S. Diot, R. Loubère and S. Clain The Multidimensional Optimal Order Detection method in the three-dimensional case: very high-order finite volume method for hyperbolic systems International Journal for Numerical Methods in Fluids 73
In this paper, we extend the Multidimensional Optimal Order Detection (MOOD) method, both the convection equation, and the Euler system to 3D mixed meshes and simplify the u2 detection process previously developed. The optimal high order of accuracy is numerically assessed on smooth solutions, whereas spurious oscillations near singularities are prevented. Finally, the intrinsic positivity-preserving property of the MOOD method is confirmed in 3D, and we provide computational cost estimates that supports the MOOD method competitiveness.
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