The smoothed particle hydrodynamics (SPH) method is usually expected to be an efficient numerical tool for calculating the multiphase phenomena in compressors. However, numerical instability arises around the interfaces due to the pressure inconsistency. By analyzing different formula of the pressure term under SPH approximation, we show that the frequently-used formulation (n=-1) leads to the worst performance and is thus not recommended. By contrast, we suggest the formulas n=0 and 1 in future practical SPH applications.

This article first studies the stability conditions of a Chua system depending on six parameters. After, using the averaging method, as well as the methods of the Gröbner basis and real solution classification, we provide sufficient conditions for the existence of three limit cycles bifurcating from a zero-Hopf equilibrium of the Chua system. As we know, this last phenomena is first found. Some examples are presented to verify the established results.