We will present an original Very High-Order Finite Volume method for
conservation laws on unstructured meshes called Multi-dimensional
Optimal Order Detection (MOOD) and its extension to the Euler system for
hydrodynamics. In order to deal with problems generated by high-order
approximations, 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 but the MOOD method is more easily able to take
physical constraints such as density and pressure positivity into
account through the ?a posteriori? detection. Moreover implementation of
the method into a existing first-order code does not involve important
difficulties since no modification of the solver is needed. Numerical
results on classical and demanding test cases for advection and Euler
system will be presented on polygonal meshes to support the promising
potential of this approach. |