Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of the order. The numerical experiments are carried out to validate the above conclusions, which provide some significant guides for the development of the new NEMs. It can be concluded that NEMs have great potential to solve thermal hydraulic problems effectively, and can be used in the engineering design code.