On the locking-free three-field virtual element methods for Biot's consolidation model in poroelasticity

We propose and analyze two locking-free three-field virtual element methods for Biot's consolidation model in poroelasticity. One is a high-order scheme, and the other is a low-order scheme. For time discretization, we use the backward Euler scheme. The proposed methods are well-posed, and optimal error estimates of all the unknowns are obtained for fully discrete solutions. The generic constants in the estimates are uniformly bounded as the Lamé coefficient λ tends to infinity, and as the constrained specific storage coefficient is arbitrarily small. Therefore the methods are free of both Poisson locking and pressure oscillations. Numerical results illustrate the good performance of the methods and confirm our theoretical predictions.

Development of a Multiphase Particle Method for Melt-Jet Breakup Behavior of Molten Core in Severe Accident

In a hypothetical severe accident in a light water reactor (LWR) nuclear power plant, there is a possibility that molten core released from the reactor vessel gets in contact with water in the containment vessel. In this so-called fuel-coolant interactions (FCIs) process, the melt jet will breakup into fragments, which is one of the important factors for a steam explosion, as a potential threat to the integrity of the containment vessel. The particle method could directly and easily capture the large deformed interfaces by particle motions, benefiting from its Lagrangian description and meshless framework. In order to investigate the melt-jet breakup with solidification processes, a multiphase particle method with arbitrary high order scheme is presented in this study. In addition, an interfacial particle shifting scheme is developed to suppress the unnatural particle penetration between different phases. The convergence rate with different order is firstly confirmed by a verification test in terms of both explicit and implicit calculations. Then, a transient heat conduction between two materials is carried out and quite good results are obtained. After that, a rising bubble benchmark is performed to show the feasibility of modelling for deformation and collapse. Improvements of clear interface are indicated compared with previous reported results. Two important multiphase instabilities, namely the Rayleigh-Taylor instability and the Kelvin-Helmholtz instability, are studied since they play important roles during the melt-jet breakup. The results achieved so far indicate that the developed particle method is capable to analyze the melt-jet breakup with heat transfer.