Abstract: Computational performance of the positive-definite shape-preserving conservative Semi-Lagrangian with rational funetion advection (CSLR) scheme is analyzed through a couple of idealized experiments in Cartesian plane coordinates and the spherical Yin-Yang coordinate system.Numerical convergence rate of the CSLR scheme is studied by using several error norms in both on-and two-dimensional computations.The numerical results reveal that the rational function adopted in the CSLR scheme eliminates numerical oscillation at discontinuous points,guarantees positive definition and acquires the 1st-2nd-order convergence rate in case of smooth distribution.At discontinuous points or steep-slope regions,in addition to the application of the multi-dimensional splitting algorithm,however, the convergence rate is reduced due to the special character of rational function.The convergence rate of the CSLR scheme decreases in the spherical coordinate because of the spherical curvature.