A stable penalty method for the compressible Navier-Stokes equations. 3: Multidimensional domain decomposition schemes

Journal Article · Sat Aug 01 04:00:00 EDT 1998 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/S1064827596299470· OSTI ID:328392

Hesthaven, J S ^[1]

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1. Brown Univ., Providence, RI (United States). Div. of Applied Mathematics

This paper, concluding the trilogy, develops schemes for the stable solution of wave-dominated unsteady problems in general three-dimensional domains. The schemes utilize a spectral approximation in each subdomain and asymptotic stability of the semidiscrete schemes is established. The complex computational domains are constructed by using nonoverlapping quadrilaterals in the two-dimensional case and hexahedrals in the three-dimensional space. To illustrate the ideas underlying the multidomain method, a stable scheme for the solution of the three-dimensional linear advection-diffusion equation in general curvilinear coordinates is developed. The analysis suggests a novel, yet simple, stable treatment of geometric singularities like edges and vertices. The theoretical results are supported by a two-dimensional implementation of the scheme. The main part of the paper is devoted to the development of a spectral multidomain scheme for the compressible Navier-Stokes equations on conservation form and a unified approach for dealing with the open boundaries and subdomain boundaries is presented. Well posedness and asymptotic stability of the semidiscrete scheme is established in a general curvilinear volume, with special attention given to a hexahedral domain. The treatment includes a stable procedure for dealing with boundary conditions at a solid wall. The efficacy of the scheme for the compressible Navier-Stokes equations is illustrated by obtaining solutions to subsonic and supersonic boundary layer flows with various types of boundary conditions. The results are found to agree with the solution of the compressible boundary layer equations.

• Sponsoring Organization: National Science Foundation, Washington, DC (United States); USDOE, Washington, DC (United States)
• DOE Contract Number: FG02-95ER25239
• OSTI ID: 328392
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 20; ISSN SJOCE3; ISSN 1064-8275
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
BOUNDARY CONDITIONS
CALCULATION METHODS
COMPRESSIBLE FLOW
FLUID MECHANICS
NAVIER-STOKES EQUATIONS