Mesh Adaptation Strategy Research Articles

Influence of current diffusion in superconducting magnet fabricated by high stabilizer aluminum on quench propagation

The development of conductors with an aluminum super-stabilizer was proposed for some applications of accelerator detector magnets for high-energy physics and superconducting magnet storage energy devices. The conductors are designed with the cryogenics stabilization by using a large amount of low resistance aluminum stabilizer. However, it has induced to some new problems. One of these is the effect of the current redistribution between superconducting strands and stabilizer on the quench propagation and stability. In this study, we assume a superconducting magnet to be immersed in liquid helium. A quasi-three-dimensional model is proposed to study thermal diffusion in superconducting magnet and current diffusion is based on the solution of Maxwell's equation. The uniform temperature distribution in the cross-sectional area of conductor is taken into account due to the high thermal conduction of stabilizer and small size compared with the length. An adaptive mesh scheme COLSYS is employed to capture the solution of temperature and current in the front of normal position. The computational model includes nonlinear thermal and electrical characteristics in superconducting strands and aluminum stabilizer and heat transfer of helium. The influence of current re-distribution between stabilizer and superconducting strands on the quench is studied.

An optimal design system for spot welding locations

An optimal design system using adaptive meshes for spot welding locations in shell structures has been developed. In order to find out the optimal spot welding locations, iterative finite element analysis is necessary. The optimization process also requires that every mesh employed should be as uniform as possible in its quality. For this purpose an h-version of adaptive meshing scheme based on a background mesh has been proposed. The background meshes ares constructed with quadrilateral elements on three-dimensional surfaces by using a domain decomposition method. Sample problems are solved to demonstrate the effectiveness and capability of the developed system.

Adaptive finite element analysis of mode I fracture in cement‐based materials

AbstractMicroscopic studies using advanced experimental techniques have provided better insight into the fracture mechanisms in cement‐based materials. A clear understanding of fracture mechanisms is critical for the development of rigorous computational models for analysing fracture. Fracture analysis is usually carried out by finite element method. Accuracy of FE analysis depends upon the choice of mesh and for the predictions to be reliable, discretization errors are to be minimized. In cohesive crack approach, the non‐linearity is limited to the boundary conditions along the geometric discontinuity while the bulk of the material retains its elastic nature. The paper presents a mesh‐adaptive strategy based on ZZ error estimator to model discrete crack propagation in cement‐based materials. Examples of simulations have demonstrated the potential of the mesh‐adaptive technique in modelling the evolution of the localized strain profiles as well as failure of concrete test specimen. Copyright © 2001 John Wiley & Sons, Ltd.

Adaptive meshing for two-dimensional thermoelastic problems using Hermite boundary elements

In the present work, error indicators for the potential and elastostatic problems are used in a combined fashion to implement an adaptive meshing scheme for the solution of two-dimensional steady-state thermoelastic problems using the Boundary Element Method. These error indicators exploit in their formulation the possibility of generating two different numerical solutions from just one analysis using Hermite elements. The first solution is the standard one obtained from an analysis using Hermite elements. The second is a “reduced” solution obtained representing the field variables inside an element using some of the degrees of freedom of the Hermite element together with Lagrangian shape functions. The basic idea behind the computation of the error indicator is to compare these two solutions, on an element by element basis, to obtain an estimate of the magnitude of the error in the numerical solution corresponding to the Hermite elements. In this sense, it is assumed that the bigger the difference between these two solutions, the bigger the error in the original solution with Hermite elements. Since the thermoelastic problem in its uncoupled fashion is considered, the former approach is applied to both problems, heat conduction and thermoelastic. Since both numerical solutions for each one of these problems are obtained from just one analysis, the computational cost of the proposed error indicators is very low.

Parallel Adaptive Mesh Refinement with Load Balancing on Heterogeneous Cluster

The efficient solution of many large-scale scientific calculations depends on unstructured mesh strategies. For example, problems where the solution changes rapidly in small regions of the domain require an adaptive mesh strategy. In this paper we discuss the main algorithmic issues to be addressed with an integrated approach to solving these problems on heterogeneous parallel architectures. We review new parallel algorithms to solve two significant problems that arise in this context: the mesh refinement, partitioning and load balancing. The procedure to support parallel refinement and redistribution of two dimensional unstructured finite element meshes on heterogeneous computers is presented. The solver is based on the parallel conjugate gradient method. The error indicator and the resulting refinement parameters are computed in parallel.

An h-adaptive finite element method with highly stretched elements for compressible Navier–Stokes equations

A technique of approximating boundary layers in viscous flow simulations with significantly stretched elements is presented. The elements are introduced automatically within a framework of a general mesh adaptation strategy. The discrete equations are effectively solved with a GMRES procedure preconditioned by the block Jacobi or Gauss–Seidel iterations. Numerical examples of flows with shock-boundary layer interaction and the Reynolds number up to 2·10 6 are presented.

Discrete Hamilton's equations for arbitrary Lagrangian–Eulerian dynamics of viscous compressible flow

A number of different arbitrary Lagrangian–Eulerian (ALE) formulations of continuum fluid and solid dynamics problems have been developed, to address applications where more conventional Lagrangian or Eulerian modeling techniques are difficult to apply. In general these ALE formulations are based on finite difference or weighted residual finite element solutions of the partial differential equations for the system. An alternative, energy based ALE model for fluid dynamics simulations may be obtained, by direct application of Hamilton's canonical equations to a finite element discretization of an open, deforming control volume. Formulated in terms of convected coordinates and incorporating an adaptive mesh scheme, this modeling approach yields a simple but general description of viscous compressible flows. Numerical application of the method demonstrates accurate results in the solution of several shock problems, whether the calculations are performed using a Lagrangian, an Eulerian, or an ALE mesh.

Three-dimensional welding analysis using an adaptive mesh scheme

One major problem arising in finite element analysis of welding is the long computer times required for a complete three-dimensional analysis. An adaptive strategy for coupled thermo-mechanical analysis of welding is applied in order to reduce the computer time. The paper describes a generic posteriori error formulation that evaluates both the thermal and the mechanical error distribution. It is combined with a hierarchic remeshing strategy using a so-called graded element. The error indicator together with the known movement of the local heat source is used to predict areas of refinement. An increased accuracy is obtained with a reduced computational effort.

Mesh adaptation strategies for shallow water flow

We show how the mesh adaptation technique can be exploited for the numerical simulation of shallow water flow. The shallow water equations are numerically approximated by the Galerkin finite element method, using linear elements for the elevation field and quadratic elements for the unit width discharge field; the time advancing scheme is of a fractional step type. The standard mesh refinement technique is coupled with the numerical solver; movement and elimination of nodes of the initial triangulation is not allowed. Two error indicators are discussed and applied in the numerical examples. The conclusion focuses the relevant advantages obtained by applying this adaptive approach by considering specific test cases of steady and unsteady flows

Surface mesh quality evaluation

This paper proposes a method to evaluate the size quality as well as the shape quality of constrained surface meshes, the constraint being either a given metric or the geometric metric associated with the surface geometry. In the context of numerical simulations, the metric specifications are those related to the finite element method. The proposed measures allow to validate the surface meshes within a general mesh adaption scheme, the metric map being usually provided via an a posteriori error estimate. Several examples of surface meshes are proposed to illustrate the relevance of the approach. Copyright © 1999 John Wiley & Sons, Ltd.

Surface mesh quality evaluation

This paper proposes a method to evaluate the size quality as well as the shape quality of constrained surface meshes, the constraint being either a given metric or the geometric metric associated with the surface geometry. In the context of numerical simulations, the metric specifications are those related to the finite element method. The proposed measures allow to validate the surface meshes within a general mesh adaption scheme, the metric map being usually provided via an a posteriori error estimate. Several examples of surface meshes are proposed to illustrate the relevance of the approach. Copyright © 1999 John Wiley & Sons, Ltd.

Error estimation for boundary element method

In this paper, six error indicators obtained from dual boundary integral equations are used for local estimation, which is an essential ingredient for all adaptive mesh schemes in BEM. Computational experiments are carried out for the two-dimensional Laplace equation. The curves of all these six error estimators are in good agreement with the shape of the error curve. The results show that the adaptive mesh based on any one of these six error indicators converges faster than does equal mesh discretization.

Mesh gradation control

This paper gives a procedure to control the size variation in a mesh adaption scheme where the size specication (the so-called control space) is used to govern the mesh generation stage. The method consists in replacing the initial control space by a reduced one by means of size or metric. It allows to improve, a priori, the quality of the adapted mesh and to speed up the adaption procedure. Several numerical examples show the eciency of the reduction scheme. ? 1998 John Wiley & Sons, Ltd.

A parallel and adaptive continuation method for semilinear bifurcation problems

In this paper we propose an efficient continuation method for the following of solution branches of parametrized semilinear elliptic problems. In order to limit the time required for the computation of a whole branch of accurate solutions, we combine a mesh adaptation strategy with parallel programming on a computer network. The first computer is devoted to the continuation on a coarse mesh, the others share out the correction of every roughly generated solution on a sequence of a posteriori refined meshes. A numerical example illustrating the performance of the method is given.

Tetrahedral and hexahedral mesh adaptation for CFD problems

This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.

Qualité des maillages de surfaces

This Note deals with the size quality as well as the shape quality of constrained surface meshes, the constraint being either the metric associated with the domain of definition of the surface or the metric associated with the surface geometry. The shape requirements are those of the finite element method. The proposed measures allow to validate the surface mesh within a general mesh adaption scheme as can be found in numerical computations of finite element problems for which the metric map is provided via an a posteriori error estimate.

An adaptive meshing automatic scheme based on the strain energy density function

Proposes an automatic adaptive meshing scheme. Error in strain energy is directly obtained through strain energy density function (SED). Versatility of this function, in comparison with that of others, is looked at in detail. Mesh enrichment method consists of a series of h‐refinement steps and concludes with a single p‐refinement step. Adds that an examination of the accuracy of the element used in the refinement procedure is made. This scheme has been implemented in ZATILAN, a FE code developed in the Department of the Mechanical Engineering of the University of the Basque Country.

Mesh adaptation strategies for problems in fluid dynamics

Mesh adaptation procedures are reviewed and discussed with particular emphasis on methods that are based on mesh movement (r-refinement) and mesh enrichment (h-refinement). Although the need for adaptive refinement is common to many areas of scientific computation, the examples in this survey paper are drawn almost exclusively from the domain of computational fluid dynamics.

A WAVE EQUATION MODEL TO SOLVE THE MULTIDIMENSIONAL TRANSPORT EQUATION

We try to formalize and study how mesh adaptation improves the approximation of interpolated functions or of PDE solutions. We first define an adaptive solution, in the sense that the pair (mesh,function) satisfies a non-linear coupled equation. In order to build optimal mesh adaptation strategies, we also define a functional model, the ‘continuous metric’, which leads to propose the best mesh for a given function and a given norm. We then describe how convergence of adaptive solutions can be better than for non-adaptive ones; this involves some recent refinements concerning what we called early capturing of details, a specific property of good adaptive strategies. We give some typical numerical illustrations. Convergence properties depend very much on how mesh adaptation is performed and we exhibit theoretical limits for the maximum order of accuracy reachable for some family of mesh adaptation methods. Copyright © 2003 John Wiley & Sons, Ltd.

Heavy ion fusion research in Spain

The indirect-direct illumination scheme has been investigated, and simulations were performed using the radiation-hydrodynamics code Sara, showing good agreement with experiments performed at CEL-V Limeil (France) in the PHEBUS laser. The use of an externally guided implosion of the fuel has been suggested, where two pellets, each being accelerated from opposite mouths of a cannon barrel, will collide and implode in a central cavity. A detailed opacity model ( Jimena-Dca) has been developed that treats absorption bands that result from many-particle configurations using the original Mozskowski's formalism; our average ion model ( Jimena-Ai) also includes that model. Frequency-dependent opacities for intermediate- and high- Z plasmas have been computed and tested through the WORKOP series. An adaptive mesh scheme has been implemented in the two-dimensional Arwen code based on an implicit Riemann solver and part of a Lagrangian flux-corrected transport staggered-mesh (RMFCT) scheme. The code can handle several materials on a Eulerian mesh, and includes simple ion and laser energy sources. A two-dimensional code for radiation-hydrodynamics ( Multi-2D) has been developed that uses non-structured triangular grids, and includes arbitrary Eulerian-Lagrangian hydrodynamics, radiation transport by discrete ordinates, and laser or heavy ion beam deposition. The inventory and radiological code ACAB has been extensively used to determine the activation in inertial fusion reactors and has been improved to include pulsed regimes and fission process. A molecular dynamics code has been developed in collaboration with LLNL to study neutron damage in SiC. DENIM is actively participating as one of the main proponents of the European Heavy Ion Ignition Facility of the European authorities, together with GSI Darmstadt, ENEA Frascatti and KfK Karlsruhe.