Stability and Numerical Diffusion Analysis of Nodal Expansion Method for Convection-diffusion Equation

The stability and numerical diffusion analysis of nodal expansion method (NEM) for convection-diffusion equation was studied. The stabilities and numerical diffusion analyses for NEM with different order basis functions by exact solution of the discretization equation and numerical experiment results were done, and the results from NEM were compared with the results from both the center difference scheme and the first order upwind difference scheme of the finite volume method. The results show that the even order NEM is conditionally stable with Peclet number (Pe) being less than limit value,Pe limit value also increases with the order of expansion functions, and stability range and accuracy are better than those of center difference scheme. The odd order of NEM is unconditionally stable, however, with the increase of Pe, the numerical diffusion becomes lager and the calculation error becomes bigger. In addition, when Pe reaches certain value, the numerical diffusion even exceeds that of the first order upwind difference scheme.