000190425 001__ 190425
000190425 005__ 20190316235742.0
000190425 0247_ $$2doi$$a10.1137/S1064827596299470
000190425 022__ $$a1064-8275
000190425 02470 $$2ISI$$a000075434800004
000190425 037__ $$aARTICLE
000190425 245__ $$aA stable penalty method for the compressible Navier-Stokes equations: III. Multidimensional domain decomposition schemes
000190425 269__ $$a1998
000190425 260__ $$bSIAM PUBLICATIONS$$c1998
000190425 336__ $$aJournal Articles
000190425 520__ $$aThis 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.
000190425 6531_ $$adomain decomposition
000190425 6531_ $$astable penalty methods
000190425 6531_ $$aspectral methods
000190425 6531_ $$aNavier-Stokes 	equations
000190425 700__ $$g232231$$aHesthaven, Jan S.$$0247428
000190425 773__ $$j20$$tSIAM Journal on Scientific Computing$$k1$$q62-93
000190425 8564_ $$uhttps://infoscience.epfl.ch/record/190425/files/SIAM%20J%20Sci%20Comput%201998%20Hesthaven.pdf$$zPublisher's version$$s660838$$yPublisher's version
000190425 909C0 $$xU12703$$0252492$$pMCSS
000190425 909CO $$ooai:infoscience.tind.io:190425$$qGLOBAL_SET$$pSB$$particle
000190425 917Z8 $$x102085
000190425 937__ $$aEPFL-ARTICLE-190425
000190425 970__ $$aHesthaven1998e/MCSS
000190425 973__ $$rREVIEWED$$sPUBLISHED$$aOTHER
000190425 980__ $$aARTICLE