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. Boscheri, Walter; Loubère, Raphaël; Maire, Pierre-Henri: A 3D cell-centered ADER MOOD finite volume method for solving updated Lagrangian hyperelasticity on unstructured grids (2022)
  3. Busto, S.; Dumbser, M.: A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers (2022)
  4. Eimer, Matthias; Borsche, Raul; Siedow, Norbert: Implicit finite volume method with a posteriori limiting for transport networks (2022)
  5. 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)
  6. Gulizzi, Vincenzo; Almgren, Ann S.; Bell, John B.: A coupled discontinuous Galerkin-finite volume framework for solving gas dynamics over embedded geometries (2022)
  7. Haidar, Ali; Marche, Fabien; Vilar, Francois: \textitAposteriori finite-volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equations (2022)
  8. He, Zhiwei; Ruan, Yucang; Yu, Yaqun; Tian, Baolin; Xiao, Feng: Self-adjusting steepness-based schemes that preserve discontinuous structures in compressible flows (2022)
  9. Montanino, Andrea; Franci, Alessandro; Rossi, Riccardo; Zuccaro, Giulio: Finite element formulation for compressible multiphase flows and its application to pyroclastic gravity currents (2022)
  10. Nguyen, Tuan Dung; Besse, Christophe; Rogier, François: High-order Scharfetter-Gummel-based schemes and applications to gas discharge modeling (2022)
  11. Avesani, Diego; Dumbser, Michael; Vacondio, Renato; Righetti, Maurizio: An alternative SPH formulation: ADER-WENO-SPH (2021)
  12. 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)
  13. 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)
  14. 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)
  15. 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)
  16. Chiocchetti, Simone; Peshkov, Ilya; Gavrilyuk, Sergey; Dumbser, Michael: High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension (2021)
  17. Fernández-Fidalgo, Javier; Ramírez, Luis; Tsoutsanis, Panagiotis; Colominas, Ignasi; Nogueira, Xesús: A reduced-dissipation WENO scheme with automatic dissipation adjustment (2021)
  18. Figueiredo, J.; Clain, S.: A MOOD-MUSCL hybrid formulation for the non-conservative shallow-water system (2021)
  19. Gaburro, Elena; Dumbser, Michael: A posteriori subcell finite volume limiter for general (P_NP_M) schemes: applications from gasdynamics to relativistic magnetohydrodynamics (2021)
  20. Ji, Xing; Shyy, Wei; Xu, Kun: A gradient compression-based compact high-order gas-kinetic scheme on 3D hybrid unstructured meshes (2021)

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