| 1. |
- Ansanay-Alex, Guillaume, et al.
(författare)
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A finite volume stability result for the convection operator in compressible flows. . . and some finite element applications
- 2008
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Ingår i: Finite Volumes for Complex Applications V. - : Hermes Science Publications. - 9781848210356 ; , s. 185-192
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Konferensbidrag (refereegranskat)abstract
- In this paper, we build a L2-stable discretization of the non-linear convection termin Navier-Stokes equations for non-divergence-free flows, for non-conforming low order Stokesfinite elements. This discrete operator is obtained by a finite volume technique, and its stability relies on a result interesting for its own sake: the L2-stability of the natural finite volume convection operator in compressible flows, under some compatibility condition with the discrete mass balance. Then, this analysis is used to derive a boundary condition to cope with physical situations where the velocity cannot be prescribed on inflow parts of the boundary of the computational domain. We finally collect these ingredients in a pressure correction scheme for low Mach number flows, and assess the capability of the resulting algorithm to compute a natural convection flow with artificial (open) boundaries.
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| 2. |
- Gallouët, Thierry, et al.
(författare)
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Convergence of a finite volume scheme for the convection-diffusion equation with L1 data
- 2012
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Ingår i: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 81:279, s. 1429-1454
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we prove the convergence of a finite-volume schemefor the time-dependent convection–diffusion equation with an L1 right-handside. To this purpose, we first prove estimates for the discrete solution andfor its discrete time and space derivatives. Then we show the convergence of asequence of discrete solutions obtained with more and more refined discretiza-tions, possibly up to the extraction of a subsequence, to a function which metsthe regularity requirements of the weak formulation of the problem; to thispurpose, we prove a compactness result, which may be seen as a discrete ana-logue to Aubin-Simon’s lemma. Finally, such a limit is shown to be indeed aweak solution.
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| 3. |
- Hoffman, Johan, et al.
(författare)
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FEniCS-HPC: Coupled Multiphysics in Computational Fluid Dynamics
- 2017
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Ingår i: High-Performance Scientific Computing. - Cham : Springer. - 9783319538617 - 9783319538624 ; , s. 58-69
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Konferensbidrag (refereegranskat)abstract
- We present a framework for coupled multiphysics in computational fluid dynamics, targeting massively parallel systems. Our strategy is based on general problem formulations in the form of partial differential equations and the finite element method, which open for automation, and optimization of a set of fundamental algorithms. We describe these algorithms, including finite element matrix assembly, adaptive mesh refinement and mesh smoothing; and multiphysics coupling methodologies such as unified continuum fluid-structure interaction (FSI), and aeroacoustics by coupled acoustic analogies. The framework is implemented as FEniCS open source software components, optimized for massively parallel computing. Examples of applications are presented, including simulation of aeroacoustic noise generated by an airplane landing gear, simulation of the blood flow in the human heart, and simulation of the human voice organ.
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| 4. |
- Larcher, Aurélien, 1983-, et al.
(författare)
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A Monotone Scheme for the k-epsilon RNG M}odel
- 2008
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Ingår i: Finites Volume for Complex Applications V. - : Hermes Science Publications.
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Konferensbidrag (refereegranskat)abstract
- In this paper, we design a finite-volume based numerical scheme for the solution of the nonlinear balance equations of RNG variants of the well-known k-ε model.In this class of models, the description of the turbulence relies on two variables, the turbulent kinetic energy k and its dissipation rate ε, which, for physical reasons, must remain positive.When standard upwinding techniques for the convection terms are used, the presented scheme is proved to preserve the positivity of these two unknowns, and, through a topological degree argument, to admit at least a solution.A numerical convergence study shows a first order convergence rate in both time and space.When using a MUSCL discretization for the approximation of the convection terms, the scheme becomes of second order in space.
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| 5. |
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