A fully implicit scheme algorithm for solving viscoelastic-plastic media flow

In the numerical simulation of lithosphere dynamics, conventional viscoelastic plastic models rotate the stress tensor explicitly and then advect it with the particle-in-cell method or field methods to integrate the constitutive equation in time. We put forward a fully implicit method for modeling viscoelastic plastic flows in the non-Newtonian mechanics, which develops the classic schemes with the upwind discontinuous Galerkin method. We carry out detailed comparisons between our fully implicit method and conventional methods through numerical experiments. Results show that our method is competitive with the classic ones and has a higher numerical accuracy when the Deborah number is large. The proposed algorithm with a third-order WENO (Weighted Essentially Non-Oscillatory) limiter is capable of simultaneously eliminating the numerical oscillations and preserving high-order resolution results during the large-time simulation.

Automated summary

This paper presents a fully implicit method for modeling viscoelastic plastic flows in non-Newtonian mechanics, and compares it with conventional methods through numerical experiments. Results show that the proposed method is competitive with traditional ones and achieves higher numerical accuracy when the Deborah number is large. The algorithm, with a third-order WENO limiter, can simultaneously eliminate numerical oscillations and preserve high-order resolution results during long-time simulations.