Effect of Reconstruction Scheme on the Plasma Fluid Modeling With Original and Reformulated Ion-Related Modeling Equations Using HLL Flux Scheme

In this paper, we would like to investigate the effect of spatial reconstruction schemes on the plasma fluid model with original and reformulated ion-related modeling equations by using the Harten–Lax–van Leer (HLL) flux scheme. The results based on the 1-D fluid model equations for electropositive plasma show that the appearance of unphysical oscillations near-sheath edges strongly depends on the reconstruction schemes (e.g., $\kappa =1/2,1 /3$ , and first-order scheme) when the original ion equations utilize the incorrect ion sound speed. The unphysical oscillations disappear no matter what the spatial reconstruction scheme is applied if the reformulated ion equations with correct ion sound speed are used instead. For electronegative plasma, the kappa reconstruction scheme causes numerical instability when using either the incorrect or correct numerical ion sound speed, but the min-mod reconstruction scheme does not. The numerical results show that for either electropositive or electronegative discharges, both the second-order HLL scheme with min-mod reconstruction and the first-order HLL schemes can produce stable solution, while the accuracy of the former is slightly better than the later. Finally, some examples with an extension to the 2-D-axisymmetric electropositive and electronegative plasmas are demonstrated.