A high-order time formulation of the RBC schemes for unsteady compressible Euler equations
Article dans une revue avec comité de lecture
Date
2015Journal
Journal of Computational PhysicsAbstract
Residual-Based Compact (RBC) schemes can approximate the compressible Euler equations with a high space-accuracy on a very compact stencil. For instance on a 2-D Cartesian mesh, the 5th and 7th-order accuracy can be reached on a 5x5-point stencil. The time integration of the RBC schemes uses a fully implicit method of 2nd-order accuracy (Gear method) usually solved by a dual-time approach. This method is efficient for computing compressible flows in slow unsteady regimes, but for quick unsteady flows, it may be costly and not accurate enough. A new time-formulation is proposed in the present paper. Unusually, in a RBC scheme the time derivative occurs, through linear discrete operators due to compactness, not only in the main residual but also in the other two residuals (in 2-D) involved in the numerical dissipation. To extract the time derivative, a space-factorization method which preserves the high accuracy in space is developed for reducing the algebra to the direct solution of simple linear systems on the mesh lines. Then a time-integration of high accuracy is selected for the RBC schemes by comparing the efficiency of four classes of explicit methods. The new time-formulation is validated for the diagonal advection of a Gaussian shape, the rotation of a hump, the advection of a vortex for a long time and the interaction of a vortex with a shock.
Files in this item
Collections
Related items
Showing items related by title, author, creator and subject.
-
Article dans une revue avec comité de lectureVAN GORP, Adrien; BIGERELLE, Maxence; GRELLIER, Alain; IOST, Alain; NAJJAR, Denis (Elsevier, 2007)This paper proposes a new multi-scale measurement approach performed to compare the surface roughness and the visual aspect of polished surfaces. In this investigation, five specimens of glass moulds presenting different ...
-
Article dans une revue avec comité de lectureESPINO-PÉREZ, Etzael; BRAS, Julien; DUCRUET, Violette J.; GUINAULT, Alain; DUFRESNE, Alain; DOMENEK, Sandra (Elsevier, 2013)In the aim of producing fully organic bionanocomposite based on poly(lactide) (PLA), cellulose nanowhiskers (CNW) were grafted by n-octadecyl-isocyanate (CNW-ICN) applying an in situ surface grafting method. The compatibilizing ...
-
Article dans une revue avec comité de lectureBIGERELLE, Maxence; IOST, Alain (NRC Research Press, 2007)Dans cette note, nous analysons l’entropie de mélange d’un système physique à l’équilibre par la théorie algorithmique de l’information. Nous montrons l’existence d’un isomorphisme entre cette entropie et la taille du ...
-
Article dans une revue avec comité de lectureRUELLAN, Alexandre; DUCRUET, Violette J.; GRATIA, Audrey; SAELICES JIMENEZ, Lidia; GUINAULT, Alain; SOLLOGOUB, Cyrille; CHOLLET, Guillaume; DOMENEK, Sandra (Wiley, 2016)A used-as-shipped biobased and biodegradable by-product of the palm oil refining increases polylactide (PLA) elongation at break up to 130% and allows film blowing without further additives. PLA blends are biodegradable ...
-
Article dans une revue avec comité de lectureBELKADI, Farouk; DHUIEB, Mohamed Anis; AGUADO, José Vicente; LAROCHE, Florent; BERNARD, Alain; CHINESTA, Francisco (Elsevier, 2020)The key role of information and communication technologies (ICT) to improve manufacturing productivity within the paradigm of factory of the future is often proved. These tools are used in a wide range of product lifecycle ...