International Journal of Computational Engineering Science

A parallel computational strategy based on a distributed-memory environment is presented for simulating combined finite-discrete element systems comprising a large number of separate bodies. An explicit central difference scheme is used for the temporal integration of the governing equations. Some key issues, such as partitioning algorithms, load balance schemes and contact handling methods are discussed. A dual-level domain decomposition strategy is proposed to perform the dynamic domain decomposition. An implementation of this proposed strategy on cluster computing systems is described. MPI is adopted as the message passing library in this implementation. Numerical examples show that this implementation is suitable for simulating large scale problems. A dragline bucket filling model with 3 million degrees of freedom is built to demonstrate the parallel efficiency and scalability on a PC cluster.

It is very much desired to have subsystems resulting from finite difference modeling of partial differential equations where the matrices are block diagonal as the work required to solve such subsystems is reduced greatly. The simulation nodes in the red/black order and bound by the usual five-point finite difference molecule have their coefficient matrix with such pattern. In this paper, we attempt to have such subsystems for the coefficient matrix for the nodes bound by the nine-point molecule. This can be accomplished by the knight's move. A comparison of the performances between this model and the usual nine-point model is given. We note that the coefficient matrix favors the acceleration of the basic iterative methods.

Mesomechanical constitutive modeling is applied to modeling cumulative damage and necking. The model is applied to the description of necking in specimens under uniaxial tension, and compared with experimental results received with specimens of pure iron and Fe-2.75wt%Si alloy. The process is modeled as a change in the structure; i.e. as a successive loss of continuity of the substructure of barriers resisting plastic deformation. It is shown that this model can be used for the evaluation of continuum damage, and of the description of: (i) the stress-strain diagrams up to rupture, (ii) the effect of the length of the specimen, (iii) the development of the form of the neck and its final form at rupture, (iv) the creation of internal residual energy.

Two higher-order compact finite difference approaches, the Hermitian and the Lax-Wendroff are examined by applying them to the viscous Burgers' equation. The difference equations obtained by the two methods were integrated in time through the third-order Strong-Stability-Preserving Runge-Kutta scheme. Absolute errors are computed by using an exact solution. The results are also compared with a second order central difference scheme. The Hermitian approach is far easier to implement. On uniform grids the Lax-Wendroff scheme produces smaller errors during the initial stages, but both methods are equally good for larger durations of integration. The convergence rate of the Hermitian scheme is slightly higher than the Lax-Wendroff scheme although both are of fourth order. Both schemes are unstable beyond a certain step size in time and space. When numerical boundary conditions are imposed, second-order conditions produce the best results whereas linear extrapolation proved to be the worst. It was also observed that large domains were required to implement the numerical boundary conditions properly. There was no detrimental effect on the accuracy of the results obtained through either of the two schemes when the size of the domain was greatly increased. Both schemes showed remarkable improvement in accuracy when clustered grids were employed. However much smaller time steps are required for stable solutions.

This paper presents an efficient, simple and new method for solving Economic Dispatch (ED) problem with line flow constraints through the application of Evolutionary Programming (EP). The controllable system quantities in the base-case state are optimized to minimize some defined objective function subject to the base-case operating constraints. A 10-bus system is taken for investigation. The ED results obtained using EP are compared with those obtained using quadratic programming. The investigations reveal that the proposed algorithm is relatively simple, reliable, efficient and suitable for on-line applications.

This work aim to present a numerical method for solving ideal Magnetohydrodynamic equilibrium equations for Ultra Low Aspect Ratio Tokamak with pinch. Discretization and acceleration techniques are discussed and applications to realistic tokamak configurations are shown.

This paper depicts numerical analysis on impulse turbine of 0.6 m diameter with fixed guide vanes for wave energy conversion. From the earlier investigations, it is found that one of the reasons for the mismatch between computed and experimental data is due to neglecting tip clearance effect. Hence, a three-dimensional (3-D) model with tip clearance has been generated with structured grids to predict the internal flow and performance of the turbine. As a result, it is found that the comparison between computed and experimental data is good. Computation has been carried out for various tip clearances to understand the effect of tip clearance leakage flow on such unconventional turbine. The change in flow behavior in the turbine blade passage due to tip clearance flow has been studied by comparing the results with without tip clearance, which is impossible by experiments. It is predicted that the efficiency of the turbine has been reduced about 4%, due to tip clearance flow at higher flow coefficients.

In the companion papers [1,2], authors introduced the concepts of k-version of finite element method and k, hk, pk, hkp-processes of the finite element method for boundary value problems described by self-adjoint and non-self adjoint operators using Ĥ^k,p(Ω) spaces with specific details including numerical studies for weak forms and least square processes. It was demonstrated that a variationally consistent (VC) weak form is possible when the differential operator is self-adjoint, however, in case of non-self-adjoint operators the weak forms are variationally inconsistent (VIC) which lead to degenerate computational processes that can produce spurious oscillations in the computed solutions. In this paper we demonstrate that when the boundary value problems are described by non-linear differential operators, Galerkin processes and weak forms can never be variationally consistent and hence result in degenerate computational processes and suffer from same problems as in the case of non-self-adjoint operators plus more due to the presence of non-linearity. In the proposed mathematical and computational frame-work, upwinding methods are neither required nor used. The k-version of FEM over Ĥ^k,p spaces for the Galerkin method with weak forms, though meritorious in comparison to Ĥ^1,p(Ω) spaces, but it is plagued due to problems arising from variational inconsistency.

We demonstrate that the order of the space k in Ĥ^k,p(Ω) Hilbert spaces is an independent parameter in all computational processes in addition to the characteristic length h of the discretizations and the degree p of the local approximations. This gives rise to k-version of finite element method and thus, associated k, hk, pk, and hpk processes. The global differentiability of a finite element solution is only dependent on k. The h, p and hp-adaptive processes can not yield global differentiability of order higher than the order of the space containing the local approximations. It is shown that variational consistency of the integral forms and higher order global differentiability of a computed solution by increasing k in Ĥ^k,p(Ω) spaces are two most important features of mathematical and computational frame work if one wishes the computational process to (1) be non-degenerate and (2) yield solution with the same characteristics in terms of global differentiability as the theoretical solution.

In this paper, we illustrate the important variational aspects of the least squares finite element processes for non-linear partial differential equations of stationary processes. Variationally consistent least squares finite element method (LSFEM) using p-version basis functions in Ĥ^k,p(Ω) spaces provides a remarkably general framework for numerical simulation of any BVP described by non-linear differential operators in which any desired order of global smoothness or global differentiability is achievable. The proposed mathematical framework indeed allows one to numerically simulate characteristics of the theoretical solutions of any non-linear BVP regardless of the nature of the differential operator. Stationary one-dimensional Burgers equation is used as a model problem to present supporting numerical studies. Many issues and concepts related to upwinding methods and the behaviors of commonly encountered problems in Galerkin method for non-linear differential operators in BVP are considered, discussed and explained.

A numerical method is presented to simulate dendritic crystal growth on a fixed mesh. The hyperbolic convective equation for the continuous phase field which identifies the solid and liquid phases is solved by the least-squares finite element method, and the heat conduction equation for the temperature field is solved by the Galerkin finite element method. Without special treatments this method can handle complicated interfacial shapes and physical features.

Switched reluctance motor (SRM) has been the subject of many investigations in recent years. The SR technology is a feasible and economically advantageous option for future electromotor production in Iran.

However, computational intensive analysis methods (e.g. finite element (FE) analysis) and iterative search for optimal values of design parameters (e.g. genetic algorithms) cannot be jointly carried out online. In this paper, we outline a three-stages design process for determination of the optimal electromotor specifications. In the first stage, FE analysis is used for computation of performance characteristics associated with various design parameters. Next, an interpolator is trained to establish a mapping from design parameters to performance characteristics. Finally the latter values are optimized via multicriteria genetic algorithm.

The steady-state laminar and incompressible vapor flow in four partially-heated concentric annular heat pipe (CAHP) is studied. The governing equations are solved numerically, using finite volume approach based on collocated grids. The first order upwind scheme and the QUICK scheme are used in the numerical solution. The vapor pressure distributions and velocity profiles along the annular vapor space are predicted for a number of test cases in the range of low to moderate radial Reynolds numbers. The results show that in a partially-heated annular heat pipe, as the radial Reynolds number increases, a number of recirculation zones may be created at both ends of the evaporator and condenser sections. The size and location of the recirculation zones are predicted and their effects on the performance of an annular heat pipe are discussed qualitatively.

In this paper, inelastic pile-soil-structure interaction for dynamic analysis is formulated by coupling finite element and boundary element methods. Linear beam-column finite elements are used to model the piles and structural elements. The continuum is assumed to be elastic and an efficient step by step time integration scheme is implemented by using half space integral formulation. Inelastic modeling of soil media is done by a rational approximation to continuum with nonlinear interface springs along the piles. Modified Özdemir's inelastic model is implemented and systems of equations are coupled for piles and pile groups. By using this mixed type of formulation, it is possible to get computationally most efficient and accurate results. In order to verify the proposed formulation, the result of a reported full-scale statnamic load tests are compared.