DISTRIBUTION OF RANDOM ELEMENTS SUBJECTED TO A FLEXIBLE BOUNDARY CONDITION

The probability distribution function of n random elements subjected to the flexible boundary condition is derived. The probability density is a descending curve and converges to a delta function as n tends to infinity. The distribution of the minimum value is discussed in context of ordered statistics.

Efficient Flexible Boundary Conditions for Long Dislocations

We present a novel efficient implementation of the flexible boundary condition(FBC)method,initially proposed by Sinclair et al.,for large single-periodic problems.Efficiency is primarily achieved by constructing a hierarchical matrix(H-matrix)representation of the periodic Green matrix,reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost linear in the number of pad atoms.In addition,our implementation is supported by various other tools from numerical analysis,such as a residual-based transformation of the boundary conditions to accelerate the convergence.We assess the method for a comprehensive set of examples,relevant for predicting mechanical properties,such as yield strength or ductility,including dislocation bow-out,dislocation-precipitate interaction,and dislocation cross-slip.The main result of our analysis is that the FBC method is robust,easy-to-use,and up to two orders of magnitude more efficient than the current state-of-the-art method for this class of problems,the periodic array of dislocations(PAD)method,in terms of the required number of per-atom force computations when both methods give similar accuracy.This opens new prospects for large-scale atomistic simulations—without having to worry about spurious image effects that plague classical boundary conditions.

Immersed Boundary-Lattice Boltzmann Coupling Scheme for Fluid-Structure Interaction with Flexible Boundary

Coupling the immersed boundary(IB)method and the lattice Boltzmann(LB)method might be a promising approach to simulate fluid-structure interaction(FSI)problems with flexible structures and complex boundaries,because the former is a general simulation method for FSIs in biological systems,the latter is an efficient scheme for fluid flow simulations,and both of them work on regular Cartesian grids.In this paper an IB-LB coupling scheme is proposed and its feasibility is verified.The scheme is suitable for FSI problems concerning rapid flexible boundary motion and a large pressure gradient across the boundary.We first analyze the respective concepts,formulae and advantages of the IB and LB methods,and then explain the coupling strategy and detailed implementation procedures.To verify the effectiveness and accuracy,FSI problems arising from the relaxation of a distorted balloon immersed in a viscous fluid,an unsteady wake flow caused by an impulsively started circular cylinder at Reynolds number 9500,and an unsteady vortex shedding flow past a suddenly started rotating circular cylinder at Reynolds number 1000 are simulated.The first example is a benchmark case for flexible boundary FSI with a large pressure gradient across the boundary,the second is a fixed complex boundary problem,and the third is a typical moving boundary example.The results are in good agreement with the analytical and existing numerical data.It is shown that the proposed scheme is capable of modeling flexible boundary and complex boundary problems at a second-order spatial convergence;the volume leakage defect of the conventional IB method has been remedied by using a new method of introducing the unsteady and non-uniform external force;and the LB method makes the IB method simulation simpler and more efficient.

EFFECT OF TEMPERATURE ON DISLOCATION EMISSION FROM CRACK TIP FOR BCC METAL MO

The effect of thermally activated energy on the dislocationemission from a crack tip in BCC metal Mo is simulated in this paper.Based on the correlative reference model on which the flexi- bledisplacement boundary scheme is introduced naturally, the simulationshows that as temperature in creases the critical stress intensityfactor for the first dislocation emission will decrease and the totalnumber of emitted dislocations increase for the same external load.The dislocation velocity and exten- sive distance among partialdislocations are not sensitive to temperature.

Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGK Model

This paper aims to study the numerical features of a coupling scheme between the immersed boundary(IB)method and the lattice Boltzmann BGK(LBGK)model by four typical test problems:the relaxation of a circular membrane,the shearing flow induced by a moving fiber in the middle of a channel,the shearing flow near a non-slip rigid wall,and the circular Couette flow between two inversely rotating cylinders.The accuracy and robustness of the IB-LBGK coupling scheme,the performances of different discrete Dirac delta functions,the effect of iteration on the coupling scheme,the importance of the external forcing term treatment,the sensitivity of the coupling scheme to flow and boundary parameters,the velocity slip near non-slip rigid wall,and the origination of numerical instabilities are investigated in detail via the four test cases.It is found that the iteration in the coupling cycle can effectively improve stability,the introduction of a second-order forcing term in LBGK model is crucial,the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability,and the emergence of both temporal and spatial fluctuations of boundary parameters seems to be the indication of numerical instability.These elaborate results shed light on the nature of the coupling scheme and may benefit those who wish to use or improve the method.