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- Gong, Jing, et al.
(författare)
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A stable and efficient hybrid scheme for viscous problems in complex geometries
- 2007
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Ingår i: Journal of Computational Physics. - Uppsala : Elsevier BV. - 0021-9991 .- 1090-2716. ; 226:2, s. 1291-1309
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods on complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficient and accurate.
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- Gong, Jing, 1971-
(författare)
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Hybrid Methods for Unsteady Fluid Flow Problems in Complex Geometries
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, stable and efficient hybrid methods which combine high order finite difference methods and unstructured finite volume methods for time-dependent initial boundary value problems have been developed. The hybrid methods make it possible to combine the efficiency of the finite difference method and the flexibility of the finite volume method.We carry out a detailed analysis of the stability of the hybrid methods, and in particular the stability of interface treatments between structured and unstructured blocks. Both the methods employ so called summation-by-parts operators and impose boundary and interface conditions weakly, which lead to an energy estimate and stability.We have constructed and analyzed first-, second- and fourth-order Laplacian based artificial dissipation operators for finite volume methods on unstructured grids. The first-order artificial dissipation can handle shock waves, and the fourth-order artificial dissipation eliminates non-physical numerical oscillations efficiently.A stable hybrid method for hyperbolic problems has been developed. It is shown that the stability at the interface can be obtained by modifying the dual grid of the unstructured finite volume method close to the interface. The hybrid method is applied to the Euler equation by the coupling of two stand-alone CFD codes. Since the coupling is administered by a third separate coupling code, the hybrid method allows for individual development of the stand-alone codes. It is shown that the hybrid method is an accurate, efficient and practically useful computational tool that can handle complex geometries and wave propagation phenomena.Stable and accurate interface treatments for the linear advection–diffusion equation have been studied. Accurate high-order calculation are achieved in multiple blocks with interfaces. Three stable interface procedures — the Baumann–Oden method, the “borrowing” method and the local discontinuous Galerkin method, have been investigated. The analysis shows that only minor differences separate the different interface handling procedures.A conservative stable and efficient hybrid method for a parabolic model problem has been developed. The hybrid method has been applied to the full Navier–Stokes equations. The numerical experiments support the theoretical conclusions and show that the interface coupling is stable and converges at the correct order for the Navier–Stokes equations.
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- Gong, Jing, et al.
(författare)
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Interface procedures for finite difference approximations of the advection–diffusion equation
- 2011
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Ingår i: Journal of Computational and Applied Mathematics. - Amsterdam : Elsevier B. V.. - 0377-0427 .- 1879-1778. ; 236:5, s. 602-620
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Tidskriftsartikel (refereegranskat)abstract
- We investigate several existing interface procedures for finite difference methods applied to advection–diffusion problems. The accuracy, stiffness and reflecting properties of the various interface procedures are investigated. The analysis and numerical experiments show that there are only minor differences between the various methods once a proper parameter choice has been made.
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- Nordström, Jan, et al.
(författare)
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A hybrid method for unsteady inviscid fluid flow
- 2009
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Ingår i: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 38:4, s. 875-882
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Tidskriftsartikel (refereegranskat)abstract
- We show how a stable and accurate hybrid procedure for fluid flow can be constructed. Two separate solvers, one using high order finite difference methods and another using the node-centered unstructured finite volume method are coupled in a truly stable way. The two flow solvers run independently and receive and send information from each other by using a third coupling code. Exact solutions to the Euler equations are used to verify the accuracy and stability of the new computational procedure. We also demonstrate the capability of the new procedure in a calculation of the flow in and around a model of a coral.
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- Nordström, Jan, et al.
(författare)
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A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
- 2009
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 228:24, s. 9020-9035
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Tidskriftsartikel (refereegranskat)abstract
- A stable and conservative high order multi-block method for the time-dependent compressible Navier-Stokes equations has been developed. Stability and conservation are proved using summation-by-parts operators, weak interface conditions and the energy method. This development makes it possible to exploit the efficiency of the high order finite difference method for non-trivial geometries. The computational results corroborate the theoretical analysis.
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- Nordström, Jan, et al.
(författare)
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A stable and efficient hybrid method for aeroacoustic sound generation and propagation
- 2005
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Ingår i: Comptes rendus. Mecanique. - : Elsevier BV. - 1631-0721 .- 1873-7234. ; 333:9, s. 713-718
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Tidskriftsartikel (refereegranskat)abstract
- We discuss how to combine the node based unstructured finite volume method widely used to handle complex geometries and nonlinear phenomena with very efficient high order finite difference methods suitable for wave propagation dominated problems. This fully coupled numerical procedure reflects the coupled character of the sound generation and propagation problem. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical experiments using finite difference methods that shed light on the theoretical results are performed. To cite this article: J. Nordstrom, J. Gong, C R. Mecanique 333 (2005).
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