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The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water free-surface and the two-dimensional second-order solid elastostatic equations for the bed deformation. Second, to develop a robust hybrid finite element/finite volume method for solving free-surface runup flow problems over deformable beds. The authors combine the finite volume for free-surface flows and the finite element method for bed elasticity.

The authors propose a new model for wave runup by static deformation on seabeds. The model consists of the depth-averaged shallow water system for the water free-surface coupled to the second-order elastostatic formulation for the bed deformation. At the interface between the water flow and the seabed, transfer conditions are implemented. Here, hydrostatic pressure and friction forces are considered for the elastostatic equations, whereas bathymetric forces are accounted for in the shallow water equations. As numerical solvers, the authors propose a well-balanced finite volume method for the flow system and a stabilized finite element method for elastostatics.

The developed coupled depth-averaged shallow water system and second-order solid elastostatic system is well suited for modeling wave runup by deformation on seabeds. The derived coupling conditions at the interface between the water flow and the bed topography resolve well the condition transfer between the two systems. The proposed hybrid finite volume element method is accurate and efficient for this class of models. The novel technique used for wet/dry treatment accurately captures the moving fronts in the computational domain without generating nonphysical oscillations. The presented numerical results demonstrate the high performance of the proposed methods.

Enhancing modeling and computations for wave runup problems is at an early stage in the literature, and it is a new and exciting area of research. To the best of our knowledge, solving wave runup problems by static deformation on seabeds using a hybrid finite volume element method is presented for the first time. The results of this research study, and the research methodologies, will have an important influence on a range of other scientists carrying out research in related fields.

This paper sets out to implement bounded high‐order (HO) resolution schemes in a hybrid finite volume/finite element method for the solution of the radiative transfer equation.

The hybrid finite volume/finite element method had formerly been developed using the step scheme, which is only first‐order accurate, for the spatial discretization. Here, several bounded HO resolution schemes, namely the MINMOD, CLAM, MUSCL and SMART schemes, formulated using the normalized variable diagram, were implemented using the deferred correction procedure.

The results obtained reveal an interaction between spatial and angular discretization errors, and show that the HO resolution schemes yield improved accuracy over the step scheme if the angular discretization error is small.

Although the HO resolution schemes reduce the spatial discretization error, they do not influence the angular discretization error. Therefore, the global error is only reduced if the angular discretization error is also small.

The use of HO resolution schemes is only effective if the angular refinement yields low‐angular discretization errors. Moreover, spatial and angular refinement should be carried out simultaneously.

The paper extends a methodology formerly developed in computational fluid dynamics, and aimed at the improvement of the solution accuracy, to the hybrid finite volume/finite element method for the solution of the radiative transfer equation.

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.

In the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).

Numerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.

To the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

To improve flow solutions on meshes with cells/elements which are distorted/ non‐orthogonal.

The cell‐centred finite volume (FV) discretisation method is well established in computational fluid dynamics analysis for modelling physical processes and is typically employed in most commercial tools. This method is computationally efficient, but its accuracy and convergence behaviour may be compromised on meshes which feature cells with non‐orthogonal shapes, as can occur when modelling very complex geometries. A co‐located vertex‐based (VB) discretisation and partially staggered, VB/cell‐centred (CC), discretisation of the hydrodynamic variables are investigated and compared with purely CC solutions on a number of increasingly distorted meshes.

The co‐located CC method fails to produce solutions on all the distorted meshes investigated. Although more expensive computationally, the co‐located VB simulation results always converge whilst its accuracy appears to grace‐fully degrade on all meshes, no matter how extreme the element distortion. Although the hybrid, partially staggered, formulations also allow solutions on all the meshes, the results have larger errors than the co‐located vertex based method and are as expensive computationally; thus, offering no obvious advantage.

Employing the ability of the VB technique to resolve the flow field on a distorted mesh may well enable solutions to be obtained on complex meshes where established CC approaches fail

This paper investigates a range of cell centred, vertex based and hybrid approaches to FV discretisation of the NS hydrodynamic variables, in an effort characterize their capability at generating solutions on meshes with distorted or non‐orthogonal cells/elements.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The extrudate swell phenomenon is analysed by solving, simultaneously, the Navier‐Stokes equations along with the continuity equation by means of a finite volume method. In this work, the planar jet flows of incompressible viscous Newtonian and power‐law fluids for Reynolds numbers as high as 75 are simulated. The method uses the velocity components and pressure as the primitive variables and employs an unstructured triangular grid and triangular or polygonal control volume for each separate variable. The numerical results show good agreement with previously reported experimental and numerical results. Shear thickening results in an increase in swelling ratio, while the introduction of surface tension results in a describes in swelling ratio.

The finite volume method for radiative heat transfer calculations has been parallelized using two strategies, the angular domain decomposition and the spatial domain decomposition. In the first case each processor performs the calculations for the whole domain and for a subset of control angles, while in the second case each processor deals with all the control angles but only treats a spatial subdomain. The method is applied to three‐dimensional rectangular enclosures containing a grey emitting‐absorbing medium. The results obtained show that the number of iterations required to achieve convergence is independent of the number of processors in the angular decomposition strategy, but increases with the number of processors in the domain decomposition method. As a consequence, higher parallel efficiencies are obtained in the first case. The influence of the angular discretization, grid size and absorption coefficient of the medium on the parallel performance is also investigated.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.