Finite element solution of Navier Stokes equations adapted to a priori error estimates

The paper is based on qualitative properties of the solution of the Navier-Stokes equations for incompressible fluid, and on properties of their finite element solution. In problems with corner-like singularities (e.g. on the well-known L-shaped domain) usually some adaptive strategy is used. In this paper we present an alternative approach. For flow problems on domains with corner singularities we use the a priori error estimates and asymptotic expansion of the solution to derive an algorithm for refining the mesh near the corner. It gives very precise solution in a cheap way. We present some numerical results.

Subdivision-stabilised immersed b-spline finite elements for moving boundary flows

An immersed finite element method is presented to compute flows with complex moving boundaries on a fixed Cartesian grid. The viscous, incompressible fluid flow equations are discretized with b-spline basis functions. The two-scale relation for b-splines is used to implement an elegant and efficient technique to satisfy the LBB condition. On non-grid-aligned fluid domains and at moving boundaries, the boundary conditions are enforced with a consistent penalty method as originally proposed by Nitsche. In addition, a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut-cells. The versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations.

Compressive failure of finite size unidirectional composite laminates with a region of fibre waviness

The compressive behaviour of finite unidirectional composites with a region of misaligned reinforcement is investigated via finite element analyses. Models with and without fibre bending stiffness are compared, confirming that compressive strength is accurately predicted without modelling fibre bending stiffness for real composite components which typically have waviness defects of several millimetres wavelength. Various defect parameters are investigated. Results confirm the well-known sensitivity of compressive strength to misalignment angle, and also show that compressive strength falls rapidly with the proportion of laminate width covered by the wavy region. A simple empirical equation is proposed to model the effect of a single patch of waviness in finite specimens. Other parameters such as length and position of the wavy region are found to have a smaller effect on compressive strength. The modelling approach is finally adapted to model distributed waviness and thus determine the compressive strength of composites with realistic waviness defects. © 2011 Elsevier Ltd. All rights reserved.

Warped Mixtures for Nonparametric Cluster Shapes

A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automatically inferred. We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, performs better than infinite Gaussian mixture models at recovering the true number of clusters, and produces interpretable summaries of high-dimensional datasets.

SIMPLE REMESHING SCHEME FOR THE FINITE ELEMENT BASED SIMULATION OF DOPANT DIFFUSION IN SILICON.

Process simulation programs are valuable in generating accurate impurity profiles. Apart from accuracy the programs should also be efficient so as not to consume vast computer memory. This is especially true for devices and circuits of VLSI complexity. In this paper a remeshing scheme to make the finite element based solution of the non-linear diffusion equation more efficient is proposed. A remeshing scheme based on comparing the concentration values of adjacent node was then implemented and found to remove the problems of oscillation.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

Implementation of a PI phase angle controller for finite element analysis of the BDFM

Time-stepping finite element analysis of the BDFM for a specific load condition is shown to be a challenging problem because the excitation required cannot be predetermined and the BDFM is not open loops stable for all operating conditions. A simulation approach using feedback control to set the torque and stabilise the BDFM is presented together with implementation details. The performance of the simulation approach is demonstrated with an example and computed results are compared with measurements.