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A novel approach for selecting appropriate reconstructions is implemented tothe hyperbolic conservation laws in the high-order local polynomial-basedframework, e.g., the discontinuous Galerkin (DG) and flux reconstruction (FR)schemes. The high-order polynomial approximation generally fails to correctlycapture a strong discontinuity inside a cell due to the Runge phenomenon, whichis replaced by more stable approximation on the basis of a troubled-cellindicator such as that used in the total variation bounded (TVB) limiter. Thispaper examines the applicability of a new algorithm, so-called boundaryvariation diminishing (BVD) reconstruction, to the weighted essentiallynon-oscillatory (WENO) methodology in the FR framework including the nodal typeDG method. The BVD reconstruction adaptively chooses a proper approximation forthe solution function so as to minimize the jump between values at the left-and right-side of cell boundaries without any ad hoc constant such as the TVBparameter. Several numerical tests are conducted for a linear advectionequation as well as the selection of an appropriate reconstruction, where theresults of the BVD algorithm are comparable to those using the conventional TVBlimiter. Note that the present work is limited to third or lower orderpolynomials, leaving the implementations for higher-order schemes a futurework.

A note on implementation of boundary variation diminishing algorithm to high-order local polynomial-based schemes