TY - JOUR

T1 - The use of domain decomposition in accelerating the convergence of quasihyperbolic systems

AU - Parent, Bernard

AU - Sislian, Jean P.

N1 - Funding Information:
This work has been supported by the Natural Sciences and Engineering Research Council (NSERC). The first author would like to thank all writers of free software for donating the compilers, typesetting software, vector drawing programs, and so forth, that were used in this study. The help of G. Fusina in proofreading the manuscript is greatly appreciated. The authors are also grateful for the constructive criticisms of the reviewers.

PY - 2002

Y1 - 2002

N2 - This paper proposes an alternate form of the active-domain method [K. Nakahashi and E. Saitoh, AIAA J. 35, 1280 (1997)] that is applicable to streamwise separated flows. Named the "marching window," the algorithm consists of performing pseudo-time iterations on a minimal width subdomain composed of a sequence of cross-stream planes of nodes. The upstream boundary of the subdomain is positioned such that all nodes upstream exhibit a residual smaller than the user-specified convergence threshold. The advancement of the downstream boundary follows the advancement of the upstream boundary, except in zones of significant streamwise ellipticity, where a streamwise ellipticity sensor ensures its continuous progress. Compared to the standard pseudo-time-marching approach, the marching window decreases the work required for convergence by up to 24 times for flows with little streamwise ellipticity and by up to eight times for flows with large streamwise separated regions. Storage is reduced by up to six times by not allocating memory to the nodes not included in the computational subdomain. The marching window satisfies the same convergence criterion as the standard pseudo-time-stepping methods, hence resulting in the same converged solution within the tolerance of the user-specified convergence threshold. The algorithm is not restricted to a discretization stencil and pseudo-time-stepping scheme in particular and is used here with the Yee-Roe scheme and block-implicit approximate factorization solving the Favre-averaged Navier-Stokes (FANS) equations closed by the Wilcox kω turbulence model. The eigenstructure of the FANS equations is also presented.

AB - This paper proposes an alternate form of the active-domain method [K. Nakahashi and E. Saitoh, AIAA J. 35, 1280 (1997)] that is applicable to streamwise separated flows. Named the "marching window," the algorithm consists of performing pseudo-time iterations on a minimal width subdomain composed of a sequence of cross-stream planes of nodes. The upstream boundary of the subdomain is positioned such that all nodes upstream exhibit a residual smaller than the user-specified convergence threshold. The advancement of the downstream boundary follows the advancement of the upstream boundary, except in zones of significant streamwise ellipticity, where a streamwise ellipticity sensor ensures its continuous progress. Compared to the standard pseudo-time-marching approach, the marching window decreases the work required for convergence by up to 24 times for flows with little streamwise ellipticity and by up to eight times for flows with large streamwise separated regions. Storage is reduced by up to six times by not allocating memory to the nodes not included in the computational subdomain. The marching window satisfies the same convergence criterion as the standard pseudo-time-stepping methods, hence resulting in the same converged solution within the tolerance of the user-specified convergence threshold. The algorithm is not restricted to a discretization stencil and pseudo-time-stepping scheme in particular and is used here with the Yee-Roe scheme and block-implicit approximate factorization solving the Favre-averaged Navier-Stokes (FANS) equations closed by the Wilcox kω turbulence model. The eigenstructure of the FANS equations is also presented.

KW - Convergence acceleration

KW - Domain decomposition

KW - FANS

KW - Pseudo-time stepping

KW - RANS

KW - Space marching

KW - Viscous hypersonic flow

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U2 - 10.1006/jcph.2002.7048

DO - 10.1006/jcph.2002.7048

M3 - Article

AN - SCOPUS:0037054352

VL - 179

SP - 140

EP - 169

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

M1 - 97048

ER -