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Mesh Generation (mesh + generation)
Selected AbstractsFlow Distribution During Cardiopulmonary Bypass in Dependency on the Outflow Cannula PositioningARTIFICIAL ORGANS, Issue 11 2009Tim A.S. Kaufmann Abstract Oxygen deficiency in the right brain is a common problem during cardiopulmonary bypass (CPB). This is linked to an insufficient perfusion of the carotid and vertebral artery. The flow to these vessels is strongly influenced by the outflow cannula position, which is traditionally located in the ascending aorta. Another approach however is to return blood via the right subclavian artery. A computational fluid dynamics (CFD) study was performed for both methods and validated by particle image velocimetry (PIV). A 3-dimensional computer aided design model of the cardiovascular (CV) system was generated from realtime computed tomography and magnetic resonance imaging data. Mesh generation (CFD) and rapid prototyping (PIV) were used for the further model creation. The simulations were performed assuming usual CPB conditions, and the same boundary conditions were applied for the PIV validation. The flow distribution was analyzed for 55 cannula positions inside the aorta and in relation to the distance between the cannula tip and the vertebral artery branch for subclavian cannulation. The study reveals that the Venturi effect due to the cannula jet appears to be the main reason for the loss in cerebral perfusion seen clinically. It provides a PIV-validated CFD method of analyzing the flow distribution in the CV system and can be transferred to other applications. [source] Non-locking tetrahedral finite element for surgical simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009Grand Roman Joldes Abstract To obtain a very fast solution for finite element models used in surgical simulations, low-order elements, such as the linear tetrahedron or the linear under-integrated hexahedron, must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately, the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper, we extend the average nodal pressure (ANP) tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing Total Lagrangian Explicit Dynamics algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared with the ANP element in case of models consisting of multiple materials. Copyright © 2008 John Wiley & Sons, Ltd. [source] Geometrical modeling of granular structures in two and three dimensions.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009Application to nanostructures Abstract A granular structure can be modeled by a parallelepiped containing spherical balls in three dimensions or by a rectangle filled with disks in two dimensions. These grains (spherical balls or disks) are separated by interfaces called grain boundaries and their size correspond to a size distribution, which is obtained experimentally. The geometrical modeling of such a structure consists in determining the repartition of the set of disjoint grains according to these specifications. In this paper, a new constructive algorithm based on an advancing-front approach, usually used in the context of mesh generation, is proposed. This algorithm is nearly linear in complexity, robust and fast in both two and three dimensions. Enhancements in computing time and density are observed and reported via comparisons with existing methods. Moreover, we propose a method to transform spherical balls (disks) into polyhedral (polygonal) cells similar to the real grain shapes. Examples of nanostructure modeling in two and three dimensions are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2009Yasushi Ito Abstract An octree-based mesh generation method is proposed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy-to-implement, easy-to-understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes. A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly. Laplacian-like smoothing, angle-based smoothing and local optimization-based untangling methods are used with certain restrictions to further improve the mesh quality. Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries. Copyright © 2008 John Wiley & Sons, Ltd. [source] Towards automatic structured multiblock mesh generation using improved transfinite interpolationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008C. B. AllenArticle first published online: 4 OCT 200 Abstract The quality of any numerical flowfield solution is inextricably linked to the quality of the mesh used. It is normally accepted that structured meshes are of higher quality than unstructured meshes, but are much more difficult to generate and, furthermore, for complex topologies a multiblock approach is required. This is the most resource-intensive approach to mesh generation, since block structures, mesh point distributions, etc., need to be defined before the generation process, and so is seldom used in an industrial design loop, particularly where a novice user may be involved. This paper considers and presents two significant advances in multiblock mesh generation: the development of a fast, robust, and improved quality interpolation-based generation scheme and a fully automatic multiblock optimization and generation method. A volume generation technique is presented based on a form of transfinite interpolation, but modified to include improved orthogonality and spacing control and, more significantly, an aspect ratio-based smoothing algorithm that removes grid crossover and results in smooth meshes even for discontinuous boundary distributions. A fully automatic multiblock generation scheme is also presented, which only requires surface patch(es) and a target number of mesh cells. Hence, all user input is removed from the process, and a novice user is able to obtain a high-quality mesh in a few minutes. It also means the code can be run in batch mode, or called as an external function, and so is ideal for incorporation into a design or optimization loop. To demonstrate the power and efficiency of the code, multiblock meshes of up to 256 million cells are presented for wings and rotors in hover and forward flight. Copyright © 2007 John Wiley & Sons, Ltd. [source] Advanced 4-node tetrahedronsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006Rong Tian Abstract Tetrahedral elements are indispensable to complex finite element structural analysis. Two existing and two newly developed advanced 4-node tetrahedrons are studied in this paper. The existing elements that use complicated displacement fields are significantly simplified. The spurious zero-energy modes typical of all these elements are identified to be rigid-body-alike modes and are found to be naturally suppressible, making it possible to avoid any stabilization techniques and unknown parameters in formulation. Through the simplified form, we connect these four tetrahedrons and view them in a general framework of the partition-of-unity-based approximation. This general view allows us to reveal many promising features of the newly developed tetrahedrons by comparing them with their existing counterparts: the newly developed tetrahedrons have straightforward formulation, no unsuppressed zero-energy modes, no stabilization required, no unknown parameters contained, and a high consistency in implementation, in addition to good accuracy and extremely straightforward mesh generation. Copyright © 2006 John Wiley & Sons, Ltd. [source] Generalized nodes and high-performance elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005Rong Tian Abstract The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition-of-unity-based finite-element approximation. Construction of the partition-of-unity-based approximation is accomplished by a physically defined local function of displacements. A 4-node quadratic tetrahedral element and a 3-node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition-of-unity-based finite-element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple. Copyright © 2005 John Wiley & Sons, Ltd. [source] An integrated procedure for three-dimensional structural analysis with the finite cover methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005Kenjiro Terada Abstract In this paper an integrated procedure for three-dimensional (3D) structural analyses with the finite cover method (FCM) is introduced. In the pre-process of this procedure, the geometry of a structure is modelled by 3D-CAD, followed by digitization to have the corresponding voxel model, and then the structure is covered by a union of mathematical covers, namely a mathematical mesh independently generated for approximation purposes. Since the mesh topology in the FCM does not need to conform to the physical boundaries of the structure, the mesh can be regular and structured. Thus, the numerical analysis procedure is free from the difficulties mesh generation typically poses and, in this sense, enables us to realize the mesh-free analysis. After formulating the FCM with interface elements for the static equilibrium state of a structure, we detail the procedure of the finite cover modelling, including the geometry modelling with 3D-CAD and the identification of the geometry covered by a regular mesh for numerical integration. Prior to full 3D modelling and analysis, we present a simple numerical example to confirm the equivalence of the performance of the FCM and that of the standard finite element method (FEM). Finally, representative numerical examples are presented to demonstrate the capabilities of the proposed analysis procedure. Copyright © 2005 John Wiley & Sons, Ltd. [source] LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transformINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004W. R. Quadros Abstract A new mesh generation algorithm called ,LayTracks', to automatically generate an all quad mesh that is adapted to the variation of geometric feature size in the domain is described. LayTracks combines the merits of two popular direct techniques for quadrilateral mesh generation,quad meshing by decomposition and advancing front quad meshing. While the MAT has been used for the domain decomposition before, this is the first attempt to use the MAT, for the robust subdivision of a complex domain into a well defined sub-domain called ,Tracks', for terminating the advancing front of the mesh elements without complex interference checks and to use radius function for providing sizing function for adaptive meshing. The process of subdivision of a domain is analogous to, formation of railway tracks by laying rails on the ground. Each rail starts from a node on the boundary and propagates towards the medial axis (MA) and then from the MA towards the boundary. Quadrilateral elements are then obtained by placing nodes on these rails and connecting them inside each track, formed by adjacent rails. The algorithm has been implemented and tested on some typical geometries and the quality of the output mesh obtained are presented. Extension of this technique to all hexahedral meshing is discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source] An imprint and merge algorithm incorporating geometric tolerances for conformal meshing of misaligned assembliesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004David R. White Abstract A size tolerant algorithm for imprinting and merging adjacent part geometries is presented in this paper. This approach cleans up misaligned and dirty assembly geometry that is intended for conformal mesh generation. The algorithm first discretizes the boundary edges of adjacent faces into linear segments. The segments are then intersected and a partial intersection graph is calculated from the intersection results. The intersections are calculated by accounting for size tolerances to minimize the effect of misaligned parts on the meshing process. The partial intersection graph is next used to imprint the adjacent faces as appropriate. The imprints are generated using virtual geometry so that the tolerant topology created therein can be employed. Several examples are given to demonstrate the resulting improvement in the mesh quality of conformal meshes. The approach is shown to work robustly with misaligned and poorly defined parts. Copyright © 2004 John Wiley & Sons, Ltd. [source] c-Type method of unified CAMG and FEA.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 20032D non-linear, 3D linear, Part 1: Beam, arch mega-elements Abstract Computer-aided mesh generation (CAMG) dictated solely by the minimal key set of requirements of geometry, material, loading and support condition can produce ,mega-sized', arbitrary-shaped distorted elements. However, this may result in substantial cost saving and reduced bookkeeping for the subsequent finite element analysis (FEA) and reduced engineering manpower requirement for final quality assurance. A method, denoted as c-type, has been proposed by constructively defining a finite element space whereby the above hurdles may be overcome with a minimal number of hyper-sized elements. Bezier (and de Boor) control vectors are used as the generalized displacements and the Bernstein polynomials (and B-splines) as the elemental basis functions. A concomitant idea of coerced parametry and inter-element continuity on demand unifies modelling and finite element method. The c-type method may introduce additional control, namely, an inter-element continuity condition to the existing h-type and p-type methods. Adaptation of the c-type method to existing commercial and general-purpose computer programs based on a conventional displacement-based finite element method is straightforward. The c-type method with associated subdivision technique can be easily made into a hierarchic adaptive computer method with a suitable a posteriori error analysis. In this context, a summary of a geometrically exact non-linear formulation for the two-dimensional curved beams/arches is presented. Several beam problems ranging from truly three-dimensional tortuous linear curved beams to geometrically extremely non-linear two-dimensional arches are solved to establish numerical efficiency of the method. Incremental Lagrangian curvilinear formulation may be extended to overcome rotational singularity in 3D geometric non-linearity and to treat general material non-linearity. Copyright © 2003 John Wiley & Sons, Ltd. [source] Parallel computing of high-speed compressible flows using a node-based finite-element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003T. Fujisawa Abstract An efficient parallel computing method for high-speed compressible flows is presented. The numerical analysis of flows with shocks requires very fine computational grids and grid generation requires a great deal of time. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed seamlessly in parallel in terms of nodes. Local finite-element mesh is generated robustly around each node, even for severe boundary shapes such as cracks. The algorithm and the data structure of finite-element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. The inter-processor communication is minimized by renumbering the nodal identification number using ParMETIS. The numerical scheme for high-speed compressible flows is based on the two-step Taylor,Galerkin method. The proposed method is implemented on distributed memory systems, such as an Alpha PC cluster, and a parallel supercomputer, Hitachi SR8000. The performance of the method is illustrated by the computation of supersonic flows over a forward facing step. The numerical examples show that crisp shocks are effectively computed on multiprocessors at high efficiency. Copyright © 2003 John Wiley & Sons, Ltd. [source] Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cellsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Soji Yamakawa Abstract A new fully automatic hex-dominant mesh generation technique of an arbitrary 3D geometric domain is presented herein. The proposed method generates a high-quality hex-dominant mesh by: (1) controlling the directionality of the output hex-dominant mesh; and (2) avoiding ill-shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex-dominant mesh consisting mostly of hexahedral elements, with additional prism and tetrahedral elements. Rectangular solid cells are packed on the boundary of and inside the input domain to obtain ideal node locations for a hex-dominant mesh. Each cell has a potential energy field that mimics a body-centred cubic (BCC) structure (seen in natural substances such as NaCl) and the cells are moved to stable positions by a physically based simulation. The simulation mimics the formation of a crystal pattern so that the centres of the cells provide ideal node locations for a hex-dominant mesh. Via the advancing front method, the centres of the packed cells are then connected to form a tetrahedral mesh, and this is converted to a hex-dominant mesh by merging some of the tetrahedrons. Copyright © 2003 John Wiley & Sons, Ltd. [source] Voxel-based meshing and unit-cell analysis of textile compositesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2003Hyung Joo Kim Abstract Unit-cell homogenization techniques are frequently used together with the finite element method to compute effective mechanical properties for a wide range of different composites and heterogeneous materials systems. For systems with very complicated material arrangements, mesh generation can be a considerable obstacle to usage of these techniques. In this work, pixel-based (2D) and voxel-based (3D) meshing concepts borrowed from image processing are thus developed and employed to construct the finite element models used in computing the micro-scale stress and strain fields in the composite. The potential advantage of these techniques is that generation of unit-cell models can be automated, thus requiring far less human time than traditional finite element models. Essential ideas and algorithms for implementation of proposed techniques are presented. In addition, a new error estimator based on sensitivity of virtual strain energy to mesh refinement is presented and applied. The computational costs and rate of convergence for the proposed methods are presented for three different mesh-refinement algorithms: uniform refinement; selective refinement based on material boundary resolution; and adaptive refinement based on error estimation. Copyright © 2003 John Wiley & Sons, Ltd. [source] Guaranteed-quality triangular mesh generation for domains with curved boundariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2002Charles Boivin Guaranteed-quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert's Delaunay refinement algorithm to two-dimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries. We provide implementation details for two-dimensional boundary patches such as lines, circular arcs, cubic parametric curves, and interpolated splines. We present guaranteed-quality triangular meshes generated with curved boundaries, and propose solutions to some problems associated with the use of curved boundaries. Copyright © 2002 John Wiley & Sons, Ltd. [source] Remeshing for metal forming simulations,Part I: Two-dimensional quadrilateral remeshingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002Dae-Young Kwak Abstract In this paper, a general framework of practical two-dimensional quadrilateral remeshing, which includes the determination of remeshing time, automatic quadrilateral mesh generation, and data transfer process, will be formulated. In particular, the current work contains new algorithms of mesh density specification according to the distribution of effective strain-rate gradients, mesh density smoothing by fast Fourier transform (FFT) and low-pass filtering techniques, coarsening it by node placement scheme, and a modified Laplacian mesh smoothing technique. The efficiency of the developed remeshing scheme was tested through three practical two-dimensional metal forming simulations. The results clearly indicate that the algorithms proposed in this study make it possible to simulate two-dimensional metal forming problems efficiently and automatically. Copyright © 2002 John Wiley & Sons, Ltd. [source] Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009L. Cea Abstract In this paper a layer-structured finite volume model for non-hydrostatic 3D environmental free surface flow is presented and applied to several test cases, which involve the computation of gravity waves. The 3D unsteady momentum and mass conservation equations are solved in a collocated grid made of polyhedrons, which are built from a 2D horizontal unstructured mesh, by just adding several horizontal layers. The mesh built in such a way is unstructured in the horizontal plane, but structured in the vertical direction. This procedure simplifies the mesh generation and at the same time it produces a well-oriented mesh for stratified flows, which are common in environmental problems. The model reduces to a 2D depth-averaged shallow water model when one single layer is defined in the mesh. Pressure,velocity coupling is achieved by the Semi-Implicit Method for Pressure-Linked Equations algorithm, using Rhie,Chow interpolation to stabilize the pressure field. An attractive property of the model proposed is the ability to compute the propagation of short waves with a rather coarse vertical discretization. Several test cases are solved in order to show the capabilities and numerical stability of the model, including a rectangular free oscillating basin, a radially symmetric wave, short wave propagation over a 1D bar, solitary wave runup on a vertical wall, and short wave refraction over a 2D shoal. In all the cases the numerical results are compared either with analytical or with experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source] Incorporating spatially variable bottom stress and Coriolis force into 2D, a posteriori, unstructured mesh generation for shallow water modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009D. Michael Parrish Abstract An enhanced version of our localized truncation error analysis with complex derivatives (LTEA,CD ) a posteriori approach to computing target element sizes for tidal, shallow water flow, LTEA+CD , is applied to the Western North Atlantic Tidal model domain. The LTEA + CD method utilizes localized truncation error estimates of the shallow water momentum equations and builds upon LTEA and LTEA,CD-based techniques by including: (1) velocity fields from a nonlinear simulation with complete constituent forcing; (2) spatially variable bottom stress; and (3) Coriolis force. Use of complex derivatives in this case results in a simple truncation error expression, and the ability to compute localized truncation errors using difference equations that employ only seven to eight computational points. The compact difference molecules allow the computation of truncation error estimates and target element sizes throughout the domain, including along the boundary; this fact, along with inclusion of locally variable bottom stress and Coriolis force, constitute significant advancements beyond the capabilities of LTEA. The goal of LTEA + CD is to drive the truncation error to a more uniform, domain-wide value by adjusting element sizes (we apply LTEA + CD by re-meshing the entire domain, not by moving nodes). We find that LTEA + CD can produce a mesh that is comprised of fewer nodes and elements than an initial high-resolution mesh while performing as well as the initial mesh when considering the resynthesized tidal signals (elevations). Copyright © 2008 John Wiley & Sons, Ltd. [source] A particle finite element method applied to long wave run-upINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006J. Birknes Abstract This paper presents a Lagrangian,Eulerian finite element formulation for solving fluid dynamics problems with moving boundaries and employs the method to long wave run-up. The method is based on a set of Lagrangian particles which serve as moving nodes for the finite element mesh. Nodes at the moving shoreline are identified by the alpha shape concept which utilizes the distance from neighbouring nodes in different directions. An efficient triangulation technique is then used for the mesh generation at each time step. In order to validate the numerical method the code has been compared with analytical solutions and a preexisting finite difference model. The main focus of our investigation is to assess the numerical method through simulations of three-dimensional dam break and long wave run-up on curved beaches. Particularly the method is put to test for cases where different shoreline segments connect and produce a computational domain surrounding dry regions. Copyright © 2006 John Wiley & Sons, Ltd. [source] 2D nearly orthogonal mesh generationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2004Yaoxin Zhang Abstract The Ryskin and Leal (RL) system is the most widely used mesh generation system for the orthogonal mapping. However, when this system is used in domains with complex geometry, particularly in those with sharp corners and strong curvatures, serious distortion or overlapping of mesh lines may occur and an acceptable solution may not be possible. In the present study, two methods are proposed to generate nearly orthogonal meshes with the smoothness control. In the first method, the original RL system is modified by introducing smoothness control functions, which are formulated through the blending of the conformal mapping and the orthogonal mapping; while in the second method, the RL system is modified by introducing the contribution factors. A hybrid system of both methods is also developed. The proposed methods are illustrated by several test examples. Applications of these methods in a natural river channel are demonstrated. It is shown that the modified RL systems are capable of producing meshes with an adequate balance between the orthogonality and the smoothness for complex computational domains without mesh distortions and overlapping. Copyright © 2004 John Wiley & Sons, Ltd. [source] Automatic unstructured surface mesh generation for complex configurationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Udo Tremel In this paper a new object-oriented (OO) approach is presented for automatic parallel advancing front based surface mesh generation and adaptive remeshing for complex configurations. Based on the ST++-system the advantages of the OO design and implementation compared to the traditional structural approach are described. Algorithmic enhancements to the advancing front method are explained, enabling a robust NURBS based triangulation process directly on B-rep CAD data. The message passing (MPI) parallelization strategy together with the achievable performance improvements are demonstrated. With the outlined parallel geometry analysis/rasterization a powerful method is described to derive automatically a well suited mesh size specification without any user-interaction from scratch. The application of this method to a complex ,real world' example finishes this paper. Copyright © 2004 John Wiley & Sons, Ltd. [source] Adaptive grid based on geometric conservation law level set method for time dependent PDENUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009Ali R. Soheili Abstract A new method for mesh generation is formulated based on the level set functions, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values (Liao et al. J Comput Phys 159 (2000), 103,122; Osher and Sethian J Comput Phys 79 (1988), 12; Sethian, Level set methods and fast marching methods, Cambridge University Press, 1999; Di et al. J Sci Comput 31 (2007), 75,98). The intersection of the level contours of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to the Geometric Conservation Law (GCL) method (Cao et al., SIAM J Sci Comput 24 (2002), 118,142.). This method has precise control over the Jacobian of transformation because of using the GCL method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified dataNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2007Mehdi Dehghan Abstract Parabolic partial differential equations with overspecified data play a crucial role in applied mathematics and engineering, as they appear in various engineering models. In this work, the radial basis functions method is used for finding an unknown parameter p(t) in the inverse linear parabolic partial differential equation ut = uxx + p(t)u + ,, in [0,1] × (0,T], where u is unknown while the initial condition and boundary conditions are given. Also an additional condition ,01k(x)u(x,t)dx = E(t), 0 , t , T, for known functions E(t), k(x), is given as the integral overspecification over the spatial domain. The main approach is using the radial basis functions method. In this technique the exact solution is found without any mesh generation on the domain of the problem. We also discuss on the case that the overspecified condition is in the form ,0s(t)u(x,t)dx = E(t), 0 < t , T, 0 < s(t) < 1, where s and E are known functions. Some illustrative examples are presented to show efficiency of the proposed method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source] Design Optimization of Blood Shearing Instrument by Computational Fluid DynamicsARTIFICIAL ORGANS, Issue 6 2005Jingchun Wu Abstract:, Rational design of blood-wetted devices requires a careful consideration of shear-induced trauma and activation of blood elements. Critical levels of shear exposure may be established in vitro through the use of devices specifically designed to prescribe both the magnitude and duration of shear exposure. However, it is exceptionally difficult to create a homogeneous shear-exposure history by conventional means. This study was undertaken to develop a Blood Shearing Instrument (BSI) with an optimized flow path which localized shear exposure within a rotating outer ring and a stationary conical spindle. By adjustment of the rotational speed and the gap dimension, the BSI is designed to generate shear stress magnitudes up to 1500 Pa for exposure time between 0.0015 and 0.20 s with a pressure drop of 100 mm Hg. Computational fluid dynamics (CFD) revealed that a flow path designed by first-order analysis and intuition exhibited unfavorable pressure gradient, vortices, and undesirable regions of reverse flow. An optimized design was evolved utilizing a parameterized geometric model and automatic mesh generation to eliminate vortices and reversal flow and to avoid unfavorable pressure gradients. Analysis of the flow and shear fields for the extreme limits of the shear gap demonstrated an improvement in homogeneity due to shape optimization and the limitations of an annular shear device for achieving completely uniform shear exposure. [source] | ||||||||||