Large eddy simulation of wind flow around dome structures by the finite element method

In this paper, a stabilized finite element technique, actualized by streamline upwind Petrov-Galerkin (SUPG) stabilized method and three-step finite element method (FEM), for large eddy simulation (LES) is developed to predict the wind flow with high Reynolds numbers. Weak form of LES motion equation is combined with the SUPG stabilized term for the spatial finite element discretization. An explicit three-step scheme is implemented for the temporal discretization. For the numerical example of 2D wind flow over a square rib at Re=4.2×105, the Smagorinsky’s subgrid-scale (SSGS) model, the DSGS model, and the DSGS model with Cabot near-wall model are applied, and their results are analyzed and compared with experimental results. Furthermore, numerical examples of 3D wind flow around a surface-mounted cube with different Reynolds numbers are performed using DSGS model with Cabot near-wall model based on the present stabilized method to study the wind field and compared with experimental and numerical results. Finally, vortex structures for wind flow around a surface-mounted cube are studied by present numerical method. Stable and satisfactory results are obtained, which are consistent with most of the measurements even under coarse mesh.

In previous papers, we proposed finite element schemes based on the Petrov-Galerkin weak formulation using exponential weighting functions for solving accurately, and in a stable manner, the flow field of an incompressible viscous fluid. In this paper, we present the Petrov-Galerkin finite element scheme for turbulent flow fields based on large eddy simulation using the standard Smagorinsky model with the Van Driest damping function. The filtered incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth explicit differencing for both convection an diffusion terms. In order to evaluate more accurately a mass matrix, the well-known multi-pass algorithm was also adopted in this study. Numerical results obtained are compared through flow around a rectangular cylinder at Re = 22,000 with the experimental data and other existing numerical data.

Waves caused by steady ship motion are analyzed by the finite element method on the basis of the concept of the superposition of analytical and finite element solutions. The radiation condition is substituted by assuming appropriate radiating waves. Wave motions in a certain domain Ωa around the ship is assumed as a linear combination of the radiating waves and certain finite element solutions.The amplitude of the radiating waves can be determined by the condition of continuity on the surface of the domain Ωa, which can be expressed as the form of a single collocation equation.The finite element formulation can be developed by the same way as linear elastic problems, and its analysis can be performed easily by the use of general-purpose-programs for structural analysis. Numerical results obtained by the present method is compared with those by the previous authors, and they show good agreement.

Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows

We develop a class of mixed finite element schemes for stationary magnetohydrodynamics (MHD) models, using the magnetic field B \mathbfit {B} and the current density j \mathbfit {j} as discretization variables. We show that Gauss’s law for the magnetic field, namely ∇ ⋅ B = 0 \nabla \cdot \mathbfit {B}=0 , and the energy law for the entire system are exactly preserved in the finite element schemes. Based on some new basic estimates for H ( d i v ) H(\mathrm {div}) finite elements, we show that the new finite element scheme is well-posed. Furthermore, we show the existence of solutions to the nonlinear problems and the convergence of the Picard iterations and the finite element methods under some conditions.

Stabilized finite element method for viscoplastic flow: formulation and a simple progressive solution strategy

Energy-preserving finite element methods for a class of nonlinear wave equations

In this paper the appraisal of a folding dome structure under the influence of wind loading is discussed. The foldable structure considered is constructed from an assembly of interconnected elements, together with a flexible membrane, all of which are initially stored in a compact form and on deployment expand, like an umbrella, into a dome structure. Loading on the dome was obtained from a wind tunnel analysis of the pressure distribution over the roof of a 1:10 scale model of the structure. The critical loading obtained from the wind tunnel investigation was used, together with individual member and material tests, to form a series of numerical non-linear finite element models which were, in turn, used to investigate the forces within the structure. The numerical analysis was used to determine the critical wind loading that the structure can sustain, as well as providing a method by which to investigate the failure modes of the structure. In order to enhance the load carrying capacity of the dome it was found that both the strength and stiffnesss of the structural nodes needed to be enhanced and in addition, changes were necessary to substantially increase the stiffness of the individual member end caps.

*† ‡ , The solution for bulk fluid motion of a bidirectional coaxial vortex for application in vortex engine has been derived. The vortex engine is a novel combustion chamber in which swirl motion of reactants are used to maintain the chamber walls cool. The flow field has been considered both analytically and numerically. The model is based on incompressible, steady, axisymmetric, and non-reactive flow conditions. The governing PDEs are reduced to a system of nonlinear ODEs and then, by a coordinate transformation, their singularity has been relaxed. Solution domain has been decomposed into the inner viscous and outer inviscid regions, then, the velocity and pressure fields are obtained analytically. To verify the results, these ODEs are solved numerically via finite element method and by using the Galerkin and modified weighted residual formulations. The analytical and numerical results are in good agreement with each other. In comparison with other studies, the present calculated azimuthal velocity is more supportive of the experimental and numerical results and also confirms the presence of a forced-free vortex flow pattern. Location of the nontranslating vortex layer, mantle, is illuminated as well. Nomenclature i A = inlet area a = chamber radius b = chamber discharge radius Cμ = coefficient for the turbulence viscosity ij K = element stiffness matrix in the finite element formulation L = chamber length e l = an equivalent length scale for the turbulence i N = shape functions P =

Numerical solution of a multidimensional sedimentation problem using finite volume-element methods

The handling and control of towed cable and body systems onboard surface ships and submarines presents a significant technical challenge to design engineers in the defense and ocean industries. The current approaches rely heavily on the empirical methods and the time-consuming and costly prototype testing. Computer simulation provides a cost effective way to reduce the high risks associated with the towed cable/body system. However, the current dynamic analysis of towed cables is mostly done by the finite difference (FD) method in stead of the finite element (FE) method that is widely used in almost all engineering fields. This paper presents an alternative FE method to simulate the dynamics of towed cable and body system, in which the large rigid body motion is coupled with small elastic deformation. The newly derived FE method is formulated in terms of element nodal positions, which is different from the existing FE methods that use displacements. The alternative FE method solves for the cable position directly in order to eliminate accumulated numerical errors arising from existing FE methods that solve for displacements first in order to obtain the cable position over very long period of time. The alternative FE formulation is implemented and applied to real applications to demonstrate its robustness by comparing simulation results with the experimental and sea trial data.

A three-dimensional edge-crack finite element for fracture mechanics applications

The objective of this investigation is to predict the natural frequency of a laminated carbon fiber reinforced thermoplastics (CF/PEEK) plate with a hole by using the finite element method. In the finite element formulation, a parabolic isoparametric plate bending element is used and the first-order shear deformation theory based on the Mindlin type is considered. The good agreement between the numerical and the experimental results of CF/PEEK unidirectional and cross-ply laminated plates with a hole shows that the natural frequencies and modes can be predicted by the present method. Futhermore, the changes of frequencies and modes of the antisymmetrically angle-ply and the cross-ply laminated plates with the size of the hole, the stacking sequence of lamina and the plate length-to-width ratio are examined by F. E. M. under simply supported and clamped boundary conditions.

Geometrically complex geological features, such as faults, cross stratified beds and large scale inclined strata, can have very significant effects on the flow of reservoir fluids. Standard finite difference methodology lacks the geometric flexibility required for modeling flow through or around such structures. Triangle based discretization methods, by contrast, offer an attractive means to discretize and simulate flow through geometrically complex features accurately. In this paper, a triangle based mixed finite element – finite volume technique for compositional reservoir simulation is developed. The formulation is of IMPES type and is applicable to three phase, multicomponent systems in two dimensions. Most previous mixed finite element formulations were restricted to two phase or fully miscible systems. The compositional approach presented here extends these earlier techniques though it retains the general structure of the more limited formulations. Specifically, the governing equations are cast in terms of a pressure equation and a series of component mass balance equations expressed in terms of the ‘total’ velocity. A triangle based mixed finite element method is applied to the solution of the pressure equation while a finite volume technique is employed for solution of the component mass balance equations. The overall methodology is particularly well suited for the modeling of flow through complex geological strata characterized by heterogeneous, generally anisotropic permeability fields. This is demonstrated explicitly through application of a preliminary implementation of the method to the simulation of flow through a faulted cross section with a complex permeability description. Extension of the formulation to the three dimensional case is also discussed.

A combined finite element and finite difference scheme for computer simulation of microstructure evolution and its application to pore–boundary separation during sintering