Abstract
A higher-order computational scheme utilizing quintic spline interpolation, QSI method, has been proposed. The derivatives in the governing equations are evaluated by differentiating the quintic spline function. This computational method was applied to one- and two-dimensional pure advection problems. As a result, it was shown that the numerical accuracy in the QSI method is superior to a fifth-order upwind difference. In addition, two-dimensional cavity flows were solved with staggered and collocated grid systems. In the results of QSI scheme, it was shown that the accuracy of the QSI method is rather improved in the collocated system and that the accuracy is generally better than that of the 5th-order upwind difference.
