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Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

A fully coupled numerical model to simulate the complex behaviour of soil deformation, water flow, airflow, and heat flow in porous media is developed. The following thermal effects are taken into account: heat transfer through conduction and convection, flow, as well as viscosity and density variation of the fluids due to temperature gradients. The governing equations in terms of soil displacements, water and air pressures, and temperature are coupled non‐linear partial differential equations and are solved by the finite element method. Two examples are presented to demonstrate the model performances.

This paper presents the physical, mathematical and numerical models forming the main structure of the numerical analysis of the thermal, hydral and mechanical behaviour of normal, high‐performance concrete (HPC) and ultra‐high performance concrete (UHPC) structures subjected to heating. A fully coupled non‐linear formulation is designed to predict the behaviour, and potential for spalling, of heated concrete structures for fire and nuclear reactor applications. The physical model is described in more detail, with emphasis being placed upon the real processes occurring in concrete during heating based on tests carried out in several major laboratories around Europe as part of the wider high temperature concrete (HITECO) research programme. A number of experimental and modelling advances are presented in this paper. The stress‐strain behaviour of concrete in direct tension, determined experimentally, is input into the model. The hitherto unknown micro‐structural, hydral and mechanical behaviour of HPC/UHPC were determined experimentally and the information is also built into the model. Two examples of computer simulations concerning experimental validation of the model, i.e. temperature and gas pressure development in a radiatively heated HPC wall and hydro‐thermal and mechanical (damage) performance of a square HPC column during fire, are presented and discussed in the context of full scale fire tests done within the HITECO research programme.

Extends the stress update algorithm and the tangent operator recently proposed for generalized plasticity by De Borst and Heeres to the case of partially saturated soils, where on top of the hydrostatic and deviatoric components of the (effective) stress tensor suction has to be considered as a third independent variable. The soil model used for the applications is the Bolzon‐Schrefler‐Zienkiewicz model, which is an extension of the Pastor‐Zienkiewicz model to partial saturation. The algorithm is incorporated in a code for partially saturated soil dynamics. Back calculation of a saturation test and simulation of surface subsidence above an exploited gas reservoir demonstrate the advantage of the proposed algorithm in terms of iteration convergence of the solution.

Using finite element (FE) method corrects the microstress field resulting from the theory of homogenization in the region of composite in vicinity of the boundary. Obtains the corrected microstress field via an unsmearing procedure based on the known global solution and local peturbation. Analyses two examples: near a free boundary and next to a constrained border. FE models are constructed using both commercial FE code and the authors’ program for homogenization with some interfacing procedures. Shows qualitative results of computations and estimates influence on the microstress description of the local perturbation near the boundary.

The stress recovery procedures discussed in the present paper refer to a multi‐layered element of assembled Timoshenko beam elements. Directly calculated stresses for a multi‐layered beam model strongly depend on properties of the approximation functions, and are unrealistic. Thus, an enhanced procedure which circumvents the limitations of the interface variables model, and hierarchical model is proposed. Each material layer of the beam element is covered by one quadrilateral 9‐node element, providing a parabolic approximation of displacements. The stresses are evaluated using 2 × 2 Gauss points, projected to corner nodes, and smoothed within material layers. Numerical calculations show very good accordance of stresses yielded by this procedure with 2D results.

This paper presents a mathematical model for the analysis of cohesive fracture propagation through a non‐homogeneous porous medium. Governing equations are stated within the frame of Biot's theory, accounting for the flow through the solid skeleton, along the fracture and across its sides toward the surrounding medium. The numerical solution is obtained in a 2D context, exploiting the capabilities of an efficient mesh generator, and requires continuous updating of the domain as the fractures enucleate and propagate. It results that fracture paths and their velocity of propagation, usually assumed as known, are supplied directly by the model without introducing any simplifying assumption.

This paper presents a multi‐level frontal algorithm and its implementation and applications on parallel computation. A multi‐frontal program is given which may be used for unsymmetric finite element matrix equations. The parallel program is developed on a cluster of workstations. The PVM (parallel virtual machine) system is used to handle communications among networked workstations. The method has advantages such as numbering of the finite element mesh in an arbitrary manner, simple programming organisation, smaller core requirements and computation times. An implementation of this parallel method on workstations is discussed, the speedup and efficiency of this method being demonstrated and compared with general domain decomposition method based on band matrix methods by numerical examples.

In this paper, an algebraic multigrid method is suggested for the fully coupled thermo‐hydro‐mechanical analysis in deforming porous media. The mathematical model consists of balance equations of mass, linear momentum and energy and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressure, gas pressure and displacement. The gas phase is considered to be an ideal gas composed of dry air and vapour, which are regarded as two miscible species. Phase change as well as heat transfer through conduction and convection and latent heat transfer (evaporation‐condensation) are taken into account. The problem hence presents an interaction problem between several fields with very different response characteristics. Further, the matrices are non‐symmetric and not diagonally dominated. Numerical examples are given to demonstrate the efficiency of this method.

This paper aims to introduce modeling, numerical simulation and convergence analysis of the problem of nanoparticles’ transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles’ concentration, deposited nanoparticles’ concentration on the pore-walls and entrapped nanoparticles concentration in pore-throats.

A nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, and then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated.

Three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions were stated and proved. The theorem is proved by induction states that after a number of iterations, the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, whereas the error estimations are presented in a table for different values of the number of time steps, number of iterations and mesh size.

The domain of the computations is relatively small; however, it is straightforward to extend this method to the oil reservoir (large) domain by keeping similar definitions of CFL number and other physical parameters.

The model of the problem under consideration has not been studied before. Also, both solution technique and convergence analysis have not been used before with this model.