A novel variable resolution global spectral method on the sphere

A variable resolution global spectral method is created on the sphere using High resolution Tropical Belt Transformation (HTBT). HTBT belongs to a class of map called reparametrisation maps. HTBT parametrisation of the sphere generates a clustering of points in the entire tropical belt; the density of the grid point distribution decreases smoothly in the domain outside the tropics. This variable resolution method creates finer resolution in the tropics and coarser resolution at the poles. The use of FFT procedure and Gaussian quadrature for the spectral computations retains the numerical efficiency available with the standard global spectral method. Accuracy of the method for meteorological computations are demonstrated by solving Helmholtz equation and non-divergent barotropic vorticity equation on the sphere. (C) 2011 Elsevier Inc. All rights reserved.

Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier-Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant. (C) 2012 Elsevier Inc. All rights reserved.

Finite Element Method For A Nonlocal Problem Of Kirchhoff Type

The nonlocal term in the nonlinear equations of Kirchhoff type causes difficulties when the equation is solved numerically by using the Newton-Raphson method. This is because the Jacobian of the Newton-Raphson method is full. In this article, the finite element system is replaced by an equivalent system for which the Jacobian is sparse. We derive quasi-optimal error estimates for the finite element method and demonstrate the results with numerical experiments.

Numerical Investigation of Heat Transfer from a Two-Dimensional Sudden Expansion Flow Using Nanofluids

Laminar forced convection heat transfer from two-dimensional sudden expansion flow of different nanofluids is studied numerically. The governing equations are solved using the unsteady stream function-vorticity method. The effect of volume fraction of the nanoparticles and type of nanoparticles on heat transfer is examined and found to have a significant impact. Local and average Nusselt numbers are reported in connection with various nanoparticle, volume fraction, and Reynolds number for expansion ratio 2. The Nusselt number reaches peak values near the reattachment point and reaches asymptotic value in the downstream. Bottom wall eddy and volume fraction shows a significant impact on the average Nusselt number.

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN. (c) 2012 Elsevier Ltd. All rights reserved.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

SPLIT-STEP FORWARD MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Ito form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order gamma = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

Prior image-constrained l(1)-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography

A novel approach that can more effectively use the structural information provided by the traditional imaging modalities in multimodal diffuse optical tomographic imaging is introduced. This approach is based on a prior image-constrained-l(1) minimization scheme and has been motivated by the recent progress in the sparse image reconstruction techniques. It is shown that the proposed framework is more effective in terms of localizing the tumor region and recovering the optical property values both in numerical and gelatin phantom cases compared to the traditional methods that use structural information. (C) 2012 Optical Society of America

Minimal residual method provides optimal regularization parameter for diffuse optical tomography

The inverse problem in the diffuse optical tomography is known to be nonlinear, ill-posed, and sometimes under-determined, requiring regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of this regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). DOI: 10.1117/1.JBO.17.10.106015]

A numerical approach to determine the sufficiency of given boundary data sets for uniquely estimating interior elastic properties

We consider an inverse elasticity problem in which forces and displacements are known on the boundary and the material property distribution inside the body is to be found. In other words, we need to estimate the distribution of constitutive properties using the finite boundary data sets. Uniqueness of the solution to this problem is proved in the literature only under certain assumptions for a given complete Dirichlet-to-Neumann map. Another complication in the numerical solution of this problem is that the number of boundary data sets needed to establish uniqueness is not known even under the restricted cases where uniqueness is proved theoretically. In this paper, we present a numerical technique that can assess the sufficiency of given boundary data sets by computing the rank of a sensitivity matrix that arises in the Gauss-Newton method used to solve the problem. Numerical experiments are presented to illustrate the method.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Fracture Analysis of High strength and Ultra high strength Concrete beams by using Finite Element Method

This paper presents the details of nonlinear finite element analysis (FEA) of three point bending specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete (UHSC). Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Cracking strength criterion has been used for simulation of crack propagation by conducting nonlinear FEA. The description about FEA using crack strength criterion has been outlined. Bi-linear tension softening relation has been used for modeling the cohesive stresses ahead of the crack tip. Numerical studies have been carried out on fracture analysis of three point bending specimens. It is observed from the studies that the computed values from FEA are in very good agreement with the corresponding experimental values. The computed values of stress vs crack width will be useful for evaluation of fracture energy, crack tip opening displacement and fracture toughness. Further, these values can also be used for crack growth study, remaining life assessment and residual strength evaluation of concrete structural components.

Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws

A computational tool called ``Directional Diffusion Regulator (DDR)'' is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws. The direction based regulator when used with dimension splitting solvers, is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect. The basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities, with the upwind bias decreasing smoothly to a minimum in the farthest direction. The discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables (say density, pressure, temperature, Mach number or even wave velocity etc.). DDR is applied to both the non-convective as well as whole unsplit dissipative flux terms of some numerical schemes, mainly of Local Lax-Friedrichs, to solve some benchmark problems describing inviscid compressible flow, shallow water dynamics and magneto-hydrodynamics. The first order solutions consistently improved depending on the extent of grid non-alignment to discontinuities, with the major influence due to regulation of non-convective diffusion. The application is also experimented on schemes such as Roe, Jameson-Schmidt-Turkel and some second order accurate methods. The consistent improvement in accuracy either at moderate or marked levels, for a variety of problems and with increasing grid size, reasonably indicate a scope for DDR as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework. (C) 2012 Elsevier Inc. All rights reserved.

Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C (0) interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H (2), H (1) and L (2) norms. L (a) norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.

Numerical Investigation on Laminar Flow Due to Sudden Expansion Using Nanofluids

Laminar two-dimensional sudden expansion flow of different nanofluids is studied numerically. The governing equations are solved using stream function-vorticity method. The effect of volume fraction of the nanoparticles and type of nanoparticles on flow behaviour is examined and found significant impact. The flow response to Reynolds number in the presence of nanoparticles is examined. The presence of nanoparticles decreases the flow bifurcation Reynolds number. The size and the reattachment length of the bottom wall recirculation increase with increasing volume fraction and particle density. The effect of volume fraction and density of nanoparticles on friction factor is reported. The bottom wall recirculation strongly respond to the variation in volume faction and type of particles. However, weak response is observed for top wall recirculation.