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. Boscheri, Walter; Dimarco, Giacomo: High order modal discontinuous Galerkin implicit-explicit Runge Kutta and linear multistep schemes for the Boltzmann model on general polygonal meshes (2022)
  2. Fernández, E. Guerrero; Díaz, M. J. Castro; Dumbser, M.; de Luna, T. Morales: An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density (2022)
  3. Avesani, Diego; Dumbser, Michael; Vacondio, Renato; Righetti, Maurizio: An alternative SPH formulation: ADER-WENO-SPH (2021)
  4. 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)
  5. Busto, Saray; Dumbser, Michael; Gavrilyuk, Sergey; Ivanova, Kseniya: On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows (2021)
  6. Busto, S.; Río-Martín, L.; Vázquez-Cendón, M. E.; Dumbser, M.: A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes (2021)
  7. Chan, Agnes; Gallice, Gérard; Loubère, Raphaël; Maire, Pierre-Henri: Positivity preserving and entropy consistent approximate Riemann solvers dedicated to the high-order MOOD-based finite volume discretization of Lagrangian and Eulerian gas dynamics (2021)
  8. Figueiredo, J.; Clain, S.: A MOOD-MUSCL hybrid formulation for the non-conservative shallow-water system (2021)
  9. Gaburro, Elena; Dumbser, Michael: A posteriori subcell finite volume limiter for general (P_NP_M) schemes: applications from gasdynamics to relativistic magnetohydrodynamics (2021)
  10. Ji, Xing; Shyy, Wei; Xu, Kun: A gradient compression-based compact high-order gas-kinetic scheme on 3D hybrid unstructured meshes (2021)
  11. Liu, Yangyang; Yang, Liming; Shu, Chang; Zhang, Huangwei: A multi-dimensional shock-capturing limiter for high-order least square-based finite difference-finite volume method on unstructured grids (2021)
  12. Li, Wanai; Liu, Yang: The (p)-weighted limiter for the discontinuous Galerkin method in solving compressible flows on tetrahedral grids (2021)
  13. Michel-Dansac, Victor; Berthon, Christophe; Clain, Stéphane; Foucher, Françoise: A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction (2021)
  14. Prieto-Arranz, Alberto; Ramírez, Luis; Couceiro, Iván; Colominas, Ignasi; Nogueira, Xesús: A well-balanced SPH-ALE scheme for shallow water applications (2021)
  15. Zhang, Huaibao; Xu, Chunguang; Dong, Haibo: An extended seventh-order compact nonlinear scheme with positivity-preserving property (2021)
  16. Bourriaud, Alexandre; Loubère, Raphaël; Turpault, Rodolphe: A priori neural networks versus a posteriori MOOD loop: a high accurate 1D FV scheme testing bed (2020)
  17. 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)
  18. Dong, Qiannan; Su, Shuai; Wu, Jiming: A decoupled and positivity-preserving DDFVS scheme for diffusion problems on polyhedral meshes (2020)
  19. Duan, Zhaowen; Wang, Z. J.: A high-order flux reconstruction method for 3D mixed overset meshes (2020)
  20. Giuliani, Andrew; Krivodonova, Lilia: A moment limiter for the discontinuous Galerkin method on unstructured tetrahedral meshes (2020)

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