On a solution reconstruction and limiting procedure for unstructured finite volumes

The present paper deals with the continuous work of extending the application of a multidimensional-type solution reconstruction and limiting procedure into the finite volume (FV) computation of 2D compressible flows. Based on a MUSCL-type technique, this reconstruction procedure identifies and cures poor connected grids without suffering from loss of accuracy by taking into account geometrical characteristics of computational triangular and hybrid meshes and is independent of the Riemann solver used. Monotonicity in the solution is enforced by a limiting strategy that implements well-known edge-type limiters hence avoiding the procedure of solving any minimization problems. Through several test cases, it is observed that the methodology provides quite desirable performances in retaining the formal order of accuracy, controlling numerical oscillations as well as capturing key flow features.