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A new scheme applied to the finite volume method for solving the partial differential equations of fluid flow is proposed. The Lagrange interpolating polynomial with a setting of zero for the spatial domain at the cell faces, and the present time at the cell center is adopted for the new scheme to estimate the values of the variables at the cell faces, the derivative values of the variables with respect to the spatial domain at the cell faces and the derivative values of the variables with respect to time at the cell center for spatial and temporal discretization of the discretized equation. The new scheme was verified by comparing the solutions of the new scheme to the benchmark numerical solutions and the published numerical solutions of two dimensional laminar natural convection in a square cavity. From the comparison, the results show that the solutions of the new scheme agree well with the benchmark numerical solutions and the published numerical solutions.

A New Scheme for the Finite Volume Method Verified with Two Dimensional Laminar Natural Convection in a Square Cavity