Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Multi-dimensional limiting process for three-dimensional flow physics analyses
Journal of Computational Physics
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
Monoslope and multislope MUSCL methods for unstructured meshes
Journal of Computational Physics
L ∞ stability of the MUSCL methods
Numerische Mathematik
Very high-order finite volume method for one-dimensional convection diffusion problems
MMES'11/DEEE'11/COMATIA'11 Proceedings of the 2nd international conference on Mathematical Models for Engineering Science, and proceedings of the 2nd international conference on Development, Energy, Environment, Economics, and proceedings of the 2nd international conference on Communication and Management in Technological Innovation and Academic Globalization
Journal of Computational Physics
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In this paper, 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.