Abstract
In this study, numerical methods for the basic equations of the Maxwell fluid, which is one of the viscoelastic fluids, were investigated on the two-dimensional collocated grid system by the finite volume method. On the basis of the numerical method proposed by the authors previously, that for the stress terms in the momentum equations were proposed in this study. By the proposed numerical method, the stress terms are calculated with the spatially compact velocity distribution, and it was demonstrated by the numerical experiments that the method can avoid the unphysically oscillated results. Additionally, for the pressure calculation, the C-HSMAC method which controls the divergence of the velocity was applied to the Maxwell fluid and in the numerical experiments it was shown that the method prevented the numerical oscillation of stresses which may happen by using the SMAC method. Furthermore, the proposed method was applied to the numerical experiments in which the elastic character is dominant. As a result of the computations, it was demonstrated that the proposed method and the C-HSMAC method enable to qualitatively predict the elastic behaviors of the Maxwell fluid.
