Understand Slope Limiter -- Graphically

Abstract: In this article, we illustrate how the concept of slope limiter can be interpreted graphically, i.e., how the slope of reconstructed piecewise linear function is limited by four bounding lines that connect cell-averaged data and its neighboring cell-averaged data. It is then conjectured that the same graphical rule can be generalized from uniform mesh to non-uniform mesh, such that the high-resolution total variance diminishing (TVD) region of slope limiter for non-uniform meshes can be obtained.