Home About us Contact
|
Home About us Contact | ||
|
|
||
Unstructured Meshes (unstructured + mesh)
Selected AbstractsLaminar and turbulent flow calculations through a model human upper airway using unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007P. Nithiarasu Abstract In this paper, numerical investigation of airflow through a human upper airway is presented using an unstructured-based characteristic-based split (CBS) scheme. The CBS scheme used in the present study employs a fully explicit matrix-free solution procedure along with artificial compressibility. A one equation Spalrat,Allmaras (SA) turbulence model is employed to study low and moderate Reynolds number flows. A detailed discussion of the qualitative and quantitative results is presented. The results show a strong influence of the Reynolds number on the flow pattern and quantities of interest, pressure drop and wall shear stress. It is also apparent that SA model can be employed on unstructured meshes to predict the steady flow with good accuracy. Thus, the novelties of the present paper are: use of the unstructured mesh-based solution algorithm and the successful application of the SA model to a typical human upper airway. Copyright © 2006 John Wiley & Sons, Ltd. [source] Simplified model for mould filling simulations using CVFEM and unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2007K. C. Estacio Abstract In this work, the finite volume method is used to numerically solve the fluid governing equations of the filling phase of thermoplastic injection in a narrow gap with free surfaces, subject to heat transfer, using a semi-Lagrangian formulation in an unstructured mesh. The modified-Cross model with Arrhenius temperature dependence is employed to describe the viscosity of the melt. The pressure field is obtained using the control volume finite element method. The three-dimensional temperature field is solved by a semi-Lagrangian scheme based on the finite volume method. A simpler two-dimensional model for temperature field is also deduced and presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] A parallel implicit/explicit hybrid time domain method for computational electromagneticsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2009Z. Q. Xie Abstract The numerical solution of Maxwell's curl equations in the time domain is achieved by combining an unstructured mesh finite element algorithm with a cartesian finite difference method. The practical problem area selected to illustrate the application of the approach is the simulation of three-dimensional electromagnetic wave scattering. The scattering obstacle and the free space region immediately adjacent to it are discretized using an unstructured mesh of linear tetrahedral elements. The remainder of the computational domain is filled with a regular cartesian mesh. These two meshes are overlapped to create a hybrid mesh for the numerical solution. On the cartesian mesh, an explicit finite difference method is adopted and an implicit/explicit finite element formulation is employed on the unstructured mesh. This approach ensures that computational efficiency is maintained if, for any reason, the generated unstructured mesh contains elements of a size much smaller than that required for accurate wave propagation. 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 approach is parallelized, to enable large-scale simulations to be effectively performed. Examples are included to demonstrate the numerical performance that can be achieved. Copyright © 2009 John Wiley & Sons, Ltd. [source] Parallel DSMC method using dynamic domain decompositionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005J.-S. Wu Abstract A general parallel direct simulation Monte Carlo method using unstructured mesh is introduced, which incorporates a multi-level graph-partitioning technique to dynamically decompose the computational domain. The current DSMC method is implemented on an unstructured mesh using particle ray-tracing technique, which takes the advantages of the cell connectivity information. In addition, various strategies applying the stop at rise (SAR) (IEEE Trans Comput 1988; 39:1073,1087) scheme is studied to determine how frequent the domain should be re-decomposed. A high-speed, bottom-driven cavity flow, including small, medium and large problems, based on the number of particles and cells, are simulated. Corresponding analysis of parallel performance is reported on IBM-SP2 parallel machine up to 64 processors. Analysis shows that degree of imbalance among processors with dynamic load balancing is about ,,½ of that without dynamic load balancing. Detailed time analysis shows that degree of imbalance levels off very rapidly at a relatively low value with increasing number of processors when applying dynamic load balancing, which makes the large problem size fairly scalable for processors more than 64. In general, optimal frequency of activating SAR scheme decreases with problem size. At the end, the method is applied to compute two two-dimensional hypersonic flows, a three-dimensional hypersonic flow and a three-dimensional near-continuum twin-jet gas flow to demonstrate its superior computational capability and compare with experimental data and previous simulation data wherever available. Copyright © 2005 John Wiley & Sons, Ltd. [source] Coupled solution of the species conservation equations using unstructured finite-volume methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010Ankan Kumar Abstract A coupled solver was developed to solve the species conservation equations on an unstructured mesh with implicit spatial as well as species-to-species coupling. First, the computational domain was decomposed into sub-domains comprised of geometrically contiguous cells,a process similar to additive Schwarz decomposition. This was done using the binary spatial partitioning algorithm. Following this step, for each sub-domain, the discretized equations were developed using the finite-volume method, and solved using an iterative solver based on Krylov sub-space iterations, that is, the pre-conditioned generalized minimum residual solver. Overall (outer) iterations were then performed to treat explicitness at sub-domain interfaces and nonlinearities in the governing equations. The solver is demonstrated for both two-dimensional and three-dimensional geometries for laminar methane,air flame calculations with 6 species and 2 reaction steps, and for catalytic methane,air combustion with 19 species and 24 reaction steps. It was found that the best performance is manifested for sub-domain size of 2000 cells or more, the exact number depending on the problem at hand. The overall gain in computational efficiency was found to be a factor of 2,5 over the block (coupled) Gauss,Seidel procedure. All calculations were performed on a single processor machine. The largest calculations were performed for about 355 000 cells (4.6 million unknowns) and required 900,MB of peak runtime memory and 19,h of CPU on a single processor. Copyright © 2009 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] Numerical simulation of three-dimensional free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003V. Maronnier Abstract A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2) : 439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems,one for the predicted velocity field and the other for the volume fraction of liquid,are to be solved. Then, a generalized Stokes problem is solved and the velocity field is corrected. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. The three-dimensional implementation is discussed. Efficient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements. Numerical results are presented for complex geometries arising in mold filling. Copyright © 2003 John Wiley & Sons, Ltd. [source] Particle-scale simulation of the flow and heat transfer behaviors in fluidized bed with immersed tubeAICHE JOURNAL, Issue 12 2009Yongzhi Zhao Abstract A kind of new modified computational fluid dynamics-discrete element method (CFD-DEM) method was founded by combining CFD based on unstructured mesh and DEM. The turbulent dense gas,solid two phase flow and the heat transfer in the equipment with complex geometry can be simulated by the programs based on the new method when the k-, turbulence model and the multiway coupling heat transfer model among particles, walls and gas were employed. The new CFD-DEM coupling method that combining k-, turbulence model and heat transfer model, was employed to simulate the flow and the heat transfer behaviors in the fluidized bed with an immersed tube. The microscale mechanism of heat transfer in the fluidized bed was explored by the simulation results and the critical factors that influence the heat transfer between the tube and the bed were discussed. The profiles of average solids fraction and heat transfer coefficient between gas-tube and particle-tube around the tube were obtained and the influences of fluidization parameters such as gas velocity and particle diameter on the transfer coefficient were explored by simulations. The computational results agree well with the experiment, which shows that the new CFD-DEM method is feasible and accurate for the simulation of complex gas,solid flow with heat transfer. And this will improve the farther simulation study of the gas,solid two phase flow with chemical reactions in the fluidized bed. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Conservative semi-Lagrangian advection on adaptive unstructured meshesNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2004Armin Iske Abstract A conservative semi-Lagrangian method is designed in order to solve linear advection equations in two space variables. The advection scheme works with finite volumes on an unstructured mesh, which is given by a Voronoi diagram. Moreover, the mesh is subject to adaptive modifications during the simulation, which serves to effectively combine good approximation quality with small computational costs. The required adaption rules for the refinement and the coarsening of the mesh rely on a customized error indicator. The implementation of boundary conditions is addressed. Numerical results finally confirm the good performance of the proposed conservative and adaptive advection scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 388,411, 2004 [source] Parallel operation of CartaBlanca on shared and distributed memory computersCONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 1 2004N. T. Padial-Collins Abstract We describe the parallel performance of the pure Java CartaBlanca code on heat transfer and multiphase fluid flow problems. CartaBlanca is designed for parallel computations on partitioned unstructured meshes. It uses Java's thread facility to manage computations on each of the mesh partitions. Inter-partition communications are handled by two compact objects for node-by-node communication along partition boundaries and for global reduction calculations across the entire mesh. For distributed calculations, the JavaParty package from the University of Karlsruhe is demonstrated to work with CartaBlanca. Copyright © 2004 John Wiley & Sons, Ltd. [source] Parsimonious finite-volume frequency-domain method for 2-D P,SV -wave modellingGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2008R. Brossier SUMMARY A new numerical technique for solving 2-D elastodynamic equations based on a finite-volume frequency-domain approach is proposed. This method has been developed as a tool to perform 2-D elastic frequency-domain full-waveform inversion. In this context, the system of linear equations that results from the discretization of the elastodynamic equations is solved with a direct solver, allowing efficient multiple-source simulations at the partial expense of the memory requirement. The discretization of the finite-volume approach is through triangles. Only fluxes with the required quantities are shared between the cells, relaxing the meshing conditions, as compared to finite-element methods. The free surface is described along the edges of the triangles, which can have different slopes. By applying a parsimonious strategy, the stress components are eliminated from the discrete equations and only the velocities are left as unknowns in the triangles. Together with the local support of the P0 finite-volume stencil, the parsimonious approach allows the minimizing of core memory requirements for the simulation. Efficient perfectly matched layer absorbing conditions have been designed for damping the waves around the grid. The numerical dispersion of this FV formulation is similar to that of O(,x2) staggered-grid finite-difference (FD) formulations when considering structured triangular meshes. The validation has been performed with analytical solutions of several canonical problems and with numerical solutions computed with a well-established FD time-domain method in heterogeneous media. In the presence of a free surface, the finite-volume method requires 10 triangles per wavelength for a flat topography, and fifteen triangles per wavelength for more complex shapes, well below the criteria required by the staircase approximation of O(,x2) FD methods. Comparisons between the frequency-domain finite-volume and the O(,x2) rotated FD methods also show that the former is faster and less memory demanding for a given accuracy level, an attractive feature for frequency-domain seismic inversion. We have thus developed an efficient method for 2-D P,SV -wave modelling on structured triangular meshes as a tool for frequency-domain full-waveform inversion. Further work is required to improve the accuracy of the method on unstructured meshes. [source] Development of a finite element radiation model applied to two-dimensional participating mediaHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 6 2005Hong Qi Abstract A finite element method (FEM) for radiative heat transfer has been developed and it is applied to 2D problems with unstructured meshes. The present work provides a solution for temperature distribution in a rectangular enclosure with black or gray walls containing an absorbing, emitting, isotropically scattering medium. Compared with the results available from Monte Carlo simulation and finite volume method (FVM), the present FEM can predict the radiative heat transfer accurately. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(6): 386,395, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20076 [source] Laminar and turbulent flow calculations through a model human upper airway using unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007P. Nithiarasu Abstract In this paper, numerical investigation of airflow through a human upper airway is presented using an unstructured-based characteristic-based split (CBS) scheme. The CBS scheme used in the present study employs a fully explicit matrix-free solution procedure along with artificial compressibility. A one equation Spalrat,Allmaras (SA) turbulence model is employed to study low and moderate Reynolds number flows. A detailed discussion of the qualitative and quantitative results is presented. The results show a strong influence of the Reynolds number on the flow pattern and quantities of interest, pressure drop and wall shear stress. It is also apparent that SA model can be employed on unstructured meshes to predict the steady flow with good accuracy. Thus, the novelties of the present paper are: use of the unstructured mesh-based solution algorithm and the successful application of the SA model to a typical human upper airway. Copyright © 2006 John Wiley & Sons, Ltd. [source] Simplified model for mould filling simulations using CVFEM and unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2007K. C. Estacio Abstract In this work, the finite volume method is used to numerically solve the fluid governing equations of the filling phase of thermoplastic injection in a narrow gap with free surfaces, subject to heat transfer, using a semi-Lagrangian formulation in an unstructured mesh. The modified-Cross model with Arrhenius temperature dependence is employed to describe the viscosity of the melt. The pressure field is obtained using the control volume finite element method. The three-dimensional temperature field is solved by a semi-Lagrangian scheme based on the finite volume method. A simpler two-dimensional model for temperature field is also deduced and presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz,Zhu error estimatorINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2003M. Picasso Abstract The framework of Formaggia and Perotto (Numerische Mathematik 2001; 89: 641,667) is considered to derive a new anisotropic error indicator for a Laplace problem in the energy norm. The matrix containing the error gradient is approached using a Zienkiewicz,Zhu error estimator. A numerical study of the effectivity index is proposed for anisotropic unstructured meshes, showing that our indicator is sharp. An anisotropic adaptive algorithm is implemented, aiming at controlling the estimated relative error. Copyright © 2003 John Wiley & Sons, Ltd. [source] Comparison of three second-order accurate reconstruction schemes for 2D Euler and Navier,Stokes compressible flows on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2001N. P. C. Marques Abstract This paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier,Stokes flows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6,17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10° ramp and a supersonic bump; and two viscous laminar compressible flow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational efficiency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier,Stokes flow calculations is recommended. Copyright © 2001 John Wiley & Sons, Ltd. [source] Quasi optimal finite difference method for Helmholtz problem on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010Daniel T. Fernandes Abstract A quasi optimal finite difference method (QOFD) is proposed for the Helmholtz problem. The stencils' coefficients are obtained numerically by minimizing a least-squares functional of the local truncation error for plane wave solutions in any direction. In one dimension this approach leads to a nodally exact scheme, with no truncation error, for uniform or non-uniform meshes. In two dimensions, when applied to a uniform cartesian grid, a 9-point sixth-order scheme is derived with the same truncation error of the quasi-stabilized finite element method (QSFEM) introduced by Babu,ka et al. (Comp. Meth. Appl. Mech. Eng. 1995; 128:325,359). Similarly, a 27-point sixth-order stencil is derived in three dimensions. The QOFD formulation, proposed here, is naturally applied on uniform, non-uniform and unstructured meshes in any dimension. Numerical results are presented showing optimal rates of convergence and reduced pollution effects for large values of the wave number. Copyright © 2009 John Wiley & Sons, Ltd. [source] Polygonal finite elements for topology optimization: A unifying paradigmINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2010Cameron Talischi Abstract In topology optimization literature, the parameterization of design is commonly carried out on uniform grids consisting of Lagrangian-type finite elements (e.g. linear quads). These formulations, however, suffer from numerical anomalies such as checkerboard patterns and one-node connections, which has prompted extensive research on these topics. A problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members, leading to mesh-dependent sub-optimal designs. Thus, to address the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities. Copyright © 2009 John Wiley & Sons, Ltd. [source] Higher-resolution convection schemes for flow in porous media on highly distorted unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008Sadok Lamine Abstract Higher-resolution schemes are presented for convective flow approximation on highly distorted unstructured grids. The schemes are coupled with continuous full-tensor Darcy-flux approximations. A sequence of non-uniform and distorted grid formulations are developed and compared for a range of unstructured meshes with variable grid spacing. The higher-order schemes are constructed using non-uniform grid slope limiters such that they are stable with a local maximum principle, ensuring that solutions are free of spurious oscillations. Benefits of the resulting schemes are demonstrated for classical test problems in reservoir simulation including cases with full-tensor permeability fields. The test cases involve a range of unstructured grids with variations in grid spacing, orientation and permeability that lead to flow fields that are poorly resolved by standard simulation methods. The higher-order formulations are shown to effectively reduce numerical diffusion, leading to improved resolution of concentration and saturation fronts. 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] A distributed memory parallel implementation of the multigrid method for solving three-dimensional implicit solid mechanics problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004A. Namazifard Abstract We describe the parallel implementation of a multigrid method for unstructured finite element discretizations of solid mechanics problems. We focus on a distributed memory programming model and use the MPI library to perform the required interprocessor communications. We present an algebraic framework for our parallel computations, and describe an object-based programming methodology using Fortran90. The performance of the implementation is measured by solving both fixed- and scaled-size problems on three different parallel computers (an SGI Origin2000, an IBM SP2 and a Cray T3E). The code performs well in terms of speedup, parallel efficiency and scalability. However, the floating point performance is considerably below the peak values attributed to these machines. Lazy processors are documented on the Origin that produce reduced performance statistics. The solution of two problems on an SGI Origin2000, an IBM PowerPC SMP and a Linux cluster demonstrate that the algorithm performs well when applied to the unstructured meshes required for practical engineering analysis. Copyright © 2004 John Wiley & Sons, Ltd. [source] Hierarchic finite element bases on unstructured tetrahedral meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Mark Ainsworth Abstract The problem of constructing hierarchic bases for finite element discretization of the spaces H1, H(curl), H(div) and L2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non-uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements. Copyright © 2003 John Wiley & Sons, Ltd. [source] A vertex-based finite volume method applied to non-linear material problems in computational solid mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003G. A. Taylor Abstract A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and three-dimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted. Copyright © 2002 John Wiley & Sons, Ltd. [source] Toward large scale F.E. computation of hot forging process using iterative solvers, parallel computation and multigrid algorithmsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5-6 2001K. Mocellin Abstract The industrial simulation code Forge3® is devoted to three-dimensional metal forming applications. This finite element software is based on an implicit approach. It is able to carry out the large deformations of viscoplastic incompressible materials with unilateral contact conditions. The finite element discretization is based on a stable mixed velocity,pressure formulation and tetrahedral unstructured meshes. Central to the Newton iterations dealing with the non-linearities, a preconditioned conjugate residual method (PCR) is used. The parallel version of the code uses an SPMD programming model and several results on complex applications have been published. In order to reduce the CPU time computation, a new solver has been developed which is based on multigrid theory. A detailed presentation of the different elements of the method is given: the geometrical approach based on embedded meshes, the direct resolution of the velocity,pressure system, the use of PCR method as an original smoother and for solving the coarse problem, the full multigrid method and the required preconditioning by an incomplete Cholesky factorization for problems with complex contact conditions. By considering different forging cases, the theoretical properties of the multigrid method are numerically verified, optimizations of the solver are presented and finally, the results obtained on several industrial problems are given, showing the efficiency of the new solver that provides speed-up larger than 5. Copyright © 2001 John Wiley & Sons, Ltd. [source] The generation of hexahedral meshes for assembly geometry: survey and progress,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001Timothy J. Tautges Abstract The finite element method is being used today to model component assemblies in a wide variety of application areas, including structural mechanics, fluid simulations, and others. Generating hexahedral meshes for these assemblies usually requires the use of geometry decomposition, with different meshing algorithms applied to different regions. While the primary motivation for this approach remains the lack of an automatic, reliable all-hexahedral meshing algorithm, requirements in mesh quality and mesh configuration for typical analyses are also factors. For these reasons, this approach is also sometimes required when producing other types of unstructured meshes. This paper will review progress to date in automating many parts of the hex meshing process, which has halved the time to produce all-hex meshes for large assemblies. Particular issues which have been exposed due to this progress will also be discussed, along with their applicability to the general unstructured meshing problem. Published in 2001 by John Wiley & Sons, Ltd. [source] A variational multiscale Newton,Schur approach for the incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2010D. Z. Turner Abstract In the following paper, we present a consistent Newton,Schur (NS) solution approach for variational multiscale formulations of the time-dependent Navier,Stokes equations in three dimensions. The main contributions of this work are a systematic study of the variational multiscale method for three-dimensional problems and an implementation of a consistent formulation suitable for large problems with high nonlinearity, unstructured meshes, and non-symmetric matrices. In addition to the quadratic convergence characteristics of a Newton,Raphson-based scheme, the NS approach increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form. As a result, more computations are performed at the element level. Using a variational multiscale framework, we construct a two-level approach to stabilizing the incompressible Navier,Stokes equations based on a coarse and fine-scale subproblem. We then derive the Schur complement form of the consistent tangent matrix. We demonstrate the performance of the method for a number of three-dimensional problems for Reynolds number up to 1000 including steady and time-dependent flows. Copyright © 2009 John Wiley & Sons, Ltd. [source] Implicit symmetrized streamfunction formulations of magnetohydrodynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008K. S. Kang Abstract We apply the finite element method to the classic tilt instability problem of two-dimensional, incompressible magnetohydrodynamics, using a streamfunction approach to enforce the divergence-free conditions on the magnetic and velocity fields. We compare two formulations of the governing equations, the standard one based on streamfunctions and a hybrid formulation with velocities and magnetic field components. We use a finite element discretization on unstructured meshes and an implicit time discretization scheme. We use the PETSc library with index sets for parallelization. To solve the nonlinear problems on each time step, we compare two nonlinear Gauss-Seidel-type methods and Newton's method with several time-step sizes. We use GMRES in PETSc with multigrid preconditioning to solve the linear subproblems within the nonlinear solvers. We also study the scalability of this simulation on a cluster. Copyright © 2008 John Wiley & Sons, Ltd. [source] Low-cost implicit schemes for all-speed flows on unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2008T. Kloczko Abstract Matrix-free implicit treatments are now commonly used for computing compressible flow problems: a reduced cost per iteration and low-memory requirements are their most attractive features. This paper explains how it is possible to preserve these features for all-speed flows, in spite of the use of a low-Mach preconditioning matrix. The proposed approach exploits a particular property of a widely used low-Mach preconditioner proposed by Turkel. Its efficiency is demonstrated on some steady and unsteady applications. Copyright © 2008 John Wiley & Sons, Ltd. [source] A robust methodology for RANS simulations of highly underexpanded jetsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008G. Lehnasch Abstract This work aims at developing/combining numerical tools adapted to the simulation of the near field of highly underexpanded jets. An overview of the challenging numerical problems related to the complex shock/expansion structure encountered in these flows is given and an efficient and low-cost numerical strategy is proposed to overcome these, even on short computational domains. Based on common upwinding algorithms used on unstructured meshes in a mixed finite-volume/finite-element approach, it relies on an appropriate utilization of zonal anisotropic remeshing algorithms. This methodology is validated for the whole near field of cold air jets issuing from axisymmetric convergent nozzles and yielding various underexpansion ratios. In addition, the most usual corrections of the k,, model used to take into account the compressibility effects on turbulence are precisely assessed. Copyright © 2007 John Wiley & Sons, Ltd. [source] An eigenvector-based linear reconstruction scheme for the shallow-water equations on two-dimensional unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007Sandra Soares Frazão Abstract This paper presents a new approach to MUSCL reconstruction for solving the shallow-water equations on two-dimensional unstructured meshes. The approach takes advantage of the particular structure of the shallow-water equations. Indeed, their hyperbolic nature allows the flow variables to be expressed as a linear combination of the eigenvectors of the system. The particularity of the shallow-water equations is that the coefficients of this combination only depend upon the water depth. Reconstructing only the water depth with second-order accuracy and using only a first-order reconstruction for the flow velocity proves to be as accurate as the classical MUSCL approach. The method also appears to be more robust in cases with very strong depth gradients such as the propagation of a wave on a dry bed. Since only one reconstruction is needed (against three reconstructions in the MUSCL approach) the EVR method is shown to be 1.4,5 times as fast as the classical MUSCL scheme, depending on the computational application. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||||||||