Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source. The English text was polished by Yunming Chen.     

Adaptive finite element method for analysis of pollutant dispersion in shallow water

A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts ： （ 1 ） computation of the velocity flow field and water surface elevation, and （2） computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy, as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.     

Adaptive finite element method for high-speed flow-structure interaction

An adaptive finite element method for high-speed flow-structure interaction is presented. The cell-centered finite element method is combined with an adaptive meshing technique to solve the Navier-Stokes equations for high-speed compressible flow behavior. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite element method. The finite element formulation and computational procedure are described. Interactions between the high-speed flow, structural heat transfer, and deformation are studied by two applications of Mach 10 flow over an inclined plate, and Mach 4 flow in a channel. The project supported by the Thailand Research Fund (TRF)     

Turbulent flow calculations using unstructured and adaptive meshes

A method of efficiently computing turbulent compressible flow over complex two-dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of the flow field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady state is achieved using an unstructured multigrid algorithm. Turbulence modelling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element aerofoil geometries are computed and compared with experimental data.     

Adaptive delaunay triangulation with multidimensional dissipation scheme for high-speed compressible flow analysis

IntroductionHigh-speed compressible flows normally involve many complex flow phenomena,suchas shock waves,flow expansions,and shock-shock interactions[1].Effects of thesephenomena are critical in the design of high-speed structures.These flows are charact…     

Modified Multidimensional Dissipation Scheme on Unstructured Meshes for High-speed Compressible Flow Analysis

A Roe's flux-difference splitting scheme, combining with the entropy fix method according to Van Leer et al., and the H-correction entropy fix method by Pandolfi and D'Ambrosio, is proposed. The presented scheme eliminates unphysical flow behaviors such as a spurious bump of the carbuncle phenomenon that occurs on the bow shock from flow over a blunt body, and the expansion shock generated from flow over a forward facing step. The proposed scheme is further extended to obtain high-order spatial and temporal solution accuracy. The scheme is, in addition, combined with an adaptive meshing technique that generates unstructured triangular meshes to resemble the flow phenomena for reducing computational effort. The entire procedure is evaluated by solving several benchmarks as well as complex steady-state and transient high-speed compressible flow problems.     

Adaptive nodeless variable finite elements with flux-based formulation for thermal–structural analysis

A nodeless variable element method with the fluxbased formulation is developed to analyze two-dimensional thermal-structural problems. The nodeless variable formula- tion provides accurate temperature distributions to yield more accurate thermal stress solutions. The flux-based formulation is used to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element meshes that can adapt and move along with the transient solution behavior. A version of a nearly optimal element size determination is proposed to provide high convergence rate of the predicted solutions. The combined procedure is evaluated by solving several thermal, structural, and thermal stress problems.     

对流_扩散问题的6节点三角形单元流线迎风有限元法和自适应网格重分技术

A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.     

A two‐phase flow interface capturing finite element method

A new interface capturing algorithm is proposed for the finite element simulation of two‐phase flows. It relies on the solution of an advection equation for the interface between the two phases by a streamline upwind Petrov–Galerkin (SUPG) scheme combined with an adaptive mesh refinement procedure and a filtering technique. This method is illustrated in the case of a Rayleigh–Taylor two‐phase flow problem governed by the Stokes equations. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical investigation of BB-AMR scheme using entropy production as refinement criterion

In this work, a parallel finite volume scheme on unstructured meshes is applied to fluid flow for multidimensional hyperbolic system of conservation laws. It is based on a block-based adaptive mesh refinement strategy which allows quick meshing and easy parallelisation. As a continuation and as an extension of a previous work, the useful numerical density of entropy production is used as mesh refinement criterion combined with a local time-stepping method to preserve the computational time. Then, we numerically investigate its efficiency through several test cases with a confrontation with exact solution or experimental data.     

A local adaptive grid procedure for incompressible flows with multigridding and equidistribution concepts

An adaptive grid solution procedure is developed for incompressible flow problems in which grid refinement based on an equidistribution law is performed in high-error-estimate regions that are flagged from a preliminary coarse grid solution. Solutions on the locally refined and equidistributed meshes are obtained using boundary conditions interpolated from the preliminary coarse grid solution, and solutions on both the refined and coarse grid regions are successively improved using a multigrid approach. For this purpose, suitable correction terms for the coarse grid equations are derived for all variables in the flagged regions. This procedure with Local Adaptation, Multigridding and Equidistribution (LAME) concepts is applied to various flow problems to demonstrate the accuracy improvements obtained using this method.     

Extended finite element method for viscous flow inside complex three‐dimensional geometries with moving internal boundaries

A three‐dimensional extended finite element method is presented to simulate Stokes flow in complex geometries with internal moving parts. Instead of re‐meshing the flow domain, the kinematics of the internal objects are imposed on the conservation equations using a constraint, implemented with a Lagrangian multiplier. To capture discontinuities of field variables, such as pressure and velocity, on the intersected elements, XFEM is used. To validate our method, it is first applied to a relatively simple problem, that is, the flow around a cylinder in a channel. The results are verified by comparing with a boundary‐fitted solution. After validation of the model and its implementation, the three‐dimensional flow in a twin‐screw extruder is simulated and the results are compared with experimental data from literature. XFEM shows very good accuracy for complex geometries with internal moving parts and narrow gap regions where the shear rate is orders of magnitude higher than in other regions. Copyright © 2011 John Wiley & Sons, Ltd.     

Solution of flow around complex‐shaped surfaces by an immersed boundary‐body conformal enrichment method

Solving the flow around objects with complex shapes may involve extensive meshing work that has to be repeated each time a change in the geometry is needed. Time consuming meshing can be avoided when the solution algorithm can tackle grids that do not fit the shape of immersed objects. This work presents applications of a recently proposed immersed boundary—body conformal enrichment method to the solution of the flow around complex shaped surfaces such as those of a metallic foam matrix. The method produces solutions of the flow satisfying accurately Dirichlet boundary conditions imposed on the immersed fluid/solid interface. The boundary of immersed objects is defined using a level‐set function, and the finite element discretization of interface elements is enriched with additional degrees of freedom, which are eliminated at element level. The method is first validated in the case of flow problems for which reference solutions on body‐conformal grids can be obtained: flow around an array of spheres and flow around periodic arrays of cylinders. Then, solutions are shown for the more complex flow inside a metallic foam matrix. A multiscale approach combining the solution at the pore level by the immersed boundary method and the macro‐scale solution with simulated permeability is used to solve actual experimental configurations. The computed pressure drop as a function of the flow rate on the macro scale configuration replicating two experimental setups is compared with the experimental data for various foam thicknesses. Copyright © 2011 National Research Council Canada     

Finite element analysis of transient fluid flow with free surface using VOF (volume-of-fluid) method and adaptive grid

The VOF method is adopted for the finite element analysis of transient fluid flow with a free surface. In particular, an adaptation technique for generating an adaptive grid is incorporated to capture a higher resolution of the free surface configuration. An adaptive grid is created through the refinement and mergence of elements. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. Also, three techniques based on the VOF method are newly developed to increase the accuracy of the analysis, namely the filling pattern, advection treatment and free surface smoothing techniques. Using the proposed numerical techniques, radial flow with a point source and the collapse of a dam are analysed. The numerical results agree well with the theoretical solutions as well as with the experimental results. Through comparisons with the numerical results of several cases using different grids, the efficiency of the proposed technique is verified. © 1998 by John Wiley & Sons, Ltd.     

Numerical simulations of the steady Navier–Stokes equations using adaptive meshing schemes

In this paper, we consider an adaptive meshing scheme for solution of the steady incompressible Navier–Stokes equations by finite element discretization. The mesh refinement and optimization are performed based on an algorithm that combines the so‐called conforming centroidal Voronoi Delaunay triangulations (CfCVDTs) and residual‐type local a posteriori error estimators. Numerical experiments in the two‐dimensional space for various examples are presented with quadratic finite elements used for the velocity field and linear finite elements for the pressure. The results show that our meshing scheme can equally distribute the errors over all elements in some optimal way and keep the triangles very well shaped as well at all levels of refinement. In addition, the convergence rates achieved are close to the best obtainable. Extension of this approach to three‐dimensional cases is also discussed and the main challenge is the efficient implementation of three‐dimensional CfCVDT generation that is still under development. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive hybrid (prismatic–tetrahedral) grids for incompressible flows

Hybrid grids consisting of prisms and tetrahedra are employed for the solution of the 3-D Navier–Stokes equations of incompressible flow. A pressure correction scheme is employed with a finite volume–finite element spatial discretization. The traditional staggered grid formulation has been substituted with a collocated mesh approach which uses fourth-order artificial dissipation. The hybrid grid is refined adaptively in local regions of appreciable flow variations. The scheme operations are performed on an edge-wise basis which unifies treatment of both types of grid elements. The adaptive method is employed for incompressible flows in both single and multiply-connected domains. © 1998 John Wiley & Sons, Ltd.     

Error analysis and adaptivity in three-dimensional linear elasticity by the usual and hypersingular boundary contour method

Two related topics are addressed in this article. The first part of the article proves that, for a certain admissible class of problems in linear elasticity, the hypersingular boundary contour method (HBCM) can be collocated at all boundary points on the surface of a three-dimensional (3-D) body, including those on boundary contours, edges and corners, because the HBCM-shape-functions satisfy, a priori, all the smoothness requirements for collocation at these points. In contrast, the hypersingular boundary element method needs, in general, relaxation of some of these smoothness requirements for its shape functions, even for collocation at regular points that lie on the boundaries of boundary elements.A hypersingular residual, obtained from the standard and hypersingular boundary integral equations (HBIEs), has been recently proposed as a local error estimator for a boundary element, for the boundary integral equation. The second part in the present article is concerned with a definition of an analogous local error estimator for the boundary contour method, for 3-D linear elasticity. This error estimator is then used to drive an h-adaptive meshing procedure. Numerical results are presented to demonstrate adaptive meshing for selected example problems.     

A finite point method for adaptive three‐dimensional compressible flow calculations

The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Computation of complex fluid flows using an adaptive grid method

Recently the concept of adaptive grid computation has received much attention in the computational fluid dynamics research community. This paper continues the previous efforts of multiple one-dimensional procedures in developing and asessing the ideas of adaptive grid computation. The focus points here are the issue of numerical stability induced by the grid distribution and the accuracy comparison with previously reported work. Two two-dimensional problems with complicated characteristics—namely, flow in a channel with a sudden expansion and natural convection in an enclosed square cavity—are used to demonstrate some salient features of the adaptive grid method. For the channel flow, by appropriate distribution of the grid points the numerical algorithm can more effectively dampen out the instabilities, especially those related to artificial boundary treatments, and hence can converge to a steady-state solution more rapidly. For a more accurate finite difference operator, which contains less undesirable numerical diffusion, the present adaptive grid method can yield a steady-state and convergent solution, while uniform grids produce non-convergent and numerically oscillating solutions. Furthermore, the grid distribution resulting from the adaptive procedure is very responsive to the different characteristics of laminar and turbulent flows. For the problem of natural convection, a combination of a multiple one-dimensional adaptive procedure and a variational formulation is found very useful. Comparisons of the solutions on uniform and adaptive grids with the reported benchmark calculations demonstrate the important role that the adaptive grid computation can play in resolving complicated flow characteristics.