A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD). We investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach.

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  1. Blachère, Florian; Chalons, Christophe; Turpault, Rodolphe: Very high-order asymptotic-preserving schemes for hyperbolic systems of conservation laws with parabolic degeneracy on unstructured meshes (2021)
  2. Figueiredo, J.; Clain, S.: A MOOD-MUSCL hybrid formulation for the non-conservative shallow-water system (2021)
  3. Gaburro, Elena; Dumbser, Michael: A posteriori subcell finite volume limiter for general (P_NP_M) schemes: applications from gasdynamics to relativistic magnetohydrodynamics (2021)
  4. Bourriaud, Alexandre; Loubère, Raphaël; Turpault, Rodolphe: A priori neural networks versus a posteriori MOOD loop: a high accurate 1D FV scheme testing bed (2020)
  5. Denicolai, Emilie; Honoré, Stéphane; Hubert, Florence; Tesson, Rémi: Microtubules (MT) a key target in oncology: mathematical modeling of anti-MT agents on cell migration (2020)
  6. Duan, Zhaowen; Wang, Z. J.: A high-order flux reconstruction method for 3D mixed overset meshes (2020)
  7. Giuliani, Andrew; Krivodonova, Lilia: A moment limiter for the discontinuous Galerkin method on unstructured tetrahedral meshes (2020)
  8. Hajduk, Hennes; Kuzmin, Dmitri; Kolev, Tzanio; Tomov, Vladimir; Tomas, Ignacio; Shadid, John N.: Matrix-free subcell residual distribution for Bernstein finite elements: monolithic limiting (2020)
  9. Ioriatti, Matteo; Dumbser, Michael; Loubère, Raphaël: A staggered semi-implicit discontinuous Galerkin scheme with a posteriori subcell finite volume limiter for the Euler equations of gasdynamics (2020)
  10. Kemm, Friedemann; Gaburro, Elena; Thein, Ferdinand; Dumbser, Michael: A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model (2020)
  11. Kucharik, Milan; Loubère, Raphaël: High-accurate and robust conservative remapping combining polynomial and hyperbolic tangent reconstructions (2020)
  12. Nogueira, Xesús; Ramírez, Luis; Fernández-Fidalgo, Javier; Deligant, Michael; Khelladi, Sofiane; Chassaing, Jean-Camille; Navarrina, Fermín: An a posteriori-implicit turbulent model with automatic dissipation adjustment for large eddy simulation of compressible flows (2020)
  13. Tann, Siengdy; Deng, Xi; Loubère, Raphaël; Xiao, Feng: Solution property preserving reconstruction BVD+MOOD scheme for compressible Euler equations with source terms and detonations (2020)
  14. Xie, Bin; Jin, Peng; Nakayama, Hiroki; Liao, ShiJun; Xiao, Feng: A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids (2020)
  15. Zhang, Huaibao; Zhang, Fan; Liu, Jun; McDonough, J. M.; Xu, Chunguang: A simple extended compact nonlinear scheme with adaptive dissipation control (2020)
  16. Zhang, L. Q.; Chen, Z.; Yang, L. M.; Shu, C.: Double distribution function-based discrete gas kinetic scheme for viscous incompressible and compressible flows (2020)
  17. Zhao, Zhuang; Qiu, Jianxian: A Hermite WENO scheme with artificial linear weights for hyperbolic conservation laws (2020)
  18. Borsche, Raul; Eimer, Matthias; Siedow, Norbert: A local time stepping method for thermal energy transport in district heating networks (2019)
  19. Boscheri, Walter; Balsara, Dinshaw S.: High order direct arbitrary-Lagrangian-Eulerian (ALE) (P_NP_M) schemes with WENO adaptive-order reconstruction on unstructured meshes (2019)
  20. Carrillo, H.; Parés, C.: Compact approximate Taylor methods for systems of conservation laws (2019)

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