LAUSR

Summary The conventional SPH method has been frustrated with the low accuracy originated from the particle inconsistency. The finite particle method (FPM) is an improved SPH method with a higher order accuracy. However, the numerical accuracy and stability of FPM depend on the uniformity of particles. Facing the disorder particles, the conventional FPM may suffer from an ill-conditioned corrective matrix and is difficult to carry out long time simulations. A popular and robust particle regularization scheme is the so-called particle shifting technology (PST) which can effectively enhance the accuracy and stability of particle methods. In the context of FPM, PST is analyzed and discussed, and a modified PST (MPST) is proposed. MPST saves great amount of computational cost with respect to the conventional PST, and acquires better features of accuracy and stability. Finally, the coupled FPM method by combining MPST and δ-SPH is developed to simulate a series of viscous flows. The numerical results indicate that, MPST is effective in improving accuracy, stability and efficiency of PST, and the coupled FPM is shown to be robust for simulating viscous flows and has a higher accuracy and stability.