Narrow Results

In this paper we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by analyzing couplings. For a given tensor dilation we construct a self-coupling of a Markov operator. It turns out that the coupling is a dual version of the extended dual transition operator studied by Gohm et al. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.

In this paper, an enhanced mapping interpolation ISPH–FVM coupling method is developed to improve the accuracy and stability of two-phase flows simulation. Similar to the original ISPH–FVM coupling method, the coupling framework between the numerical schemes of ISPH and FVM is established at the overlapping region of the ISPH particles and the FVM grids. Although the original ISPH–FVM coupling method can effectively predict movement and deformation of the two-phase interface, it is difficult to ensure the mass conservation in the flow domain during the information transfer between ISPH particles and FVM grids, thus weakening the numerical accuracy of interaction between different fluid phases. To improve the mapping interpolation accuracy and ensure the mass conservation, a volume fraction correction scheme combined with the particle approximate interpolation technique is introduced to form an enhanced mapping interpolation ISPH–FVM coupling method. The effect of surface tension is assessed by the continuum surface force (CSF) model. Several 2D/3D numerical cases are given to verify the efficiency and robustness of the present ISPH–FVM coupling method. Numerical results demonstrate that the enhanced mapping interpolation developed in the ISPH–FVM coupling method can reproduce the two-phase flow with complex interfaces effectively.

An implicit coupling finite element and peridynamic (PD) method is developed in this paper for the dynamic problems of solid mechanics with crack propagation. In this method, an implicit PD formulation is derived from the bond-based pairwise force that is described as a linear function of the displacements by using the first-order Taylor’s expansion technique. The equivalent incremental equations of the PD method and the finite element method are obtained on the basis of the Newmark and the Newton–Raphson schemes. To combine these two methods, the system is partitioned into two subregions and a convenient and efficient coupling strategy is proposed to form the coupling equivalent equation. The coupling domain is achieved by considering that the nodes and material points share the common information. Furthermore, displacement and load control-based incremental-iterative methods are adopted to solve the nonlinear equations. Several representative numerical examples are carried out and the results demonstrate the effectiveness and accuracy of the proposed coupling method.

A novel coupling phase-field lattice Boltzmann–material point (phase-field LB–MP) method is proposed in this work for multiphase fluid–solid bidirectional interaction problems. In this method, the phase-field lattice Boltzmann (LB) scheme is used to describe the multiphase incompressible fluid behaviors for its capability of dealing with binary-fluid system with large contrasts in both density and viscosity. The convected particle-domain interpolation-based material point method (MPM) is further adopted to capture the soft solid responses for its advantage in large deformation simulation and solid boundary representation. To bridge the solid and fluid phases, the Lagrangian marker points-based representation is proposed to explicitly depict the multiphase fluid–solid interface. Moreover, the hybrid bounce-back model is employed to effectively evaluate the unknown distribution functions and the contact angle specifying strategy for wetting boundary condition is developed for curved interface. The Galilean-invariant momentum exchange scheme and the distribution model are respectively taken into account to deal with hydrodynamic and capillary forces, and the interface-tracking force imposing strategy is developed for large deformation of solid. Additionally, the refilling algorithm is also considered for moving or deformable fluid–solid interface. There is no re-meshing operation needed for both fluid and solid parts in our phase-field LB–MP method. Three numerical examples are presented for progressively rigorous validations, which demonstrate that our phase-field LB–MP method has the capability of solving the multiphase fluid–deformable solid bidirectional interaction problems involving solid large deformation and binary-fluid behavior with large contrasts in both density and viscosity.