On Implementation of Monotonicity Preserving Reconstruction of Variables in EBR Schemes

A vertex-centered scheme is considered that is based on monotonicity-preserving edge-based reconstruction of variables for solving the Euler equations on unstructured meshes. Unlike a similar scheme that is based on quasi-one-dimensional WENO-reconstructions, the new method provides less dissipation and consequently a higher accuracy of the numerical solution. This property is demonstrated by solving two-dimensional model problems on uniform, quasi-uniform, and compressing triangular meshes.