Oubay Hassan

Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications

This papers summarizes two linear tetrahedral FE formulations that have been recently proposed to overcome volumetric locking in nearly incompressible explicit dynamic applications. In particular, the average nodal pressure (ANP) technique described by Bonet and Burton (Communications in Numerical Methods in Engineering 1998; 14:437–449) is briefly reviewed. In addition, the split-based formulation proposed by Zienkiewicz et al. (International Journal for Numerical Methods in Engineering 1998; 43:565–583) is described here in terms of a time integration of the nodal Jacobian. This will make it simple to compare both techniques and will enable a new combined method to be presented. The paper will then discuss the stability constraints that each technique places on the timestep size. A von-Neuman stability analysis on simple 1-D uniform meshes will show that the ANP element permits the use of much larger timesteps than the split based formulations. Finally, numerical examples corroborating in 3-D this analytical conclusions will be presented. Copyright

Unsteady flow simulation using unstructured meshes

Transient flows involving moving boundaries are more difficult to simulate, as the geometry of the computational domain changes with time. Regardless of the changes occurring in the solution, the mesh must be modified during the computation in order to accommodate the changes in the geometry. Although the literature on this subject describes a number of different approaches for handling this type of problem, the approach followed in this paper is to use unstructured mesh methods. We consider, initially, the simulation of inviscid two-dimensional transient flows involving moving bodies, employing an extension of adaptivity procedures which have been successfully used for steady state problems with the error estimation procedure coupled to an automatic triangular mesh generator. This approach is extended to produce a three-dimensional capability using tetrahedral meshes. A number of examples are included to illustrate the numerical performance of these methods.

Investigations into the applicability of adaptive finite element methods to two-dimensional infinite Prandtl number thermal and thermochemical convection

An adaptive finite element procedure is presented for improving the quality of solutions to convection-dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation-based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well-established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid-based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.

Adaptive finite element methods in geodynamics: Convection dominated mid-ocean ridge and subduction zone simulations

Purpose – The purpose of this paper is to present an adaptive finite element procedure that improves the quality of convection dominated mid-ocean ridge (MOR) and subduction zone (SZ) simulations in geodynamics. Design/methodology/approach – The method adapts the mesh automatically around regions of high-solution gradient, yielding enhanced resolution of the associated flow features. The approach utilizes an automatic, unstructured mesh generator and a finite element flow solver. Mesh adaptation is accomplished through mesh regeneration, employing information provided by an interpolation-based local error indicator, obtained from the computed solution on an existing mesh. Findings – The proposed methodology works remarkably well at improving solution accuracy for both MOR and SZ simulations. Furthermore, the method is computationally highly efficient. Originality/value – To date, successful goal-orientated/error-guided grid adaptation techniques have, to the knowledge, not been utilized within the field of geodynamics. This paper presents the first true geodynamical application of such methods.

An enhanced Immersed Structural Potential Method for fluid-structure interaction

Within the group of immersed boundary methods employed for the numerical simulation of fluid-structure interaction problems, the Immersed Structural Potential Method (ISPM) was recently introduced (Gil et al., 2010) [1] in order to overcome some of the shortcomings of existing immersed methodologies. In the ISPM, an incompressible immersed solid is modelled as a deviatoric strain energy functional whose spatial gradient defines a fluid-structure interaction force field in the Navier-Stokes equations used to resolve the underlying incompressible Newtonian viscous fluid. In this paper, two enhancements of the methodology are presented. First, the introduction of a new family of spline-based kernel functions for the transfer of information between both physics. In contrast to classical IBM kernels, these new kernels are shown not to introduce spurious oscillations in the solution. Second, the use of tensorised Gaussian quadrature rules that allow for accurate and efficient numerical integration of the immersed structural potential. A series of numerical examples will be presented in order to demonstrate the capabilities of the enhanced methodology and to draw some key comparisons against other existing immersed methodologies in terms of accuracy, preservation of the incompressibility constraint and computational speed.

A low–order unstructured–mesh approach for computational electromagnetics in the time domain

Maxwells curl equations in the time domain are solved using an explicit linear finite–element approach implemented on unstructured tetrahedral meshes. For the simulation of scattering problems, a perfectly matched layer is added at the artificial far–field boundary, created by the truncation of the physical domain prior to the numerical solution. The complete solution procedure is parallelized. The computational challenges that are encountered when attempting simulations at higher frequencies suggest that the implementation of a hybrid algorithm could have certain advantages. The hybrid approach adopted uses a combination of the finite–element procedure and the well–known low operation count/low storage finite–difference time–domain method. Examples are included to demonstrate the numerical performance of the techniques that are described.

Topology Abstraction of Surface Models for Three-Dimensional Grid Generation

Surface grid generation and the subsequent volume grid generation is the key to unstructured grid-based computational simulation. The baseline entities of the surface models under consideration for use with the proposed surface grid generator are curves and surfaces. There is a necessity to establish a topology relation between the curves and surfaces, prior to a surface gridding process. The present paper addresses issues related to this topology abstraction. Effort has also been made to generally discuss how to bridge the gap between CAD modelling and surface gridding. The proposed procedures have been incorporated into an Interactive Geometry Utility Environment (IGUE). The IGUE is a sub-environment of a Parallel Simulation User Environment (PSUE), which has been developed for unstructured grid-based computational simulation. Arbitrary computer application software can be integrated into the environment to provide a multi-disciplinary engineering analysis capability within one unified computational framework. Examples of computational applications have been included in the present paper, to demonstrate the use of the PSUE and geometry preparation procedure with an emphasis of topology abstraction.

A Review of the Development and Applications of the Cuckoo Search Algorithm

The cuckoo search is a relatively new gradient free optimization algorithm, which has been growing in popularity. The algorithm aims to replicate the particularly aggressive breeding behavior of cuckoos and it makes use of the Levy flight, which is an efficient search pattern. In this chapter, the original development of the cuckoo search is discussed and a number of modifications that have been made to the basic procedure are compared. A number of applications of the cuckoo search are described and some possible future developments of the cuckoo search algorithm are summarized.

Smooth Delaunay-Voronoï Dual Meshes for Co-Volume Integration Schemes

Yee’s scheme for the solution of the Maxwell equations [1] and the MAC algorithm for the solution of the Navier–Stokes equations [2] are examples of co-volume solution techniques. Co-volume methods, which are staggered in both time and space, exhibit a high degree of computationally efficiency, in terms of both CPU and memory requirements compared to, for example, a finite element time domain method (FETD). The co-volume method for electromagnetic (EM) waves has the additional advantage of preserving the energy and, hence, maintaining the amplitude of plane waves. It also better approximates the field near sharp edges, vertices and wire structures, without the need to reduce the element size. Initially proposed for structured grids, Yee’s scheme can be generalized for unstructured meshes and this will enable its application to industrially complex geometries [3]. Despite the fact that real progress has been achieved in unstructured mesh generation methods since late 80s, co-volume schemes have not generally proved to be effective for simulations involving domains of complex shape. This is due to the difficulties encountered when attempting to generate the high quality meshes that satisfying the mesh requirements necessary for co-volume methods. In this work, we concentrate on EM wave scattering simulations and identify the necessary mesh criteria required for a co-volume scheme. We also describe several approaches for generating two-dimensional and three-dimensional meshes satisfying these criteria. Numerical examples on the scattering of EM waves show the efficiency and accuracy that can be achieved with a co-volume method utilising the proposed meshing scheme.

The development of an hp -adaptive finite element procedure for electromagnetic scattering problems

The development of an hp-adaptive edge element procedure for the simulation of two-dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described. The interest in this paper is the accurate prediction of the scattering width for simulations involving a single frequency incident wave. Sharp, constant free, error bounds on the scattering width output are obtained by employing an a posteriori procedure. The elemental contributions to the bound gap are used to drive an adaptive solution process, with the aim of improving the accuracy of the computed output. A novel extension to previous work, is the proposed reduced-order model for the economical calculation of the bound gap for all viewing angles of the scattering width. The theory is supported by numerical examples. This paper constitutes the full length version of the paper that was originally submitted in an extended abstract form for the 2002 Robert J. Melosh medal competition for the best student paper on finite element analysis.