Traction-based Completed Adjoint Double Layer Boundary Element Method in elasticity

This paper is concerned with a traction-based Completed Adjoint Double Layer Boundary Element Method to solve for the surface traction of a system of rigid particles embedded in an elastic matrix. The main feature of the method is a single layer representation of the displacement field, which leads to a system of second-kind integral equations for the traction field, the extreme eigenvalue of which could be deflated, allowing iterative solution strategies to be effectively applied. The method is therefore most suitable for large-scale simulations of particulate solids. The method is benchmarked against some known analytic solutions, including the difficult stress singularity problems at sharp edges. The effectiveness of the method in dealing with a large number of inclusions is also demonstrated with an elongational deformation problem involving up to 25 inclusions.Research supported by the Australian Research Council (to NP-T and X-JF) and the National Natural Science Foundation of China (X-JF).     

On the path and efficiency of two micromachines with rigid tails

This paper reports on the results of investigation of the swimming of two different micro-machines. Mechanically each of these micro-machines consists of a head (containing an electromechanical power source) and a tail which moves relative to the head as a rigid body. The problem is approached theoretically by considering the types of movement which can occur for these micro-machines immersed in a viscous medium. The first micro-machine has a tail which oscillates in vertical plane, therefore the trajectory of this machine is in that plane too. The tail of the second micro-machine roates conically, so it produces a three dimensional helical path in space with its axis approximately along the direction of tail centreline.Using the boundary element method for solving the traction equations on the surface of the tail, and a time-dependent Euler kinematic scheme to plot the path, the net propulsive force and torque, the translational velocity, angular velocity and the trajectory of each machine are calculated. Evaluation of the path and the direction of motion for each micro-machine using different dimensional parameters can give an idea of the efficiency for such machines with rigid tails.     

Dissipative particle dynamics simulations for fibre suspensions in newtonian and viscoelastic fluids

A versatile model of fibre suspensions in Newtonian and viscoelastic fluids has been developed using dissipative particle dynamics method. The viscoelastic fluid is modelled by linear chains with linear connector spring force (the Oldroyd-B model), which is known to be a reasonable model for the so-called Boger fluid (a dilute suspension of polymer in a highly viscous solvent). The numerical results are in excellent agreement with the analytical results of the Oldroyd-B model in simple shear flow. An effective meso-scale model of fibre in DPD is proposed and then incorporated with simple Newtonian fluid and our Boger fluid to enable entirely study rheological properties of fibre suspensions in both Newtonian and viscoelastic solvents. The numerical results are well compared with available experimental data and other numerical models.     

A coupled conduction convection and radiation problem for three insulated cables suspended in air

The coupled heat conduction, convection and radiation problem for three heated insulated cables suspended in air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. The main feature of the solution procedure is that the multi-phases are treated as a single computational domain with unknown interfacial boundary conditions. The temperature distribution in the heated metal cylinder, in the insulating layer and in the open air together with the convective flow pattern are obtained simultaneously.     

A finite element analysis of the flow past a sphere in a cylindrical tube: PTT fluid model

In this paper, we extend the explicitly elliptic momentum equation (EEME) formulation to a class of constitutive equations of the Maxwell type without the Newtonian solvent viscosity and apply it to a simplified Phan-Thien-Tanner (PTT) model. In the coupled finite element approach, the Galerkin method is applied to the modified momentum equations and the continuity equation, while the streamline upwind Petrov/Galerkin method is applied to the constitutive equations. The program is used to study the flow past a sphere placed at the centreline in a cylindrical tube using unstructured meshes. Our numerical results for the Maxwell model agree excellently with previous results from Lunsmann et al. (1989) up to a Weissenberg number of 2. New results for the PTT model are presented up to a Weissenberg number of about 4.5. It is found that the flow exhibits shear thinning behaviour in the drag force versus the Weissenberg number. The drag behaviour is remarkably similar to the viscosity flow curve.     

The role of hydrodynamic interaction in the locomotion of microorganisms

A general Boundary Element Method is presented and benchmarked with existing Slender Body Theory results and reflection solutions for the motion of spheres and slender bodies near plane boundaries. This method is used to model the swimming of a microorganism with a spherical cell body, propelled by a single rotating flagellum. The swimming of such an organism near a plane boundary, midway between two plane boundaries or in the vicinity of another similar organism, is investigated. It is found that only a small increase (less than 10%) results in the mean swimming speed of an organism swimming near and parallel to another identical organism. Similarly, only a minor propulsive advantage (again, less than 10% increase in mean swimming speed) is predicted when an organism swims very close and parallel to plane boundaries (such as a microscopic plate and (or) a coverslip, for example). This is explained in terms of the flagellar propulsive advantage derived from an increase in the ratio of the normal to tangential resistance coefficients of a slender body being offset by the apparently equally significant increase in the cell body drag. For an organism swimming normal to and toward a plane boundary, however, it is predicted that (assuming it is rotating its flagellum, relative to its cell body, with a constant angular frequency) the resulting swimming speed decreases asymptotically as the organism approaches the boundary.     

Boundary element method based on a new second kind integral equation formulation

A boundary integral equation (BIE) formulation for elasticity problems with mixed boundary conditions, proposed by Parton and Perlin (Mathematical Methods of the Theory of Elasticity, Mir, Moscow, 1984), is implemented in this paper using quadratic boundary elements. The formulation is specialised to Stokes flow problems by setting the Poisson ratio to 0·5 in the relevant kernels. The implementation is used to analyse non-trivial three dimensional problems in elasticity and Stokes flows. The results compare well with those obtained by a direct boundary element method. An outline of the extension of the formulation to non-linear problems is also given.     

Linear viscoelastic properties of bovine brain tissue in shear

We report the results from a series of rheological tests of fresh bovine brain tissue. Using a standard Bohlin VOR shear rheometer, shear relaxation and oscillating strain sweep experiments were performed on disks of brain tissue 30 mm in diameter, with a thickness of 1.5-2 mm. The strain sweep experiment showed that the viscoelastic strain limit is of the order of 0.1% strain. Shear relaxation data do not indicate the presence of a long-term elastic modulus, indicating fluid-like behavior. A relaxation spectrum was calculated by inverting the experimental data and used to predict oscillatory response, which agreed well with measured data.     

Completed double layer boundary element algorithm in many-body problems for a multi-processor: an implementation on the CM-5

Alternative implementations on the CM-5 multi-processor of the completed double layer boundary element method for N-body problems in Stokes flow are presented. The implementations use message passing to dynamically allocate computational tasks to the processing nodes. The complexity and computational cost of the method is discussed, and timing results are given for a 16 node and a 32 node partition. The algorithm is applied to model suspensions of up to 5000 particles in a random cluster.This research is supported by the Australian Research Council.     

A domain decomposition implementation of the SIMPLE method with PVM

A parallel implementation of a finite volume method for the solution of the Navier-Stokes equations on a distributed computing environment through Parallel Virtual Machine (PVM) is reported. The numerical method is implicit and is based on the SIMPLE algorithm in which the system of equations is discretised using a hybrid scheme. An Alternative Direction Implicit (ADI) scheme, and the Thomas tri-diagonal solver are used to solve the algebraic equations. The parallelization of the program is implemented by a domain decomposition strategy on MIMD parallel architectures using PVM platform. The program was tested for laminar flow in a cavity. The parallelisation strategy and performance are discussed. It is concluded that the efficiency is strongly dependent on the grid size, block numbers and the number of processors. Different strategies to improve the computational efficiency are proposed.