conservation form for uniform mesh size grids [15] and for nonuniform mesh sizes [16]. Those locally exact schemes A new finite variable difference method (FVDM) on finite differencing is presented. The essence of this method consists in de-are characterized by determining the difference coeffitermining the optimum spatial difference such that the total variance cients so that the resulting difference equation satisfies the of the solution is a minimum under the condition that characteristic exact solution of the convection-diffusion equation with roots of the resulting difference equation are always nonnegative constant coefficients. The difference coefficients depend to ensure the numerical stability. The present FVDM is applied to on local velocities and these locally exact schemes are the locally exact numerical scheme (LENS). The optimum spatial nonlinear, resulting in their possessing the possibility of difference of the LENS is derived in terms of local mesh Reynolds numbers. By using this optimum spatial difference the numerical being free from the Godonuv theorem.
accuracy of the LENS for the linear convection-diffusion equations
Those locally exact schemes have been extended to is increased without numerical oscillations for all mesh Reynolds transport equations with absorption [17, 18] and source numbers. The present study suggests that an optimum spatial differterms [19]. The present author proposed the LENS (locally ence from the viewpoint of numerical stability and accuracy exists exact numerical scheme) [20], including the sources and according to the numerical schemes.