A corrected smoothed particle hydrodynamics method for solving transient viscoelastic fluid flows

In this work, a corrected smoothed particle hydrodynamics (CSPH) method is proposed and extended to the numerical simulation of transient viscoelastic fluid flows due to that its approximation accuracy in solving the Navier–Stokes equations is higher than that of the smoothed particle hydrodynamics (SPH) method, especially near the boundary of the domain. The CSPH approach comes with the idea of combining the SPH approximation for the interior particles with the modified smoothed particle hydrodynamics (MSPH) method for the exterior particles, this is because that the later method has higher accuracy than the SPH method although it also needs more computational cost. In order to show the validity of CSPH method to simulate unsteady viscoelastic flows problems, the planar shear flow problems, including transient Poiseuille, Couette flow and transient combined Poiseuille and Couette flow for the Oldroyd-B fluid are solved and compared with the analytical and SPH results. Subsequently, the general viscoelastic fluid based on the eXtended Pom–Pom (XPP) model is numerically investigated and the viscoelastic free surface phenomena of impacting drop are simulated by the CSPH for its extended application and the purpose of illustrating the ability of the proposed method. The numerical results are presented and compared with available solutions, which shows a very good agreement. All the numerical results show the higher accuracy and better stability of the CSPH than the SPH, especially for larger Weissenberg numbers.