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- Eliasson, Peter, et al.
(författare)
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Higher Order Accurate Solutions for Flow in a Cavity: Experiences and Lessons Learned
- 2015
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Ingår i: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. - Cham : Springer. - 9783319197999 - 9783319198002 ; , s. 189-196
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Bokkapitel (refereegranskat)abstract
- Experiences from using a higher order accurate finite difference multiblock solver to compute the time dependent flow over a cavity is summarized. The work has been carried out as part of a work in a European project called IDIHOM in a collaboration between the Swedish Defense Research Agency (FOI) and University of Linköping (LiU). The higher order code is based on Summation By Parts operators combined with the Simultaneous Approximation Term approach for boundary and interface conditions. The spatial accuracy of the code is verified by calculations over a cyclinder by monitoring the decay of the errors of known wall quantities as the grid is refined. The focus is on the validation for a test case of transonic flow over a rectangular cavity with hybrid RANS/LES calculations. The results are compared to reference numerical results from a second order finite volume code as well as with experimental results with a good overall agreement between the results.
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| 3. |
- Kupiainen, Marco, et al.
(författare)
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A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
- 2009
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Ingår i: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 41:1, s. 94-117
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Tidskriftsartikel (refereegranskat)abstract
- We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in Kreiss et al. (SIAM J. Numer. Anal. 40(5):1940-1967, 2002) and for the Euler equations of compressible fluid flow in Sjogreen and Peterson (Commun. Comput. Phys. 2:1199-1219, 2007), to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
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| 5. |
- Kupiainen, Marco, et al.
(författare)
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Large Eddy simulation of turbulent non premixed flame
- 2003
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Ingår i: In Third international symposium on turbulence and shear flow phenomena(TSFP-3), Sendai Japan 25-27 June 2003..
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 9. |
- Linders, Viktor
(författare)
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Error analysis of summation-by-parts formulations : Dispersion, transmission and accuracy
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we consider errors arising from finite difference operators on summation-by-parts (SBP) form, used in the discretisation of partial differential equations. The SBP operators are augmented with simultaneous-approximation-terms (SATs) to weakly impose boundary conditions. The SBP-SAT framework combines high order of accuracy with a systematic construction of provably stable boundary procedures, which renders it suitable for a wide range of problems.The first part of the thesis treats wave propagation problems discretised using SBP operators on coarse grids. Unless special care is taken, inaccurate approximations of the underlying dispersion relation materialises in the form of an incorrect propagation speed. We present a procedure for constructing SBP operators with minimal dispersion error. Experiments indicate that they outperform higher order non-optimal SBP operators for flow problems involving high frequencies and long simulation times.In the second part of the thesis, the formal order of accuracy of SBP operators near boundaries is analysed. We prove that the order in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. This generalises the classical theory posed on uniform and conforming grids. We further show that for a common class of SBP operators, the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid.In the final contribution if the thesis, we introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability analyses are performed for continuous and discrete problems. A general condition is obtained that is necessary and sufficient for the transmission problem to satisfy an energy estimate. The theory provides insights into the coupling of fluid flow models, multi-block formulations, numerical filters, interpolation and multi-grid implementations.
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| 10. |
- Linders, Viktor, et al.
(författare)
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Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We present a procedure for constructing Summation-by-Parts operators with minimal dispersion error both near and far from numerical interfaces. Examples of such operators are constructed and compared with purely periodic stencils as well as non-optimised Summation-by-Parts operators of higher order. Experiments show that the optimised operators are superior for wave propagation and turbulent flows involving large wavenumbers, long solution times and large ranges of resolution scales.
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