Computational Economics Research Articles

On missing boundary conditions with unsteady incompressible Navier–Stokes flows

AbstractWe investigate an unsteady viscous flow problem where ‘good’ boundary conditions are available on part of the boundary only. This problem appears when the flow phenomena one is interested in are concentrated on part of the flow region and, for reasons of computational economy, are numerically computed in this subregion only. Assuming that outside of the subregion the flow is not subjected to any acceleration forces, we develop an (abstract) combined finite‐element/boundary element scheme to compute the flow approximately. This scheme leads to a proof of the existence of a weak solution of the corresponding Navier–Stokes problem as well.

Temperature rise of an induction motor during plugging

The problem of three-dimensional transient heat flow in the stators of induction motors is solved using a finite-element formulation employing arch-shaped elements. The shape functions and exact solutions are derived algebraically for the utmost economy in computation. The temperature distribution has been determined considering convection from the surface and the two ends. The temperature distribution has also been determined by specifying the temperature of the surface and the ends. A simple cylinder is used as an example. The temperature at different locations in the stator of the induction motor has been computed during transients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

AbstractUsed in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a non‐linear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of non‐linear equations and the computational performances examined in detail. Multi‐zone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized non‐iinear boundary conditions or regions of geometric insensitivity to design variables. A series of non‐linear example problems is presented that have closed form solutions. Exact anaytical expressions tor the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Wall fire close to an horizontal surface: Numerical modelling and experimental validation

In order to contribute to a better understanding of natural fire configurations, three different experimental arrangements were considered. They simulated, at laboratory scale, three simple room fire situations.1–3 First, we tested a gas-fueled porous burner simulating a wall fire. Then an insulated floor was placed close to it. Finally the wall and the floor burnt simultaneously. Velocity and turbulence measurements were performed using a two-component laser-doppler velocimetry (LDV) system operating in the forward-scatter mode. Mean gas temperatures were obtained with a 200 μm butt-welded chromel-alumel thermocouple, located 2 mm downstream of the velocity measurement control volume. Simultaneous measurements of two velocity components proved to be very useful, especially in the characterization of the flame structure and of the entertainment process. A simple field model describing strongly buoyant diffusion flames is proposed in search of computational economy and a basic understanding of the phenomena involved. Our aim is to analyse the suitability of such a simple model for the description of the mean properties of the flow. This work showed the interaction between the burning wall, the floor and the pool fire, and especially the role played by the large-scale structures characteristic of entertainment and mixing processes in free fires.

Spawn: a distributed computational economy

The authors have designed and implemented an open, market-based computational system called Spawn. The Spawn system utilizes idle computational resources in a distributed network of heterogeneous computer workstations. It supports both coarse-grain concurrent applications and the remote execution of many independent tasks. Using concurrent Monte Carlo simulations as prototypical applications, the authors explore issues of fairness in resource distribution, currency as a form of priority, price equilibria, the dynamics of transients, and scaling to large systems. In addition to serving the practical goal of harnessing idle processor time in a computer network, Spawn has proven to be a valuable experimental workbench for studying computational markets and their dynamics. >

Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions

Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.

Efficient techniques for the decomposition of intermolecular interaction energy at SCF level and beyond

Some techniques for the decomposition of SCF interaction energy have been reviewed with particular emphasis on their basis set dependency, computational economy and simplicity. The consequences of using more approximate SCF procedures based on ZDO approximation have been also analyzed. Efficient methods for estimating intra- and inter-molecular correlation components of interaction energy are discussed.

Economic risk analysis of large engineering projects

A consistent, four-moment-based approach for quantifying time and economic risks is presented. The goal is to produce a computationally economical approach that can be used to explore the time and economic feasibility of various strategies for executing and sequencing major work packages that describe an engineering project. A three-level hierarchy of variables is used, starting with time, cost and revenue performance at the work package/revenue stream level to net present value and internal rate of return at the project decision level. The treatment of correlations between primary variables at all levels of the hierarchy is included. A modified form of the probabilistic network evaluation technique (PNET) algorithm is presented for quantifying time uncertainty. Use of limiting values (0, 1) of the PNET transitional correlation provides bounds for all decision variables. A comparison with Monte Carlo simulation of a case study is presented to demonstrate the validity and the computational economy of the analytical approach. Key words: economic risk quantification, large engineering projects, probability analysis, moment analysis, Monte Carlo simulation.

Kinematic routing using finite elements on a triangular irregular network

Automated extraction of geometry for hydraulic routing from digital elevation models (DEM) is a procedure that must be easily accomplished for widespread application of distributed hydraulically based rainfall excess‐runoff models. One‐dimensional kinematic routing on a regular grid DEM is difficult due to flow division and convergence. Two‐dimensional kinematic routing on a triangular irregular network (TIN) surmounts many of these difficulties. Because TIN DEMs typically require far fewer points to represent topography than regular grid DEMs, substantial computational economy is also realized. One‐dimensional routing using vector contour data overcomes the grid‐based routing disadvantages but often requires several orders of magnitude more storage points than a TIN. The methodology presented in this paper represents a compromise between slightly increased computational complexity and the economy of TIN topographic representation. We take the unique approach of subdividing each topographic triangle (TIN facet) into a set of coplanar triangular finite elements, performing routing on a single facet and then routing the resulting excess hydrograph to downstream facets and channels via upstream boundary conditions. Results indicate that shock conditions are readily handled, computed depths match analytic results to within ±3% and volume balances are typically within 1%. This modeling system illustrates the viability of kinematic routing over a TIN DEM derived directly from digital mapping data.

Recursive partial realization for 2-D data arrays

In this paper an attempt is made to provide a proper formalization to the partial realization problem for discrete linear causal shift invariant 2-D systems. The approach falls into the class of 2-D Pade approximations; the results, however, are new, since the rational representation matches all the samples of a 2-D partial sequence. The realization algorithm, though characterized by a high complexity, exhibits a recursive structure and allows for a good computational economy.

Use of 3-dimensional finite elements for computation of temperature distribution in the stator of an induction motor

The problem of 3-dimensional steady-state heat flow in the stator of an induction motor is solved by use of a finite element formulation and arch-shaped elements. The shape functions and exact solution matrices are derived algebraically for utmost economy in computation. The temperature distribution has been determined considering convection from the surface and the two ends. First, a simple cylinder has been taken as an example. Then, the temperature at different location in the stator of the induction motor has been computed.

Balanced repeated replications based on mixed orthogonal arrays

SUMMARY For stratified samples with arbitrary numbers of primary sampling units per stratum, one can divide the units in the stratum into two groups and then apply the balanced half-samples method to the two groups thus formed. The efficiency loss of the grouped balanced half-samples variance estimator can be substantial. Use of a mixed orthogonal array, whose numbers of symbols correspond to the numbers of units per stratum, gives a set of balanced subsamples. Unlike that of Gupta & Nigam (1987), the proposed method of analysis gives a consistent variance estimator and bias reduction for nonlinear statistics. To further reduce the number of replicates, use of nearly orthogonal arrays is considered. The balanced half-samples method (McCarthy, 1966, 1969) is commonly used for estimating the variance of nonlinear statistics from stratified samples with two primary sampling units per stratum. These samples arise naturally if deep stratification is desired as in some large-scale surveys. The method is extended (Gurney & Jewett, 1975) to the case of p primary sampling units per stratum for prime p. This extension for p > 2 is not adopted in common practice since it requires a much larger number of replicates. Also, in many survey designs the numbers of primary sampling units are unequal. A common practice is to divide the units in the stratum into two groups and then to apply the balanced half-samples method to the two groups thus formed. This has gained popularity because the software for obtaining balanced half-samples is readily available and the number of replicates required is more economical. As shown in ? 2, the resulting variance estimators can be quite inefficient and their bias based on a conditional analysis can be considerable. The conditional analysis also suggests a method of grouping to reduce the bias. The degree of grouping depends on the tradeoff between computational economy and statistical efficiency. If the efficiency loss from grouping is not justifiable, one may draw replicates by using mixed orthogonal arrays with variable numbers of symbols to accommodate the different numbers of units or groups of units in the strata. As long as an orthogonal array is used for drawing replicates, we call the method balanced repeated replications. In ? 3 we show that the analysis method of Gupta & Nigam (1987) based on mixed orthogonal arrays leads to an inconsistent variance estimator for nonlinear statistics, and propose a method that is valid for variance estimation and bias reduction

Direct solution of distribution systems

The paper reports on a direct power flow solution technique for radial distribution networks. The special topology of distribution networks has been fully exploited to make direct solution possible. A unique branch and node numbering scheme has been proposed to achieve storage and computational economy. Composite load characteristics can be easily modelled. The method developed has been extended for meshed and unbalanced distribution networks. In both cases, modifications required are few and the advantages obtained in balanced radial networks in respect of storage and computational requirements have been preserved. The proposed method has been successfully applied to the solution of a number of practical distribution networks.

A comparative study of C0 and C1 elements for linear and nonlinear transient dynamics of building frames

The C 1 continuous element based on the Euler-Bernoulli theory of bending and the C 0 continuous element based on Timoshenko's theory of bending are compared for their computational efficiency and economy for the analysis of inelastic frames subjected to transient dynamic loads. Moreover, the size of a C 0 mesh (with only linear elements) is evaluated, which is computationally equivalent to C 1 Hermitian element. Also the ranges of slenderness ratio, in which both these elements are effective and the limits of aspect ratio below which they fail are also determined through the numerical studies.

One modification of the Ericksen-Leslie equations in a two-dimensional motion

It is shown that some terms in the stress tensor can be lumped together if the motion is two-dimensional; this should lead to significant computational economy.

A New Computational Approach to the Miscible Displacement Problem

Summary A 2D miscible displacement computer code based on a pseudospectral method that uses Chebyshev expansions and a grid adaptive to the position of the front was developed. In this method, the effect of physical dispersion is explicitly included, while the effect of numerical dispersion is greatly suppressed. The code was shown to have exceptional convergence, accuracy, stability, and computational economy. It accurately predicts the position and sharpness of the displacement front for ID miscible and immiscible displacements. The code also predicts oil recoveries and breakthrough times for 2D miscible displacements with unfavorable mobility ratios that are in agreement with experimental data and is shown to be effective in resolving details of viscous fingering phenomena.

A response surface technique for fuzzy—random evaluations of local seismic hazard

Local soil amplification is one of the main phenomena contributing to local seismic hazard and consequently to local seismic risk. It is influenced both by randomness and by fuzziness. This paper offers a general fuzzy—random formulation, applicable to nonlinear soil amplification studies and hence to evaluations of local seismic hazard. The results obtainable by probabilistic analysis and also those arrived at using fuzzy analysis can be considered as consequences of particularizations of this formulation. The treatment is rendered explicit by adapting the response surface technique to the problem, as this is advantageous in terms of computational economy.

On homogeneous transforms, quaternions, and computational efficiency

Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using quaternion-vector pairs as spatial operators, is compared with homogeneous transforms in terms of computational efficiency and storage economy. The conclusion drawn is that quaternion-vector pairs are as efficient as, more compact than, and more elegant than their matrix counterparts. A robust algorithm for converting rotational matrices into equivalent unit quaternions is described, and an efficient quaternion-based inverse kinematics solution for the Puma 560 robot arm is presented. >

How formaldehyde interacts and reacts with chromium and chromium oxide surfaces: A model for chromium-polyimide binding

Chemical interactions of chromium and chromium oxide with carbonyl functional groups of a polyimide chain were investigated theoretically. Band calculations of the extended Hückel type were performed on model systems. The chromium (chromium oxide) surface was represented by a three-layered slab of material, and for computational economy, the polyimide carbonyls were represented by the formaldehyde molecule. Results suggested that while formaldehyde binds to Cr 2O 3 via its oxygen lone pair electrons, it binds to metallic Cr in a π or η 2 (dihapto) fashion. Further, the calculations indicated that formaldehyde was susceptible to decomposition when bound to clean Cr, but was not susceptible to decomposition when bound to Cr 2O 3. These differences were attributed to the relatively lower Fermi energy of Cr 2O 3. By analogy, the imide groups in polyimide may be substantially decomposed at the polyimide/Cr interface, with strong covalent bonding between the metal and the fragmented polymer.

A wind‐driven isopycnic coordinate model of the north and equatorial Atlantic Ocean: 1. Model development and supporting experiments

Numerical approximations to the dynamic equations are given which allow basin‐size ocean circulation models formulated in isopycnic coordinates to accommodate variable bottom topography and irregular coastlines. Emphasis is placed on computational economy through the use of a split‐explicit time integration scheme, on the proper formulation of the advection and Coriolis terms in the momentum equation in case of strongly varying layer thickness, and on the correct estimation of the horizontal pressure gradient force in grid boxes truncated by steep bottom slopes. The algorithms are tested in a series of two‐ and three‐layer double‐gyre experiments. In cases of steady forcing leading to a steady circulation, we are able to reproduce the expected motionless final state in coordinate layers that are below the direct influence of the wind forcing. This includes layers intersecting topographic obstacles. A long‐term (25–30 year) vacillation tentatively associated with the outcropping of isopycnals along the edge of the cyclonic gyre in a steadily forced model is documented. The paper forms the basis for a subsequent study in which circulation features obtained in a realistic North Atlantic setting will be discussed.