Showing papers in "Cmes-computer Modeling in Engineering & Sciences in 2010"

Higher-Order Stress-Strain Theory for Damage Modeling Implemented in an Element-free Galerkin Formulation

Abstract: Gradient theories have found wide applications in modeling of strain softening phenomena. This paper presents a higher order stress-strain theory to describe the damage behavior of strain softening materials. In contrast to most conventional gradient approaches for damage modeling, the present higher order theory considers strain gradients and their conjugate higher-order stress such that stable numerical solutions may be achieved. We have described the derivation of the required constitutive relationships, the governing equations and its weak form for this higher-order theory. The constitutive coefficients were obtained from a granular media approach such that the internal length scale parameter reflects the natural granularity of the underlying microstructure. The weak form was discretized using an element-free Galerkin (EFG) formulation that readily admits approximation functions of higher-order continuity. We have also discussed the implementation of essential boundary conditions and linearization of the derived discrete equations. Finally, the applicability of the derived model is demonstrated through two examples with different imperfections designed to initiate dislocation bands and shear bands, respectively.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Abstract: Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML)

Abstract: Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a second-order finite-difference time scheme. However it is often of interest to increase the order of the time-stepping scheme in order to increase the accuracy of the algorithm. This is important for instance in the case of very long simulations. We study how to define and implement a new unsplit non-convolutional PML called the Auxiliary Differential Equation PML (ADE-PML), based on a high-order Runge-Kutta time-stepping scheme and optimized at grazing incidence. We demonstrate that when a second-order time-stepping scheme is used the convolutional PML can be derived from that more general non-convolutional ADE-PML formulation, but that this new approach can be generalized to high-order schemes in time, which implies that it can be made more accurate. We also show that the ADE-PML formulation is numerically stable up to 100,000 time steps.

Two-phase flow in complex geometries: A diffuse domain approach.

Abstract: We present a new method for simulating two-phase flows in complex geometries, taking into account contact lines separating immiscible incompressible components. We combine the diffuse domain method for solving PDEs in complex geometries with the diffuse-interface (phase-field) method for simulating multiphase flows. In this approach, the complex geometry is described implicitly by introducing a new phase-field variable, which is a smooth approximation of the characteristic function of the complex domain. The fluid and component concentration equations are reformulated and solved in larger regular domain with the boundary conditions being implicitly modeled using source terms. The method is straightforward to implement using standard software packages; we use adaptive finite elements here. We present numerical examples demonstrating the effectiveness of the algorithm. We simulate multiphase flow in a driven cavity on an extended domain and find very good agreement with results obtained by solving the equations and boundary conditions in the original domain. We then consider successively more complex geometries and simulate a droplet sliding down a rippled ramp in 2D and 3D, a droplet flowing through a Y-junction in a microfluidic network and finally chaotic mixing in a droplet flowing through a winding, serpentine channel. The latter example actually incorporates two different diffuse domains: one describes the evolving droplet where mixing occurs while the other describes the channel.

An Object-Oriented MPM Framework for Simulation of Large Deformation and Contact of Numerous Grains

Abstract: The Material Point Method (MPM) is more expensive in terms of storage than other methods, as MPM makes use of both mesh and particle data. Therefore, it is critical to develop an efficient MPM framework for engineering applications, such as impact and explosive simulations. This paper presents a new architecture for MPM computer code, developed using object-oriented design, which enables MPM analysis of a mass of grains, large deformation, high strain rates and complex material behavior. It is flexible, extendible, and easily modified for a variety of MPM analysis procedures. An MPM scheme combining contact algorithm with USF, USL and MUSL formulation is presented, and an improved contact detection scheme is proposed to avoid contact occurring earlier than actual time, and several schemes are developed to reduce the memory requirement and computational cost, including the local multi-mesh contact algorithm, dynamic internal state variables for materials, dynamic grid and moving grid technique. Finally, some numerical examples are presented to demonstrate the computational efficiency and memory requirement of the framework.

Novel Algorithms Based on the Conjugate Gradient Method for Inverting Ill-Conditioned Matrices, and a New Regularization Method to Solve Ill-Posed Linear Systems

Abstract: We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the con- jugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting ill- conditioned matrices, we add a vector equation into the given matrix equation for obtaining the left-inversion of matrix (and a similar vector equation for the right- inversion) and thus we obtain an over-determined system. The resulting two modi- fications of the MCGM, namely the MCGM1 and MCGM2, are found to be much better for finding the inverses of ill-conditioned matrices, such as the Vandermonde matrix and the Hilbert matrix. We propose a natural regularization method for solv- ing an ill-posed linear system, which is theoretically and numerically proven in this paper, to be better than the well-known Tikhonov regularization. The presently proposed natural regularization is shown to be equivalent to using a new precondi- tioner, with better conditioning. The robustness of the presently proposed method provides a significant improvement in the solution of ill-posed linear problems, and its convergence is as fast as the CGM for the well-posed linear problems.

Comparison of the Fast Multipole Method with Hierarchical Matrices for the Helmholtz-BEM

Abstract: The simulation of the hydroacoustic sound radiation of ship-like struc- tures has an ever-growing importance due to legal regulations. Using the boundary element method, the overall dimension of the problem is reduced and only inte- grals over surfaces have to be considered. Additionally, the Sommerfeld radiation condition is automatically satisfied by proper choice of the fundamental solution. However, the resulting matrices are fully populated and the set-up time and memory consumption scale quadratically with respect to the degrees of freedom. Different fast boundary element methods have been introduced for the Helmholtz equation, resulting in a quasilinear complexity. Two of these methods are considered in this paper, namely the fast multipole method and hierarchical matrices. The first one applies a series expansion of the fundamental solution, whereas the second one is of pure algebraic nature and represents partitions of the original system matrix by low-rank approximations in outer-product form. The two methods are compared for a structure, which is partly immersed in water. The memory consumption, the set-up time and the time required for a matrix-vector product are investigated. Dif- ferent frequency regimes are considered. Since the diagonal multipole expansion is known to be unstable in the low-frequency regime, two types of expansions are necessary for a wideband analysis.

Numerical Solution of Dual Phase Lag Model of Bioheat Transfer Using the General Boundary Element Method

Abstract: Heat transfer processes proceeding in domain of heating tissue are discussed. The typical model of bioheat transfer bases, as a rule, on the well known Pennes equation, this means the heat diffusion equation with additional terms corresponding to the perfusion and metabolic heat sources. Here, the other approach basing on the dual-phase-lag equation (DPLE) is considered in which two time delays τq, τT (phase lags) appear. The DPL equation contains a second order time derivative and higher order mixed derivative in both time and space. This equation is supplemented by the adequate boundary and initial conditions. To solve the problem the general boundary element method is adapted. The examples of computations for 2D problem are presented in the final part of the paper. The efficiency and exactness of the algorithm proposed are also discussed.

Analysis of Thermoelastic Waves in a Two-Dimensional Functionally Graded Materials Domain by the Meshless Local Petrov-Galerkin (MLPG) Method

Abstract: This contribution focuses on the simulation of two-dimensional elastic wave propagation in functionally graded solids and structures. Gradient volume fractions of the constituent materials are assumed to obey the power law function of position in only one direction and the effective mechanical properties of the material are determined by the Mori–Tanaka scheme. The investigations are carried out by extending a meshless method known as the Meshless Local Petrov-Galerkin (MLPG) method which is a truly meshless approach to thermo-elastic wave propagation. Simulations are carried out for rectangular domains under transient thermal loading. To investigate the effect of material composition on the dynamic response of functionally graded materials, a metal/ceramic (Aluminum (Al) and Alumina (Al2O3) are considered as ceramic and metal constituents) composite is considered for which the transient thermal field, dynamic displacement and stress fields are reported for different material distributions.

MLPG Method Based on Rankine Source Solution for Modelling 3D Breaking Waves

Abstract: In this paper, the Meshless Local Petrov-Galerkin method based on Rankine source solution (MLPG_R) is further developed to model 3D breaking waves. For this purpose, the technique for identifying free surface particles called Mixed Particle Number Density and Auxiliary Function Method (MPAM) and the semi-analytical technique for estimating the domain integrals for 2D cases are extended to 3D cases. In addition, a new semi-analytical technique is developed to deal with the local spherical surface integrals. The numerical results obtained by the newly developed method will be compared with experimental data available in literature and satisfactory agreement will be shown.

A New Adaptive Algorithm for the Fast Multipole Boundary Element Method

Abstract: A new definition of the interaction list in the fast multipole method (FMM) is introduced in this paper, which can reduce the moment-to-local (M2L) translations by about 30-40% and therefore improve the efficiency for the FMM. In addition, an adaptive tree structure is investigated, which is potentially more efficient than the oct-tree structure for thin and slender domains as in the case of micro-electro-mechanical systems (MEMS). A combination of the modified inter- action list (termed L2 modification in the adaptive fast multipole BEM) and the adaptive tree structure in the fast multipole BEM has been implemented for both 3- D potential and 3-D acoustic wave problems. In the potential theory case, the code is based on the earlier adaptive algorithm proposed in (Shen, L. and Y. J. Liu (2007). "An adaptive fast multipole boundary element method for three-dimensional poten- tial problems." Computational Mechanics 39(6): 681-691) with the so called "new FMM" where the M2L translations are replaced by the exponential (M2X, X2X, and X2L) translations. Suitable changes are proposed in the algorithm for the new adaptive fast multipole BEM. Finally, a new adaptive algorithm which encompasses all these modifications and the established algorithms is presented (that is, combin- ing the original adaptive fast multipole BEM, L2 modification and adaptive tree for slender structures). Numerical results are presented to demonstrate the efficiencies of the new adaptive fast multipole BEM for solving both potential and acoustic wave problems. About 30-40% improvements in the computational efficiency are achieved with the L2 modification for all cases, and additional improvements are observed with the adaptive tree for some large-scale thin structures (MEMS mod- els), without the lost of accuracy.

Size Effects and Mesh Independence in Dynamic Fracture Analysis of Brittle Materials

Abstract: Numerical predictions of the failure load of large structures, accounting for size effects, require the adoption of appropriate constitutive relations. These relations depend on the size of the elements and on the correlation lengths of the random fields that describe material properties. The authors proposed earlier expressions for the tensile stress-strain relation of concrete, whose parameters are related to standard properties of the material, such as Young’s modulus or specific fracture energy and to size. Simulations conducted for a typical concrete showed that as size increases, the effective stress-strain diagram becomes increasingly linear, with a sudden rupture, while at the same time the coefficients of variation (CV) of the relevant parameters decrease to negligible values, situation that renders Linear Elastic Fracture Mechanics (LEFM) applicable. However, it was later observed that a hitherto unknown problem arises in the analysis of non-homogeneous materials, leading to lack of mesh objectivity: the need to know a priori the degree of fracturing. This should affect not only the truss-like Discrete Element Method (DEM) employed herein, but also finite element analysis, requiring a careful evaluation of the energy dissipated by fracture or other mechanisms in the course of the loading process. In the paper a tentative criterion is proposed to account for the effect in non-linear dynamic fracture analysis.

Shape Memory Alloy: from Constitutive Modeling to Finite Element Analysis of Stent Deployment

Abstract: The use of shape memory alloys (SMA) in an increasing number of applications in many fields of engineering, and in particular in biomedical engineering, is leading to a growing interest toward an exhaustive modeling of their macroscopic behavior in order to construct reliable simulation tools for SMA-based devices. In this paper, we review the properties of a robust three-dimensional model able to reproduce both pseudo-elastic and shape-memory effect; then we calibrate the model parameters on experimental data and, finally, we exploit the model to perform the finite element analysis of pseudo-elastic Nitinol stent deployment in a simplified atherosclerotic artery model.

An Efficient Trefftz-Based Method for Three-Dimensional Helmholtz Problems in Unbounded Domains

Abstract: The Wave Based Method (WBM) is a numerical prediction technique for Helmholtz problems. It is an indirect Trefftz method using wave functions, which satisfy the Helmholtz equation, for the description of the dynamic variables. In this way, it avoids both the large systems and the pollution errors that jeopardize accurate element-based predictions in the mid-frequency range. The enhanced computational efficiency of the WBM as compared to the element-based methods has been proven for the analysis of both three-dimensional bounded and twodimensional unbounded problems. This paper presents an extension of the WBM to the application of three-dimensional acoustic scattering and radiation problems. To this end, an appropriate function set is proposed which satisfies both the governing Helmholtz equation and the Sommerfeld radiation condition. Also, appropriate source formulations are discussed for relevant sources in scattering problems. The accuracy and efficiency of the resulting method are evaluated in some numerical examples, including the 3D cat’s eye scattering problem.

Variable kinematics and advanced variational statements for free vibrations analysis of piezoelectric plates and shells

Abstract: This paper investigates the problem of free vibrations of multilayered plates and shells embedding anisotropic and thickness polarized piezoelectric layers. Carrera’s Unified Formulation (CUF) has been employed to implement a large variety of electro-mechanical plate/shell theories. So-called Equivalent Single Layer and Layer Wise variable descriptions are employed for mechanical and electrical variables; linear to fourth order expansions are used in the thickness direction z in terms of power of z or Legendre polynomials. Various forms are considered for the Principle of Virtual Displacements (PVD) and Reissner’s Mixed Variational Theorem (RMVT) to derive consistent differential electro-mechanical governing equations. The effect of electro-mechanical stiffness has been evaluated in both PVD and RMVT frameworks, while the effect of continuity of transverse variables (transverse shear and normal stresses and transverse normal electric displacement) has been addressed by comparing various forms of RMVT. According to CUF, governing equations related to a given variational statement have been written in terms of fundamental nuclei whose form is independent of the order of expansion and of the adopted variable description. The numerical results have been restricted to simply supported orthotropic plates and shells, for which exact three-dimensional solutions are available. A large numerical investigation has been conducted to compute fundamental and higher vibrations modes. An exhaustive numerical evaluation of assumptions, related to the various PVD and RMVT forms, is given. Classical, higher-order, layer-wise and mixed assumptions have been compared to available three-dimensional solutions. The convenience of hierarchical approaches based on CUF is shown, along with the suitability of the implemented RMVT forms to accurately trace the free vibration response of piezoelectric plates and shells. RMVT applications permit the vibration modes of transverse electro-mechanical variables 1 Corresponding author: Salvatore Brischetto, Department of Aeronautics and Space Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy. Tel: +39.011.564.6869, Fax: +39.011.564.6899, Email: salvatore.brischetto@polito.it. 2 Department of Aeronautics and Space Engineering, Politecnico di Torino, Italy 260 Copyright © 2010 Tech Science Press CMES, vol.65, no.3, pp.259-341, 2010 to be accurately evaluated in the thickness plate/shell direction .

Fictitious Time Integration Method of Fundamental Solutions with Chebyshev Polynomials for Solving Poisson-type Nonlinear PDEs

Abstract: The fictitious time integration method (FTIM) previously developed by Liu and Atluri (2008a) is combined with the method of fundamental solutions and the Chebyshev polynomials to solve Poisson-type nonlinear PDEs. The method of fundamental solutions with Chebyshev polynomials (MFS-CP) is an exponentially-convergent meshless numerical method which is able to solving nonhomogeneous partial differential equations if the fundamental solution and the analytical particular solutions of the considered operator are known. In this study, the MFS-CP is extended to solve Poisson-type nonlinear PDEs by using the FTIM. In the solution procedure, the FTIM is introduced to convert a Poisson-type nonlinear PDE into a sequence of linear nonhomogeneous modified Helmholtz equations which are then formally solved by the MFS-CP. Several numerical experiments were carried out to validate the proposed methods.

Efficient Cohomology Computation for Electromagnetic Modeling

Abstract: The systematic potential design is of high importance in computational electromagnetics. For example, it is well known that when the efficient eddycurrent formulations based on a magnetic scalar potential are employed in problems which involve conductive regions with holes, the so-called thick cuts are needed to make the boundary value problem well defined. Therefore, a considerable effort has been invested over the past twenty-five years to develop fast and general algorithms to compute thick cuts automatically. Nevertheless, none of the approaches proposed in literature meet all the requirements of being automatic, computationally efficient and general. In this paper, an automatic, computationally efficient and provably general algorithm is presented. It is based on a rigorous algorithm to compute a cohomology basis of the insulating region with state-of-art reductions techniques—the acyclic sub-complex technique, among others—expressly designed for cohomology computations over simplicial complexes. Its effectiveness is demonstrated by presenting a number of practical benchmarks. The automatic nature of the proposed approach together with its low computational time enable the routinely use of cohomology computations in computational electromagnetics.

Finite Element Nonlinear Analysis for Catenary Structure Considering Elastic Deformation

Abstract: This paper numerically investigates the behavior of sag and tension of inclined catenary structure considering elastic deformation. Equilibrium equation for computing elastic catenary is formulated by employing finite element method (FEM). Minimum potential energy principle and the Lagrange multiplier method are used in the formulation to derive equilibrium equation with constraint condition for catenary length. Since stiffness and loading forces of catenary are dependent on its own geometry, the equilibrium equation is nonlinear. Using the iterative scheme such as fixed point iteration or bisection, equilibrium position and tension are found. Based on the formulation, a Fortran solver is developed in this study. With the solver, numerical analyses for example catenary structures are carried out. From the numerical examples, the sag and tension of catenary only which ignores elastic deformation are compared with those of elastic catenary of which elastic deformation is considered. By analyzing elastic catenary for various axial stiffness conditions, the asymptotic behaviors of sag and tension are examined. Inclined catenary structures with various slopes are also analyzed to study the effect of catenary slope on sag and tension.

A Comparative Study of Global and Local Meshless Methods for Diffusion-Reaction Equation

Abstract: This paper focuses on the comparative study of global and local mesh- less methods based on collocation with radial basis functions for solving two di- mensional initial boundary value diffusion-reaction problem with Dirichlet and Neumann boundary conditions. A similar study was performed for the boundary value problem with Laplace equation by Lee, Liu, and Fan (2003). In both global and local methods discussed, the time discretization is performed in explicit and implicit way and the multiquadric radial basis functions (RBFs) are used to inter- polate diffusion-reaction variable and its spatial derivatives. Five and nine nodded sub-domains are used in the local support of the local method. Uniform and non- uniform space discretization is used. Accuracy of global and local approaches is assessed as a function of the time and space discretizations, and value of the shape parameter. One can observe the convergence with denser nodes and with smaller time-steps in both methods. The global method is prone to instability due to ill- conditioning of the collocation matrix with the increase of the number of the nodes in cases N t 3000. On the other hand, the global method is more stable with re- spect to the time-step length. Numerical tests with and without noise are conducted based on the methodology proposed in Younga, Fana, Hua, and Atluri (2009). The results show larger stability of the local versions of the method in comparison with the global ones. The accuracy of the local method is comparable with the accuracy of the global method. The local method is more efficient because we solve only a small system of equations for each node in explicit case and a sparse system of equations in implicit case. Hence the local method represents a preferable choice to its global counter part.

The Hybrid Boundary Node Method Accelerated by Fast Multipole Expansion Technique for 3D Elasticity

Abstract: In this paper, a fast formulation of the hybrid boundary node method (Hybrid BNM) for solving 3D elasticity is presented. Coupling modified variational principle with the Moving Least Squares (MLS) approximation, the Hybrid BNM only requires discrete nodes constructed on the surface of a domain. The preconditioned GMERS is employed to solve the resulting system of equations. At each iteration step of the GMERS, the matrix-vector multiplication is accelerated by the fast multipole method (FMM). The fundamental solution of threedimensional elasticity problem is expanded in terms of series. An oct-tree data structure is adopted to subdivide the computational domain into well-separated cells hierarchically and to invoke the multipole expansion approximation. Formulations for the local and multipole expansions and conversion of multipole to local expansion are given. Nearly one million of total unknowns can be computed on a PC with 2.67GHz CPU and 2.0GB RAM. All the formulations are implemented in a computer code written in C++. Numerical examples demonstrate the accuracy and efficiency of the proposed approach.

A moving IRBFN-based integration-free meshless method

Abstract: A novel approximation method using integrated radial basis function networks (IRBFN) coupled with moving least square (MLS) approximants, namely moving integrated radial basis function networks (MIRBFN), is proposed in this work. In this method, the computational domain w is divided into finite sub-domains w which satisfy point-wise overlap condition. The local function interpolation is constructed by using IRBFN supported by all nodes in subdomain w. The global function is then constructed by using Partition of Unity Method (PUM), where MLS functions play the role of partition of unity. As a result, the proposed method is locally supported and yields sparse and banded interpolation matrices. The computational efficiency are excellently improved in comparison with that of the original global IRBFN method. In addition, the present method possesses the Kronecker-d property, which makes it easy to impose the essential boundary conditions. The proposed method is applicable to randomly distributed datasets and arbitrary domains. In this work, the MIRBFN method is implemented in the collocation of a first-order system formulation to solve PDEs governing various problems including heat transfer, elasticity of both compressible and incompressible materials, and linear static crack problems. The numerical results show that the present method offers high order of convergence and accuracy.

Meshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds Number

Abstract: A meshfree point collocation method has been developed for the velocity- vorticity formulation of two-dimensional, steady state incompressible Navier-Stokes equations. Particular emphasis was placed on the application of the velocity-correc- tion method, ensuring the continuity equation. The Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunc- tion with the general framework of the point collocation method. Computations are obtained for regular and irregular nodal distributions, stressing the positivity con- ditions that make the matrix of the system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through two representative, well-known, and established benchmark problems. The numerical scheme was also applied to a case with irregular geometry for marginally high Reynolds numbers.

Node Placement Method by Bubble Simulation and Its Application

Abstract: In the light of the ideas and treatment technologies about molecular dynamics simulation and bubble meshing, a new approach of node placement for the meshless method called node placement method by bubble simulation (NPBS method), is proposed Nodes are seen as the centers of the bubbles which can be moved by their interacting forces Through dynamic simulation, bubbles are placed into a near-optimal configuration, and the centers of bubbles will form a good-quality node distribution in the domain This process doesn't need updating the mesh connection constantly, ie, is totally meshfree Some example results show that the uniform point sets and non-uniform point sets generated by NPBS method have good construction, and the non-uniform point sets have also good gradualness which is prefer to have for numerical solution methods of partial dif- ferential equations in some case In addition, NPBS method has good adaptability to complex regions Since the defined interbubble force is short-range, this method has inherent parallelism Two simple parallel example results show that the parallel generated node sets are also good-quality Furthermore, the node sets optimized by bubble simulation are used in the meshless method, and by comparison, the advan- tage with the less computational error is shown And it is easy to make use of the information of neighbor bubbles generated by NPBS method for finding the nodes on the influence domain in meshless analysis Finally, the node sets generated by NPBS method are also used for triangular mesh generation and refinement in finite element method The results show that the mesh has excellent quality

A Thermal Lattice Boltzmann Model for Flows with Viscous Heat Dissipation

Abstract: A thermal BGK lattice Boltzmann model for flows with viscous heat dissipation is proposed. In this model, the temperature is solved by a separate thermal distribution function, where the equilibrium distribution function is sim- ilar to its hydrodynamic counterpart, except that the leading quantity is tempera- ture. The viscous dissipation rate is obtained by computing the second-order mo- ments of non-equilibrium distribution function, which avoids the discretization of the complex gradient term, and can be easily implemented. The proposed ther- mal lattice Boltzmann model is scrutinized by computing two-dimensional thermal Poiseuille flow, thermal Couette flow, natural convection in a square cavity, and three-dimensional thermal Poiseuille flow in a square duct. Numerical simulations indicate that the second order accurate LBM scheme is not degraded by the present thermal BGK lattice Boltzmann model.

New algorithm for evaluation of electric fields due to indirect lightning strike

Abstract: Evaluation of electric field due to indirect lightning strike is an interesting subject. Calculation of electric and magnetic fields in time domain with the consideration of ground conductivity effect in the shortest possible time is an important objective. In this paper, using dipole method, Maxwell's equation and Cooray-Rubinstein formula, a new method for calculation of electric field in time domain is proposed. In addition, this proposed algorithm can also be used to evaluate the effect at the far distance cases of observation point from lightning channel.

Algebraic Formulation of Elastodynamics: the Cell Method

Abstract: This paper completes a preceeding paper on the algebraic formulation of elastostatics (Tonti, Zarantonello (2009)). It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of dif- ferential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual subdivision of the time axis, as we did for a space cell complex. The mass matrix obtained with the direct algebraic formulation is diagonal.

A new incompressible Navier-Stokes solver combining Fourier pseudo-spectral and immersed boundary methods

Abstract: A new numerical methodology combining Fourier pseudo-spectral and immersed boundary methods - IMERSPEC - is developed for fluid flow prob- lems governed by the incompressible Navier-Stokes equations. The numerical al- gorithm consists in a classical Fourier pseudo-spectral methodology using the col- location method where wall boundary conditions are modelled by using an im- mersed boundary method (IBM). The performance of that new methodology is exemplified in two-dimensional numerical simulations of Green-Taylor decaying vortex, lid-driven cavity and flow over a square cylinder. The convergence rate, the accuracy, the influence of the Reynolds number and the external domain size are analyzed. This new method combines some advantages of high accuracy and low computational cost provided by Fourier pseudo-spectral methods (FPSM) with the possibility of tackling complex geometries given by immersed boundary method.

Analytical Solution for Single and Multiple impacts with Strain-rate Effects for Shot Peening

Abstract: Shot peening is a complex and random process which is controlled by many input parameters. Numerical methods, which are normally used for impact problems will prohibitively put strain on the computing resources since a large number of impacts are involved in the computations. In this paper, a simplified analytical approach is used to predict the residual compressive stress that includes strain-rate effects. This is based on the method proposed by Shen and Atluri (2006) with a simple modification to include the strain rate effects. The residual stresses are predicted in materials SAE1070 and Inco718. In the computations, the random variation of the input parameters are simulated to predict the residual stress variation using the Monte-Carlo method. The stress distributions computed using the analytical method compare well with the direct numerical methods and the experimental results.