper, a conservative finite-difference algorithm is proposed that uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization. These schemes use solution-dependent interpolation stencils to yield high-order accurate nonoscillatory solutions to hyperbolic conservation laws. The Euler equations in their fundamental form (conservation of mass, momentum, and energy) are solved, thus avoiding approximations and simplifications. A well-balanced formulation of the finite-difference algorithm is proposed that preserves hydrostatically balanced equilibria to round-off errors. The algorithm is verified for benchmark atmospheric flow problems.

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“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php the number of processors) shown in Figure 6. A more detailed description of our implementation of this algorithm is provided in [21].…”

Section: Tridiagonal Solvermentioning

confidence: 99%

Efficient Implementation of Nonlinear Compact Schemes on Massively Parallel Platforms

Ghosh¹,

Constantinescu²,

Brown³

2015

SIAM J. Sci. Comput.

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Weighted nonlinear compact schemes are ideal for simulating compressible, turbulent flows because of their nonoscillatory nature and high spectral resolution. However, they require the solution to banded systems of equations at each time-integration step or stage. We focus on tridiagonal compact schemes in this paper. We propose an efficient implementation of such schemes on massively parallel computing platforms through an iterative substructuring algorithm to solve the tridiagonal system of equations. The key features of our implementation are that it does not introduce any parallelization-based approximations or errors and it involves minimal neighbor-toneighbor communications. We demonstrate the performance and scalability of our approach on the IBM Blue Gene/Q platform and show that the compact schemes are efficient and have performance comparable to that of standard noncompact finite-difference methods on large numbers of processors (∼ 500, 000) and small subdomain sizes (four points per dimension per processor). Introduction.Weighted, nonlinear compact schemes use the adaptive stencil selection of the weighted, essentially nonoscillatory (WENO) [29,46] schemes to yield essentially nonoscillatory solutions with high spectral resolution; they are thus ideal for simulating compressible, turbulent flows. Notable efforts include weighted compact nonlinear schemes (WCNSs) [13,14,52,50], hybrid compact-ENO/WENO schemes [6,5,38,42], weighted compact schemes (WCSs) [30,33,51], compact-reconstruction WENO (CRWENO) schemes [19,22,18,20], and finite-volume compact-WENO (FVCW) schemes [25]. These schemes show a significant improvement in the resolution of moderate-and small-length scales compared with the resolution of the standard WENO schemes of the same (or higher) order and were applied to the simulation of compressible, turbulent flows. WCNSs [14,52,50] result in a system of equations with a linear left-hand side that can be prefactored. This is a substantial advantage; however, the spectral resolution of these schemes is only marginally higher than that of the WENO scheme. The hybrid compact-WENO, WCS, CRWENO, and FVCW schemes have a significantly higher spectral resolution, as demonstrated by both linear and nonlinear spectral analyses [38,20]. They result in solution-dependent systems of equations at each time-integration step or stage. Tests have shown that on

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Scalable Nonlinear Compact Schemes

Abstract: For information about Argonne and its pioneering science and technology programs, see www.anl.gov.

Cited by 4 publications

References 66 publications

Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

Well-Balanced Formulation of Gravitational Source Terms for Conservative Finite-Difference Atmospheric Flow Solvers

Efficient Implementation of Nonlinear Compact Schemes on Massively Parallel Platforms

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