Proposed Boundary Conditions Research Articles

All for the Money? The Ambiguity of Monetary Rewards in Firm-Initiated Ideation with Users

In firm-initiated ideation with users, the hosting organization typically dominates the commercial exploitation of users’ revealed ideas. In light of this asymmetric exploitation, offering monetary prizes for the best performing participants or the most valued ideas seems to be a reasonable form of compensation and incentivation. However, we question the sole effectiveness of monetary rewards in the context of a contest and propose two boundary conditions where non-monetary benefits proposed in the private-collective model of user innovation better explains participation: (1) If users’ personal involvement and need in the innovation domain is high, an expectation of monetary rewards is deemed less important, because users expect to better internalize collective innovation outcomes and capture private benefits (non-monetary “compensation effect”). (2) If users are supposed to allocate effort to collectively oriented activities like commenting, improving or evaluating other users’ ideas, the expectation of monetary rewards is less effective, because it induces rivalry among users (“competition effect”). We find support for these hypotheses in an empirical study where user participation in a real ideation project is regressed on survey-based measures of motivating conditions that users perceived prior to the contest. We can conclude that monetary rewards can even have detrimental effects in firm-initiated ideation, if the two proposed boundary conditions are taken together.

Novel boundary conditions for strain localization analyses in microstructural volume elements

SUMMARYMulti‐scale modeling frequently relies on microstructural representative volume elements (RVEs) on which macroscopic deformation is imposed through kinematical boundary conditions. A particular choice of these boundary conditions may influence the obtained effective properties. For strain localization and damage analyses, the RVE is pushed beyond the limits of its representative character, and the applied boundary conditions have a significant impact on the onset and the type of macroscopic material instability to be predicted.In this article, we propose a new type of boundary conditions for microstructural volume elements, called percolation‐path‐aligned boundary conditions. Intrinsically, these boundary conditions capture the constraining effect of the material surrounding the RVE upon developing localization bands. The alignment with evolving localization bands allows the highly strained band to cross the RVE and fully develop with minimal interference of the applied boundary conditions. For an illustration of the performance of the newly proposed boundary conditions, macroscopic deformation has been imposed on a voided elasto‐plastic RVE using different types of boundary conditions. It is observed that the new RVE boundary conditions provide a good estimate for the effective stiffness, are not susceptible to spurious localization, and permit the development of a full strain localization band up to failure. Copyright © 2011 John Wiley & Sons, Ltd.

A predictor–corrector scheme based on the ADI method for pricing American puts with stochastic volatility

In this paper, we introduce a new numerical scheme, based on the ADI (alternating direction implicit) method, to price American put options with a stochastic volatility model. Upon applying a front-fixing transformation to transform the unknown free boundary into a known and fixed boundary in the transformed space, a predictor–corrector finite difference scheme is then developed to solve for the optimal exercise price and the option values simultaneously. Based on the local von Neumann stability analysis, a stability requirement is theoretically obtained first and then tested numerically. It is shown that the instability introduced by the predictor can be damped, to some extent, by the ADI method that is used in the corrector. The results of various numerical experiments show that this new approach is fast and accurate, and can be easily extended to other types of financial derivatives with an American-style exercise. Another key contribution of this paper is the proposition of a set of appropriate boundary conditions, particularly in the volatility direction, upon realizing that appropriate boundary conditions in the volatility direction for stochastic volatility models appear to be controversial in the literature. A sound justification is also provided for the proposed boundary conditions mathematically as well as financially.

A parametric (inlet) flow analysis of 3D human carotid artery using realistic geometry

In this study the biomechanical characteristics of a realistic carotid artery are studied numerically using different inlet velocity profiles. Sinusoidal and experimental data measured at the common carotid artery are used to generate the velocity inlet boundary conditions at common carotid artery. The generation is done using elliptic Womersley velocity profile technique. The computation domain is generated using a computed tomography (CT) data of a real patient. Three-dimensional (3D) transient NS equations are solved in this actual domain using the proposed boundary conditions. Effects of different input conditions on the results of the simulation are discussed. This study adds more results to the paper by the authors. Those new results include wall shear stress histories for all input data (cases). Main parameters investigated at the critical parts of the carotid artery such as bifurcation and sinusoidal enlargement regions are velocity profiles, wall shear stress (WSS) and pressure distributions. Results show that the velocity inlet does not only change the magnitude of the mechanical properties but also changes the magnitude ordering between geometric points. Also there is a linear relation between velocity and WSS values. This relation is not broken at stenosis or sinus regions meaning that the relation is not affected by the geometry. But the relation between velocity and pressure is affected by the geometry of the artery. Shapes of the velocity histories at most of the selected points are very similar to the shape of the relevant inlet velocity histories while it is very different for some selected points. Study concludes that the input boundary conditions and slope/curvature discontinuities in the geometry affect the velocity, pressure and WSS distributions highly. The conclusion is supported by the development of secondary flow at inflexion regions and vortex at especially the sinus area.

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.

Boundary value problems for the shallow water equations with topography

[1] Nonviscous shallow water equations with topography are considered in one spatial dimension. The aim is to find boundary conditions which are physically suitable; that is, they let the waves move freely out of the domain and do not reflect them at the boundary in a nonphysical way (or a way that is believed to be nonphysical). Two types of boundary conditions, called linear and nonlinear, are proposed for two types of flows, namely subcritical and supercritical flows. The second aim in this article is to numerically implement these boundary conditions in a numerically effective way. This is achieved by a suitable extension of the central-upwind method for the spatial discretization and the Runge-Kutta method of second order for the time discretization. Several successful numerical experiments for which we tested the proposed boundary conditions and the numerical schemes are described. The topography was added to render the examples studied physically more interesting.

선형 공정계획 모델의 액티비티 관계의 경계조건 분석

국내 일부 건설사는 초고층 건축공사와 같이 반복 공종이 많은 건축물에 일종의 선형 공정계획인 택트 공정계획을 수립하고 수행하고 있다. 선형 공정계획 모델(Linear Scheduling Model: LSM)은 작업 공간과 시간의 정보를 제공하는 시각적 도구로써 연구가 되어왔다. CPM 네트워크 공정표의 구속조건(종료 후 종료, 시작 후 종료, 종료 후 시작, 시작 후 시작)과 마찬가지로 선형계획모델 또한 작업간의 관계간의 구속조건이 발생한다. 특히, 네트워크 공정표를 호환하기 위하여 작업간의 중요 속성간의 관계성의 경계 조건을 정의하는 것이 필요하다. 따라서 본 연구는 선형 공정계획을 수립 시 발생하는 액티비티간의 공간상의 경계조건을 분석한다. 또한 선형 공정계획의 액티비티 간의 관계성을 고려하여 현재 일부 건설회사를 중심으로 사용하고 있는 택트 공정계획에 제안한 경계조건을 반영하여 택트 공정계획 수립과 관리를 위해 고려해야 하는 주요 사항을 제시하는 것이 본 연구의 목적이다. Domestic leading construction companies has been establishing and performing TACT scheduling method, similar to linear scheduling model such as line of balance and repetitive schedule, and etc. in which repetitive construction works are involved like high-rise building. Linear scheduling model has been researched as a visual scheduling method presenting the work space and time information. Likewise scheduling constraints of CPM network such as finish-to-finish, start-to-start, finish-to-start, start-to-start, linear scheduling model also has the relationships constraints, namely boundary conditions, between activities. It is especially necessary to define the boundary conditions of the activities' relationships in order to apply the linear scheduling model to be compatible with the network schedule. Therefore, this research considers the boundary conditions between activities for establishing the linear scheduling model. This paper also applies the proposed boundary conditions to TACT schedule and then deduces the main considerations in order to establish and perform TACT schedule.

Numerical study of lattice Boltzmann methods for a convection–diffusion equation coupled with Navier–Stokes equations

Numerous lattice Boltzmann (LB) methods have been proposed for solution of the convection–diffusion equations (CDE). For the 2D problem, D2Q9, D2Q5 or D2Q4 velocity models are usually used. When LB convection–diffusion models are used to solve a CDE coupled with Navier–Stokes equations, boundary conditions are found to be critically important for accurately solving the coupled simulations. Following the idea of a regularized scheme (Latt et al 2008 Phys. Rev. E 77 056703), a regularized boundary condition for solving a CDE is proposed. A simple extrapolation scheme is also proposed for the Neumann boundary condition. Spatial accuracies of three existing and the proposed boundary conditions are discussed in details. The numerical evaluations are based on simulations of steady and unsteady natural convection flows in a cavity and an unsteady Taylor–Couette flow. Our studies show that the simplest D2Q4 model with terms of O(u) in the equilibrium distribution function is capable of obtaining results of equal accuracy as D2Q5 or D2Q9 models for the CDE. A slightly revised LB equation for solving a CDE that is used to cancel some unwanted terms does not seem to be necessary for incompressible flows. The regularized boundary condition for solving the CDE has second-order spatial accuracy and it is the best one in terms of the spatial accuracy. The regularized scheme and non-equilibrium extrapolation scheme are applicable to handle both the Dirichlet and Neumann boundary conditions. For the Neumann boundary condition with zero flux, all the five boundary conditions are applicable to give accurate results and the bounce-back scheme is the simplest one.

On the application of no-slip lateral boundary conditions to ‘coarsely’ resolved ocean models

The problem of no-slip boundary conditions as they apply to ocean models is revisited. It is argued that the setting is consistent with classical Law of the Wall theory. The rendering of no-slip boundary conditions is thus modified importantly from typical practice in ocean models. The proposed boundary condition formulation is implemented in the MITgcm. Comparisons with classically formulated free-slip and no-slip cases shows the results are somewhat between the two cases, but generally closer to free-slip.

Proposed Boundary Conditions for Gust-Airfoil Interaction Noise

This paper proposes inflow and outflow boundary conditions for direct computation of airfoil noise under the influence of atmospheric gusts. The proposed boundary conditions are based on the existing zonal sponge technique that has been used mostly to attenuate out� going disturbances and absorb reflections from computational boundaries. A modified form of the sponge technique is presented in this paper in order to enhance the accuracy of acoustic solutions especially in the far field. This type of approach has been unpublished for flows in the presence of a solid body such as an airfoil. The proposed boundary conditions

An extended macroscopic transport model for rarefied gas flows in long capillaries with circular cross section

Pressure-driven and thermally driven rarefied gas flows in long capillaries with circular cross sections are investigated. For both Poiseuille and thermal transpiration flows, a unified theoretical approach is presented based on the linear form of regularized 13-moment (R13) equations. The captured nonequilibrium effects in the processes are compared to available kinetic solutions, and the shortcomings of classical hydrodynamics, i.e., the Navier–Stokes–Fourier equations, are highlighted. Breakdown of Onsager’s symmetry is proposed as a criterion to determine the range of applicability of extended macroscopic models. Based on Onsager’s reciprocity relation it is shown that linearized R13 equations provide agreement with kinetic data for moderate Knudsen numbers, Kn≤0.25. Two-way flow pattern and thermomolecular pressure difference in simultaneous pressure-driven and temperature-driven flows are analyzed. Moreover, second-order boundary conditions for velocity slip and temperature jump are derived for the Navier–Stokes–Fourier system. The proposed boundary conditions effectively improve classical hydrodynamics in the transition flow regime.

Constraint-preserving boundary conditions in the3+1first-order approach

A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard corner and vertex treatment and with a modified finite-differences stencil for boundary points which avoids corners and vertices even in Cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong-field scenario, the Gowdy waves metric, showing the expected rate of convergence. The accumulated amount of energy-momentum constraint violations is similar or even smaller than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The application of these results to first-order Baumgarte-Shapiro-Shibata-Nakamura--like formalisms is also considered.

Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces

A lattice Boltzmann equation (LBE) method for incompressible binary fluids is proposed to model the contact line dynamics on partially wetting surfaces. Intermolecular interactions between a wall and fluids are represented by the inclusion of the cubic wall energy in the expression of the total free energy. The proposed boundary conditions eliminate the parasitic currents in the vicinity of the contact line. The LBE method is applied to micron-scale drop impact on dry surfaces, which is commonly encountered in drop-on-demand inkjet applications. For comparison with the existing experimental results [H. Dong, W.W. Carr, D.G. Bucknall, J.F. Morris, Temporally-resolved inkjet drop impaction on surfaces, AIChE J. 53 (2007) 2606–2617], computations are performed in the range of equilibrium contact angles from 31° to 107° for a fixed density ratio of 842, viscosity ratio of 51, Ohnesorge number ( Oh) of 0.015, and two Weber numbers ( We) of 13 and 103.

Applicability of elliptic-relaxation method to free-surface turbulence

The elliptic-relaxation method of Durbin (1993 J. Fluid Mech. 249 465–98), which has had remarkable success in predicting benchmark flows of many different types, is applied to prediction of free-surface turbulence for the first time. An appropriate free-surface boundary condition for the elliptic-relaxation equation is derived by taking account of the balance of dominant terms in the Reynolds-stress transport equation in the vicinity of a free surface. Test calculations for a fully developed turbulent open-channel flow are conducted. The flow consists of two kinds of impermeable boundaries, a solid wall and a free surface, and hence is quite suitable as a new benchmark flow. It is demonstrated that the proposed boundary condition does enable the elliptic-relaxation method to reproduce the correct surface-induced stress anisotropy and that the model properly describes the differences in features between wall-bounded flows and free-surface flows by its main quality in reproducing the non-local blocking effect, a kind of an elementary process of boundary–turbulence interaction. It is also found that the turbulent-transport term plays a central role in characterizing free-surface turbulence, which is therefore quite suitable for critical evaluation of the model performance.

CAA boundary conditions for airfoil noise due to high-frequency gusts

This paper proposes inflow and outflow boundary conditions for direct computation of airfoil noise under the influence of impinging gusts with a particular interest in the high frequency response. The proposed boundary conditions are based on an existing zonal sponge technique that has been used mostly to attenuate outgoing disturbances and absorb reflections from computational boundaries. A modified form of the sponge technique is presented in this paper in order to specify an incoming disturbance. The proposed boundary conditions still maintain the genuine non-reflective features that lead to accurate calculations of far-field sound intensity and directivity. It is also shown that the proposed boundary conditions enable the use of a significantly smaller domain size, and hence fewer grid cells, than used in conventional airfoil calculations, which enables the calculation of high-frequency gust-airfoil noise at a much lower computational cost. The proposed boundary conditions are validated against CAA (computational aeroacoustics) benchmark solutions after a variety of parametric tests, through which an optimal combination of the domain size, sponge thickness and a sponge coefficient is obtained for the highest efficiency. The proposed boundary conditions yield more accurate and consistent solutions particularly at the far field than the conventional ones. Further applications to high-frequency gust responses are performed to observe and demonstrate significant changes in the sound intensity and directivity varying with different frequencies and gust incidence angles.

Reprint of: CAA boundary conditions for airfoil noise due to high-frequency gusts

This paper proposes inflow and outflow boundary conditions for direct computation of airfoil noise under the influence of impinging gusts with a particular interest in the high frequency response. The proposed boundary conditions are based on an existing zonal sponge technique that has been used mostly to attenuate outgoing disturbances and absorb reflections from computational boundaries. A modified form of the sponge technique is presented in this paper in order to specify an incoming disturbance. The proposed boundary conditions still maintain the genuine non-reflective features that lead to accurate calculations of far-field sound intensity and directivity. It is also shown that the proposed boundary conditions enable the use of a significantly smaller domain size, and hence fewer grid cells, than used in conventional airfoil calculations, which enables the calculation of high-frequency gust-airfoil noise at a much lower computational cost. The proposed boundary conditions are validated against CAA (computational aeroacoustics) benchmark solutions after a variety of parametric tests, through which an optimal combination of the domain size, sponge thickness and a sponge coefficient is obtained for the highest efficiency. The proposed boundary conditions yield more accurate and consistent solutions particularly at the far field than the conventional ones. Further applications to high-frequency gust responses are performed to observe and demonstrate significant changes in the sound intensity and directivity varying with different frequencies and gust incidence angles.

Effects of rarefaction in microflows between coaxial cylinders

Microscale gas flows between two rotating coaxial circular cylinders of infinite length with different temperatures are investigated. Navier-Stokes-Fourier (NSF) and regularized 13-moment (R13) equations in their linear form are used to independently analyze velocity and temperature fields in shear-driven rotary flows, i.e., cylindrical Couette flows. Knudsen boundary layers, which present non-Newtonian stress and non-Fourier heat flow, are predicted as the dominant rarefaction effects in the linear theory. We show that the R13 system yields more accurate results for this boundary value problem by predicting the Knudsen boundary layers, which are not accessible for NSF equations. Furthermore, a set of second-order boundary conditions for velocity slip and temperature jump are derived for the NSF system. It is shown that the proposed boundary conditions effectively improve the classical hydrodynamics. The accuracy of NSF and R13 equations is discussed based on their comparison with available direct simulation Monte Carlo data.

WALL FREE ENERGY BASED POLYNOMIAL BOUNDARY CONDITIONS FOR NON-IDEAL GAS LATTICE BOLTZMANN EQUATION

In the non-ideal gas lattice Boltzmann equation (LBE), the intermolecular forces between solid and fluid can be represented by the inclusion of the wall free energy in the expression of the total free energy. We derived and investigated three types of polynomial (linear, quadratic, and cubic) wall free energy based boundary conditions for the non-ideal gas LBE method. Static cases with a liquid drop sitting on solid surfaces are examined. All the proposed boundary conditions are able to predict the equilibrium states very well in the range of moderate contact angles by incorporating the potential form of the intermolecular forces and the bounce-back rule that guarantees mass conservation. Simulations with different boundary conditions are carried out and the results are compared concerning the accuracy as well as the applicability of different polynomial boundary conditions.

A Spectral Element Approximation to Price European Options with One Asset and Stochastic Volatility

We develop a Legendre quadrilateral spectral element approximation for the Black-Scholes equation to price European options with one underlying asset and stochastic volatility. A weak formulation of the equations imposes the boundary conditions naturally along the boundaries where the equation becomes singular, and in particular, we use an energy method to derive boundary conditions at outer boundaries for which the problem is well-posed on a finite domain. Using Heston's analytical solution as a benchmark, we show that the spectral element approximation along with the proposed boundary conditions gives exponential convergence in the solution and the Greeks to the level of time and boundary errors in a domain of financial interest.

Analysis of induced-charge electro-osmotic flow in a microchannel embedded with polarizable dielectric blocks

Within the frame work of classic electromagnetic theory, a general electrical boundary condition describing the induced-charge electrokinetic phenomena at the liquid-dielectric interface is proposed in the present study. Two well-known limiting cases, i.e., perfectly insulating and perfectly polarizable wall boundary conditions, can be recovered from the present electrical boundary condition. By utilizing the proposed boundary condition, the induced-charge electro-osmosis (ICEO) flow in an infinitely long microchannel patterned with two symmetric polarizable dielectric blocks is investigated analytically. Fourier transform method is invoked to solve a biharmonic equation, which governs the (ICEO) flow field described by the stream function. Dimensionless parameters are introduced, and their effects on flow characteristics are analyzed. It is found that an increase in polarizability of the dielectric block enhances the slip velocity on its surface and thus induces a pair of counter-rotating vortices. Also, increasing the natural zeta potential on the upstream and downstream of the insulating microchannel walls leads to extinction of the vortex near the upstream insulating microchannel and suppression of the vortex near the downstream insulating microchannel.