International Journal of Computational Engineering Science

In this paper we present computations of the nonweak solutions of class C¹¹ of the strong form of transient Navier–Stokes equations for compressible flow in Lagrangian frame of reference using space–time least squares finite element formulation (STLSFEF) with primitive variables ρ, u, T. For high speed compressible flows the solutions reported here possess the same orders of continuity as the governing differential equations (GDEs). It is demonstrated that with this approach accurate numerical solutions of Navier–Stokes equations without any assumptions or approximations are possible. In the approach presented here SUPG, SUPG/DC, or SUPG/DC/LS operators are neither used nor needed. The role of diffusion, i.e., viscosity (physical or artificial) and thermal conductivity on shock structure is demonstrated. Merits of using ρ, u, T as primitive variables over ρ, u, p are discussed. Compression of air in a rigid cylinder by a rigid, massless and frictionless piston is used as a model problem. True time evolutions of class C¹¹ are reported beginning with the first time step until steady shock conditions are achieved. Comparisons with analytical solutions are presented when possible.

This paper presents a space–time least squares finite element formulation of one dimensional transient Navier–Stokes equations (governing differential equations: GDE) for compressible flow in Eulerian frame of reference using ρ, u, T as primitive variables with C¹¹ type p-version hierarchical interpolations in space and time. Time marching procedure is utilized to compute time evolutions for all values of time. For high speed gas dynamics the C¹¹ type interpolations in space and time possess the same orders of continuity in space and time as the GDE. It is demonstrated that with this approach accurate numerical solutions of Navier–Stokes equations are possible without any assumptions or approximations. In the approach presented here SUPG, SUPG/DC, SUPG/DC/LS operators are neither used nor needed. Time evolution shows resolution of shock structure (i.e., shock speed, shock relations and shock width) to be in excellent agreement with the analytical solutions. The role of diffusion, i.e., viscosity (physical or artificial) and thermal conductivity on shock structure is demonstrated. Riemann shock tube is used as model problem. Time evolutions are reported beginning with the first time step until steady shock conditions are achieved. In this approach, when the computed error functionals become zero (computationally), the computed nonweak solutions satisfy GDE accurately.

This paper presents different finite element formulations for the large deformation modelling of a viscoplastic material. A partly-explicit acceleration-pressure formulation is investigated. As the velocity is supposed to be known, we do not have to deal with the possible non-linear feature of the material. Consequently, there is no need to use any Newton-Raphson iteration. The mixed finite element discretization is based on a simple triangular mini-element P1 + /P1. Analysis concerning the bubble properties and its influences on the equation system have been done in order to simplify the formulation. This new dynamic formulation has been successfully implemented in a viscoplastic version of the code Forge2^®. Comparisons with implicit static and implicit dynamic algorithms have been performed. Numerical examples are provided to compare the different formulations. A good agreement is noticed on final results.

In this study applicability of the two-dimensional depth-averaged models to river bend reaches is investigated. Three models: CCHE2D model developed at the National Center for Computational Hydroscience and Engineering, University of Mississippi; RMA-2 from the U. S. Army Corps of Engineers; and FESWMS-2DH from the U. S. Federal Highway Administration are selected for this study. The first reach is located in the Dommel River in Netherlands and the second reach is a part of the Fall River in Colorado. The study areas consist of two consecutive and opposite bends. The mesh consists of quadrilateral elements and the number of elements for all three models is the same. Identical boundary conditions for flow at the upstream end and water surface elevation at the downstream end are specified in each case for all three models. The Manning's coefficient in each case is also the same for all three models. The computed water surface elevations and velocity profiles across various sections specifically in the bends are compared with the measurements in the field.

An unsteady Navier-Stokes (N-S) solver based on the method of operator splitting and artifical compressibility has been developed for moving boundary problem to simulate blood flow through compliant vesset. The code of the solver has been developed using Fasttalk, a high level programming language in the Fastflo environment. Galerkin finite element is used to discretized the governing equations. It has been applied to a time varying computational domain (2-D tube) as test case for validation. Consideration has been taken to retain space conservation property. Result are presented with emphasis on the depiction of vortical flow details. There has been no observable difference in vortical flow development when compared with the rigid stenotic model.

A general one-dimensional model able to study thin-walled beams of open cross-section, exhibiting moderate angles of twist, is presented. It is derived from the 3-D continuous model assuming that the beam cross-section presents a rigid deformation in, and warps out, its own plane. Comparisons with a previous model proposed by Ghobarah and Tso are also made.

In this paper a numerical investigation relative to the static behaviour of thin-walled beams of open cross-section, undergoing moderate angles of twist, is presented. The constitutive equations between nominal stresses and Green strains are assumed to be linear elastic and isotropic. The numerical results are obtained by using a finite element approach, following a classical Newton-Raphson procedure. They show the peculiarity of the non-linear dependence of the torsional torque on the corresponding angle of rotation, which can be either of hardening or softening type. Comparisons with previous numerical results available in literature are also provided.

In mobile client-server database systems, caching of frequently accessed data is an important technique that will reduce the contention on the narrow bandwidth wireless channel. As the server in mobile environments may not have any information about the state of its clients' cache(stateless server), using broadcasting approach to transmit the list of updated data to numerous concurrent mobile clients is an attractive approach. In this paper, two caching methods are proposed to support transaction semantics at mobile clients. Proposed protocols adopt asynchronous broadcasting and adaptive broadcasting as the way of sending invalidation reports, in order to dynamically adapt to system workload(update pattern, data locality). We study the performance of the proposed protocols by means of simulation experiments.