A formula for estimation of truncation errors of convection terms in a curvilinear coordinate system

A formula for truncation errors of convection terms arising from the Navier-Stokes equation in a curvilinear coordinate system is derived. These truncation error terms are interpreted in terms of grid size, grid uniformity, grid line angle, flow angle, and derivatives of flow properties to gain physical insights from the formula. The role of these factors in determining truncation errors is discussed. It is shown that an optimal grid arrangement cannot be obtained without considering the interactions between the grid and the flow field. The effect of the grid orthogonality on truncation errors is also analyzed for simple cases. The derived formula provides a useful indicator for truncation error distribution which yields guidelines for grid adaption.