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In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving near‐discontinuities and strong streamline curvature. First‐order methods showed significant artificial diffusion, whereas higher‐order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low‐order artificially diffusive schemes, especially in the numerical heat‐transfer industry. This paper presents an alternative strategy of using non‐artificially diffusive higher‐order methods, while maintaining strictly monotonic transitions through the use of simple flux‐limiter constraints. Limited third‐order upwinding is usually found to be the most cost‐effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

The purpose of this paper is to evaluate the performance of a numerical method for the solution to shallow-water equations on a staggered grid, in simulations for shear instabilities at two convective Froude numbers.

The simulations start from a small perturbation to a base flow with a hyperbolic-tangent velocity profile. The subsequent development of the shear instabilities is studied from the simulations using a number of flux-limiting schemes, including the second-order MINMOD, the third-order ULTRA-QUICK and the fifth-order WENO schemes for the spatial interpolation of the nonlinear fluxes. The fourth-order Runge-Kutta method advances the simulation in time.

The simulations determine two parameters: the fractional growth rate of the linear instabilities; and the vorticity thickness of the first nonlinear peak. Grid refinement using 32, 64, 128, 256 and 512 nodes over one wave length determines the exact values by extrapolation and the computational error for the parameters. It also determines the overall order of convergence for each of the flux-limiting schemes used in the numerical simulations.

The four-digit accuracy of the numerical simulations presented in this paper are comparable to analytical solutions. The development of this reliable numerical simulation method has paved the way for further study of the instabilities in shear flows that radiate waves.

This paper aims to tackle the problem of thermo‐solutal convection and macrosegregation during ingot solidification of metal alloys. Complex flow structures associated with the development of channels segregate and sharp gradients in the solutal field call for the implementation of accurate methods for numerical modeling of alloy solidification. In particular, the solute transport equation is convection dominated and requires special non‐oscillarity type high‐order schemes to handle the regions of channels segregates.

In the present study, a time‐splitting approach has been adopted to separately handle solute advection and diffusion. This splitting technique allows the application of accurate total variation dimensioning (TVD) schemes for solution of solute advection. Applications of second‐order Lax‐Wendroff TVD SUPERBEE and fifth‐order weighted essentially non‐oscillatory (WENO) schemes are described in the present article. Classical numerical solution of solute transport using hybrid and central‐difference schemes are also employed for the purpose of comparisons. Numerical simulations for solidification of Pb‐18%Sn in a two‐dimensional rectangular cavity have been carried out using different numerical schemes.

Numerical results show the difficulty of obtaining grid‐independent solutions with respect to local details in the region of channels. Grid convergence patterns and numerical uncertainty are found to be dependent on the applied scheme. In general, the first‐order hybrid scheme is diffusive and under predicts the formation of channels. The second‐order central‐difference scheme brings about oscillations with possible non‐physical extremes of solute composition in the region of channel segregates due to sharp gradients in the solutal field. The results obtained using TVD and WENO schemes contain no oscillations and show an excellent capture of channels formation and resolution of the interface between solute‐rich and depleted bands. Different stages of channels formation are followed by analyzing thermo‐solutal convection and macrosegregation at different times during solidification.

Accurate prediction of local variation in the solutal and flow fields in the channels regions requires grid refinement up to scales in the order of microscopic dendrite arm spacing. This imposes limitations in terms of large computational time and applicability of available macroscopic models based on classical volume‐averaging techniques.

The present study is very useful for numerical simulation of macrosegregation during ingot casting of metal alloys.

The paper provides the methodology and application of TVD schemes to predict channel segregates during columnar solidification of metal alloys. It also demonstrates the limitations of classical schemes for simulation of alloy solidification.

Deals with the non‐stationary pure convection equation in two dimensions. An attribute of the method is that the advective fluxes are approximated by taking the flow orientations into consideration. The interfacial numerical fluxes are interpolated by virtue of the rational areas which depend on the corner velocity vectors. This leads to a discrete system containing dissipative artifacts in regions normal to the local streamline. Conducts two‐dimensional fundamental studies for the flux discretization developed. These analyses give insight into the order‐of‐accuracy, and the scheme stability. According to the underlying positivity definition, this explicit scheme is, furthermore, classified as conditionally monotonic. This scheme has been applied successfully to solve smooth, sharply varied, and discontinuous transport problems.

The NIRVANA project is concerned with the development of a nonoscillatory, integrally reconstructed, volume‐averaged numerical advection scheme. The conservative, flux‐based finite‐volume algorithm is built on an explicit, single‐step, forward‐in‐time update of the cell‐average variable, without restrictions on the size of the time‐step. There are similarities with semi‐Lagrangian schemes; a major difference is the introduction of a discrete integral variable, guaranteeing conservation. The crucial step is the interpolation of this variable, which is used in the calculation of the fluxes; the (analytic) derivative of the interpolant then gives sub‐cell behaviour of the advected variable. In this paper, basic principles are described, using the simplest possible conditions: pure one‐dimensional advection at constant velocity on a uniform grid. Piecewise Nth‐degree polynomial interpolation of the discrete integral variable leads to an Nth‐order advection scheme, in both space and time. Nonoscillatory results correspond to convexity preservation in the integrated variable, leading naturally to a large‐Δt generalisation of the universal limited. More restrictive TVD constraints are also extended to large Δt. Automatic compressive enhancement of step‐like profiles can be achieved without exciting “stair‐casing”. One‐dimensional simulations are shown for a number of different interpolations. In particular, convexity‐limited cubic‐spline and higher‐order polynomial schemes give very sharp, nonoscillatory results at any Courant number, without clipping of extrema. Some practical generalisations are briefly discussed.

This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model.

The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used.

This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results.

The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow.

The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.

In this paper, we solve by a finite difference upwinded method an extended hydrodynamic model for semiconductors, with viscous terms in the momentum equation. In particular, we consider the simulation of a one‐dimensional n⁺‐n ‐n⁺ diode, whose solution exhibits at low temperatures strong discontinuities, and investigate the effect of the momentum viscosity on the shock waves. Numerical experiments, performed also on a two‐dimensional test case, demonstrate that the numerical scheme, working on non‐uniform grids, is suitable to describe solutions with strong variations in time and space. Well‐posedness for the boundary conditions is discussed, and a linear stability estimate is established for the one‐dimensional n⁺‐n ‐n⁺ diode benchmark problem.

Extant paradox theory suggests that adopting paradoxical frames, which are mental templates adopted by individuals in order to embrace contradictions, will result in superior firm performance. Superior performance is achieved through learning and creativity, fostering flexibility and resilience and unleashing human capital. The creativity mechanism of paradox theory is limited by a few propositions and a rough underlying theoretical logic. Using the extant theoretical base as a platform, the paper aims to develop a more powerful theory using a computational simulation.

This paper relies on a psychologically realistic computer simulation. Using a simulation to generate ideas from stored information, one can model and manipulate the parameters that have been shown to mediate the relationship between paradoxes and creative output – defined as the number of creative ideas generated.

Simulation results suggest that the relationship between paradoxical frames and creative output is non-monotonic – contrary to previous studies. Indeed, findings suggest that paradoxical frames can reduce, rather than enhance, creative output, in at least some cases.

An important benefit of adopting paradoxical frames is their capacity to increase creative output. This assumption is challenging to test, because one cannot measure private cognitive processes related to knowledge creation. However, they can be simulated. This allows for the extension of current theory. This new theory depicts a more complete relationship between paradoxical frames and creativity by accounting for subjective differences in how paradoxical frames are experienced along two cognitive mechanisms – differentiation and integration.

The purpose of the paper is to propose a homogenization-based topology optimization method to optimize the design of variable-density cellular structure, in order to achieve lightweight design and overcome some of the manufacturability issues in additive manufacturing.

First, homogenization is performed to capture the effective mechanical properties of cellular structures through the scaling law as a function their relative density. Second, the scaling law is used directly in the topology optimization algorithm to compute the optimal density distribution for the part being optimized. Third, a new technique is presented to reconstruct the computer-aided design (CAD) model of the optimal variable-density cellular structure. The proposed method is validated by comparing the results obtained through homogenized model, full-scale simulation and experimentally testing the optimized parts after being additive manufactured.

The test examples demonstrate that the homogenization-based method is efficient, accurate and is able to produce manufacturable designs.

The optimized designs in our examples also show significant increase in stiffness and strength when compared to the original designs with identical overall weight.

The purpose of this paper is to discuss some fundamental aspects regarding the anomalies in the passive scalar field advected by forced homogenous and isotropic turbulence, by inspection of the analytical properties of the governing equations and with the aid of direct numerical simulation (DNS) data.

Results from a pseudo‐spectral DNS of a unitary‐Schmidt‐ number passive scalar advected by a low Reynolds number flow field, Re_λ=50 and 70 (based on the Taylor microscale λ) allow for a preliminary assessment of the developed numerical model.

Manipulation of the governing equations for the scalar field (which are monotonic) reveals that the unboundedness of the scalar gradient magnitude is not ruled out by the mathematical properties of the correspondent conservation equation. Classic intermittency effects in the passive scalar field have been reproduced, such as non‐Gaussian behavior of the passive scalar statistics, loss of local isotropy, and multi‐fractal scaling of scalar structure functions. Moreover, Taylor and Richardson theories are, surprisingly, not confirmed only in the dissipation range (small‐scales anomalies).

The authors suggest that the origin of intermittency (qualitatively pictured here as violent burst in spatial gradient quantities) should be sought in the loss of monotonicity of the evolution equation of the scalar gradient.