Mesh Refinement Approach Research Articles

Anisotropic finite elements for the Stokes problem: a posteriori error estimator and adaptive mesh

We propose an a posteriori error estimator for the Stokes problem using the Crouzeix–Raviart/ P 0 pair. Its efficiency and reliability on highly stretched meshes are investigated. The analysis is based on hierarchical space splitting whose main ingredients are the strengthened Cauchy–Schwarz inequality and the saturation assumption. We give a theoretical proof of a method to enrich the Crouzeix–Raviart element so that the strengthened Cauchy constant is always bounded away from unity independently of the aspect ratio. An anisotropic self-adaptive mesh refinement approach for which the saturation assumption is valid will be described. Our theory is confirmed by corroborative numerical tests which include an internal layer, a boundary layer, a re-entrant corner and a crack simulation. A comparison of the exact error and the a posteriori one with respect to the aspect ratio will be demonstrated.

An adaptive numerical scheme for high-speed reactive flow on overlapping grids

We describe a method for the numerical solution of high-speed reactive flow in complex geometries using overlapping grids and block-structured adaptive mesh refinement. We consider flows described by the reactive Euler equations with an ideal equation of state and various stiff reaction models. These equations are solved using a second-order accurate Godunov method for the convective fluxes and a Runge–Kutta time-stepping scheme for the source term modeling the chemical reactions. We describe an extension of the adaptive mesh refinement approach to curvilinear overlapping grids. Numerical results are presented showing the evolution to detonation in a quarter-plane provoked by a temperature gradient and the propagation of an overdriven detonation in an expanding channel. The first problem, which considers a one-step Arrhenius reaction model, is used primarily to validate the numerical method, while the second problem, which considers a three-step chain-branching reaction model, is used to illustrate mechanisms of detonation failure and rebirth for the channel geometry.

World bank endorses water resources strategy

Gas cyclones have many industrial applications in solid–gas separation. The vortex finder is an essential part in gas cyclones where the shape and diameter highly affect the cyclone performance. Many optimization studies have been conducted to optimize the cylindrical vortex finder diameter. This study introduces a new vortex finder shape optimized for minimum pressure drop using the discrete adjoint method. The new optimum cyclone will save 66% from the driving power needed for the Stairmand cyclone. To efficiently perform the grid independence study for the new cyclone, a new framework using the adjoint solver and the grid convergence index is proposed and tested. The proposed framework relies on local mesh adaptation instead of the global mesh refinement approach. A comparison of numerical simulation of the new cyclone and the Stairmand cyclone confirms the superior performance of the new vortex finder shape for the pressure drop and the cut-off diameter. The results of this study open a new era gas cyclones geometry optimization by using the adjoint method instead of the traditional surrogate based optimization technique. Moreover, the computational costs for the grid independence studies will be reduced via the application of the adjoint methods.

Defect structure of a nematic liquid crystal around a spherical particle: adaptive mesh refinement approach.

We investigate numerically the structure of topological defects close to a spherical particle immersed in a uniformly aligned nematic liquid crystal. To this end we have implemented an adaptive mesh refinement scheme in an axi-symmetric three-dimensional system, which makes it feasible to take into account properly the large length scale difference between the particle and the topological defects. The adaptive mesh refinement scheme proves to be quite efficient and useful in the investigation of not only the macroscopic properties such as the defect position but also the fine structure of defects. It can be shown that a hyperbolic hedgehog that accompanies a particle with strong homeotropic anchoring takes the structure of a ring.

DNS of the Incompressible Flows Around a Circular Cylinder Using Cartesian Grid Approach with Virtual Boundary. 2nd Report. Introduction of Solution-Adaptive Mesh Refinement.

In the first report, the Cartesian grid approach with virtual boundary method was validated for applying to the DNSs of the incompressible flows around a circular cylinder. The aims of this report are to introduce the solution-adaptive mesh refinement and to develop the more effective scheme. The computational Cartesian grid is generated by using the Adaptive Mesh Refinement (AMR) approach. The DNSs of the steady and unsteady incompressible flows around a circular cylinder are considered in order to compare with the results in the first reporrt. The present solution-adaptive mesh refinement approach gives the reliable solutions and we can achieve successfully that both number of total grid points and computational time are reduced to 2/3 of the original Cartesian grid approach with the virtual boundary method.

Reconstruction of topologically correct and adaptive trilinear isosurfaces

The goal of the paper is to fit trilinear iso-surfaces out of volume data, by adopting an adaptive mesh refinement approach and therefore supporting a higher accuracy with respect to standard MC solutions. In order to be correct, adaptive refinement must be applied to a topologically correct initial mesh patch. For this reason, we designed a new, exhaustive look_up_table (ELUT) which encodes multi-entry patterns for each ambiguous configuration. Following the solution proposed by Natarajan, for each ambiguous configuration we choose, at run time, the actual pattern by evaluating the corresponding set of saddle points. Once the corresponding starting patch has been read from the ELUT, it is adaptively refined to fulfill a user-selected accuracy. Refinement is adaptive to ensure that the complexity of the fitted mesh will not become excessive. An evaluation of the results produced on some volume data set is reported, both in terms of accuracy and complexity of the meshes obtained.

Steady flow separation patterns in a 45 degree junction

Numerical and experimental techniques were used to study the physics of flow separation for steady internal flow in a 45° junction geometry, such as that observed between two pipes or between the downstream end of a bypass graft and an artery. The three-dimensional Navier–Stokes equations were solved using a validated finite element code, and complementary experiments were performed using the photochromic dye tracer technique. Inlet Reynolds numbers in the range 250 to 1650 were considered. An adaptive mesh refinement approach was adopted to ensure grid-independent solutions. Good agreement was observed between the numerical results and the experimentally measured velocity fields; however, the wall shear stress agreement was less satisfactory. Just distal to the ‘toe’ of the junction, axial flow separation was observed for all Reynolds numbers greater than 250. Further downstream (approximately 1.3 diameters from the toe), the axial flow again separated for Re [ges ] 450. The location and structure of axial flow separation in this geometry is controlled by secondary flows, which at sufficiently high Re create free stagnation points on the model symmetry plane. In fact, separation in this flow is best explained by a secondary flow boundary layer collision model, analogous to that proposed for flow in the entry region of a curved tube. Novel features of this flow include axial flow separation at modest Re (as compared to flow in a curved tube, where separation occurs only at much higher Re), and the existence and interaction of two distinct three-dimensional separation zones.

Adaptive mesh refinement approach to the construction of initial data for black hole collisions

The initial data for black hole collisions are constructed using a conformal-imaging approach and a new adaptive mesh refinement technique, a fully threaded tree (FTT). We developed a second-order accurate approach to the solution of the constraint equations on a non-uniformly refined high-resolution Cartesian mesh including second-order accurate treatment of boundary conditions at the black hole throats. FTT-based mesh refinement reduced memory and computer time requirements by several orders of magnitude compared to a uniform grid and allowed the construction of accurate initial data sets on Cartesian meshes. Test computations show quadratic convergence of the solutions with increasing numerical resolution.

Implicit discretization and nonuniform mesh refinement approaches for FD discretizations of LBGK Models

After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.

Finite Element Mesh Refinement for Discontinuous Fiber Reinforced Composites

This paper is concerned with the development of a generalized approach for mesh refinement in a short fiber reinforced composite. Mesh refinement procedures are based on the calculation of the error in energy norm for global convergence and the traction differential approach at the fiber/matrix interface for local convergence. The mesh refinement strategy is based on the use of elongated elements at the fiber/matrix interface, yielding significantly different mesh patterns than obtained by conventional mesh refinement approaches. This difference may have a critical bearing on the subsequent thermo-mechanical properties predicted by finite element analysis (FEA). It is found that the use of elongated (i.e., high aspect ratio) elements for mesh refinement results in a much more rapid computational convergence rate than obtained by conventional meshes. Converged local solutions are obtained with significantly less degrees-of-freedom (DOF) than by conventional mesh refinement methods.

An adaptive mesh refinement for the finite element method. 2nd report. h-method by global remeshing scheme.

A new mesh refinement approach on h-adaptation for FEM is discussed in this paper. Since there are some limitations in the r-method, especially for problems with rather complicated domains, h-refinement was supposed to be an alternative for such problems. An ordinary local remeshing approach in the h-method has a great difficulty in controlling the mesh size depending on the error measures. As a result, the number of elements is very easily increased, and the computational efficiency in FEM is decreased. The purpose of our global remeshing scheme reported in this paper is to solve these problems. Our approach can be summarized as follows: generate subdomain data based on error measure, input these data into the automatic mesh generator which supports the subdomain data structure, then get very smooth and controlled refined meshes. Its effects are evaluated with several examples on both stress concentration problem and conductive heat transfer problem.

An approach for automatic adaptive mesh refinement in finite element computation of magnetic fields

An approach to the estimation of errors in adaptive finite-element mesh generation is discussed. The method is based on the analysis of the continuity of H and B at the boundaries between elements. Analyses are presented in two dimensions but can be utilized in three dimensions. The method is easy to use and can reduce the number of iterations of the mesh refinement process. >

Evaluation of a groundwater corrective action at the Chem‐Dyne Hazardous Waste Site using a telescopic mesh refinement modeling approach

The available data base and hydrogeologic information for the Chem‐Dyne hazardous waste site, located in southwestern Ohio, are typical of many Superfund sites. Data are localized because investigations conducted at these sites are for the purpose of defining contaminant plumes. Little or no data are available to characterize the regional flow systems which impart a controlling influence on the rate and direction of contaminant migration. To simulate groundwater flow and contaminant transport in this setting, a telescopic mesh refinement (TMR) approach is appropriate. This approach provides the means of accurately incorporating regional controlling factors into smaller model domains and also increased grid resolution in areas of critical importance. At the Chem‐Dyne site a finite‐difference model was applied at three scales: regional, local, and site. This application of TMR integrates the regional and local flow system characteristics to analyze the effectiveness of a proposed remedial action at the site scale. The TMR modeling approach permits effective flow and transport model construction and calibration to provide quantitative analysis of system response to a groundwater extraction‐injection well clean‐up system. Calibration of the flow models demonstrates the regional importance of induced river infiltration to groundwater pumping centers and the control of surface water features on the direction of plume migration. The site‐scale transport model reveals that a significant portion of the volatile organic contaminants are not captured by the preliminary proposed system.