Search results

The purpose of this paper is to investigate the effect of numerical boundary condition implementation on local error and convergence in L2-norm of a finite volume discretization of the transient heat conduction equation subject to several boundary conditions, and for cases with volumetric heat generation, using both fully implicit and Crank-Nicolson time discretizations. The goal is to determine which combination of numerical boundary condition implementation and time discretization produces the most accurate solutions with the least computational effort.

The paper studies several benchmark cases including constant temperature, convective heating, constant heat flux, time-varying heat flux, and volumetric heating, and compares the convergence rates and local to analytical or semi-analytical solutions.

The Crank-Nicolson method coupled with second-order expression for the boundary derivatives produces the most accurate solutions on the coarsest meshes with the least computation times. The Crank-Nicolson method allows up to 16X larger time step for similar accuracy, with nearly negligible additional computational effort compared with the implicit method.

The findings can be used by researchers writing similar codes for quantitative guidance concerning the effect of various numerical boundary condition approximations for a large class of boundary condition types for two common time discretization methods.

The paper provides a comprehensive study of accuracy and convergence of the finite volume discretization for a wide range of benchmark cases and common time discretization methods.

An alternative stabilization approach has been developed for the 9‐node Lagrange plane and plate elements. In this approach, a stabilization stiffness is formulated using functions associated with the spurious zero‐energy modes. Efficiency has been increased by employing the same uniformly‐reduced integration scheme on the stabilization and underintegrated stiffness matrices. The results obtained using this rank‐sufficient element, termed the γ‐ψ element, appear to surpass those obtained with other rank‐sufficient 9‐node elements in accuracy.

A kind of generalized 3D Euler equations with periodic boundary conditions, that describes the behaviour of the small scale flow in a turbulence model is solved. A fully conservative numerical scheme, that combines pseudospectral discretization in space with a variation of Crank‐Nicholson's scheme in time, is introduced. Some numerical tests show that the numerical solution reaches an asymptotic statistic steady state. In the case of well developed isotropic turbulence, these results are shown to present a reasonable quantitative agreement with the classical theory.

We investigate the application of a least squares finite element method for the solution of fluid flow problems. The least squares finite element method is based on the minimization of the L2 norm of the equation residuals. Upon discretization, the formulation results in a symmetric, positive definite matrix system which enables efficient iterative solvers to be used. The other motivations behind the development of least squares finite element methods are the applicability of higher order elements and the possibility of using the norm associated to the least squares functional for error estimation. For steady incompressible flows, we develop a method employing linear and quadratic triangular elements and compare their respective accuracy. For steady compressible flows, an implicit conservative least squares scheme which can capture shocks without the addition of artificial viscosity is proposed. A refinement strategy based upon the use of the least squares residuals is developed and several numerical examples are used to illustrate the capabilities of the method when implemented on unstructured triangular meshes.

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared.

This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split.

In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.

A comprehensive comparison between three versions of the CBS method is provided for the first time.

This comparative study aims to investigate the rhetorical organization of Korean and English argumentative texts. In previous studies, the rhetorical organization of such texts has been categorized as either direct or indirect depending on the placement of the thesis statement (Chien, 2011). The present study attempts to document more specific rhetorical patterns using Swales (1990) concept of moves and steps.

Ten Korean EFL students with similar L1 and L2 literacy backgrounds were selected, and, adopting a within-subject design, the students wrote two argumentative essays, one in Korean and one in English, in response to two different topics. The students’ essays were analyzed at both the macro and micro levels. The focus of the macro-level analysis was on the placement of the thesis statement and of topic sentences in each of the body paragraphs. Once the macro-level analysis was done, the essays were analyzed at the micro level using Swales (1990) move analysis.

The findings suggest that both texts were organized in a similar way at the macro level, constituting a typical paper structure (i.e. introduction, body and conclusion). However, a difference appears at the micro level: the students used a variety of steps to create a move when writing in Korean, whereas little variation was found in the English texts. An analysis of the data suggests the possibility that the standardized moves and steps in the English texts may be due not to culture-specific rhetoric, but to a lack of practice with rhetorical thinking in English.

In previous studies, the rhetorical organization of texts has been categorized as either direct or indirect depending on the placement of the thesis statement. The present study uses the framework of move analysis to describe more specific organizational patterns of Korean and English writing to determine the extent to which Korean and English writing is similar in the genre of argumentative writing. Another significance of the study lies in the choice of Korean writing as a reference point for comparison with English writing. It has been widely noted that there is a dearth of research of Korean students’ writing in contrastive rhetoric. To the best of the author’s knowledge, most of the contrastive rhetoric studies were conducted with Chinese or Japanese student writers.

The approximate factorisation‐conjugate gradient squared (AF‐CGS) method has been successfully demonstrated for unsteady turbulent aerofoil flows and transonic inviscid flows in two and three dimensions. The method consists of a conjugate gradient solution of the linear system at each step with the ADI approximate factorisation as a preconditioner. In the present paper the method is adapted to obtain rapid convergence for steady aerofoil flows when compared to the basic explicit method. Modifications to the original method are described, convergence criteria are examined and the method is demonstrated for transonic flow including AGARD test case 9 for the RAE2822 aerofoil.

We present an abstract mathematical and numerical analysis for Drift‐Diffusion equation of heterojunction semiconductor devices with Fermi‐Dirac statistic. For the approximation, a mixed finite element method is considered. This can be profitably used in the investigation of the current through the device structure. A peculiar feature of this mixed formulation is that the electric displacement D and the current densities jn and jp for electrons and holes, are taken as unknowns, together with the potential φ and quas‐Fermi levels φn and φp. This enably D, jn and jp to be determined directly and accurately. For decoupled system, existence, uniqueness, regularity and stability results of the approximate solution are given. A priori and a posteriori error estimates are also presented. A nonlinear implicit scheme with local time steps is used. This algorithm appears to be efficient and gives satisfactory results. Numerical results for an heterojunction bipolar transistor, In two dimension, are presented.

The aim of the present paper is to present certain existence theorems for stochastic control systems whose state variables, χ(t;ω), are continuous functions from the set R+ = {t;t ≥ 0} into the space L2(Ω, A, μ). That is, for each t R+, χ(t;ω) is a vector‐valued random variable whose second absolute moment exists. U = μ(t), the admissible controls, are taken as measurable functions of t only. It is assumed that the initial time is fixed but allow the terminal time tf(ω) to vary with ω∈Ω. The usual space constraints and boundary conditions are also allowed to vary with ω∈Ω. The cost functional is taken to be a continuous functional over a suitable class of continuous functions.

The purpose of this paper is to propose an accurate and efficient technique for computing flow sensitivities by finite differences of perturbed flow fields. It relies on computing the perturbed flows on coarser grid levels only: to achieve the same fine-grid accuracy, the approximate value of the relative local truncation error between coarser and finest grids unperturbed flow fields, provided by a standard multigrid method, is added to the coarse grid equations. The gradient computation is introduced in a hybrid genetic algorithm (HGA) that takes advantage of the presented method to accelerate the gradient-based search. An application to a classical transonic airfoil design is reported.

Genetic optimization algorithm hybridized with classical gradient-based search techniques; usage of fast and accurate gradient computation technique.

The new variant of the prolongation operator with weighting terms based on the volume of grid cells improves the accuracy of the MAFD method for turbulent viscous flows. The hybrid GA is capable to efficiently handle and compensate for the error that, although very limited, is present in the multigrid-aided finite-difference (MAFD) gradient evaluation method.

The proposed new variants of HGA, while outperforming the simple genetic algorithm, still require tuning and validation to further improve performance.

Significant speedup of CFD-based optimization loops.

Introduction of new multigrid prolongation operator that improves the accuracy of MAFD method for turbulent viscous flows. First application of MAFD evaluation of flow sensitivities within a hybrid optimization framework.