Use of Lagrange interpolation in modeling convective kinematics

A new procedure for developing higher-order representation of cell interfac e convective flux based on Lagrange interpolation is presented. The higher- order terms may include any number of nodes across the interface and can be used for uniform and nonuniform grids without loss of generality. The prop erties of Lagrange interpolation are used to present the higher-order terms as a combination of first-order terms and linearized source terms. This te chnique satisfies the Scarborough criterion for discretized coefficients au tomatically. Two popular higher-order schemes, namely, SOU (Second-Order Up wind) and QUICK (Quadratic Upstream Interpolation for Convective Kinematics ), are used to illustrate the details of the procedure.