• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.27-40
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• 2012

The two-dimensional incompressible flow of a linear viscoelastic fluid we considered in this research has rapidly oscillating initial conditions which contain both the large scale and small scale information. In order to grasp this double-scale phenomenon of the complex flow, a multiscale analysis method is developed based on the mathematical homogenization theory. For the incompressible flow of a linear viscoelastic Maxwell fluid, a well-posed multiscale system, including averaged equations and cell problems, is derived by employing the appropriate multiple scale asymptotic expansions to approximate the velocity, pressure and stress fields. And then, this multiscale system is solved numerically using the pseudospectral algorithm based on a time-splitting semi-implicit influence matrix method. The comparisons between the multiscale solutions and the direct numerical simulations demonstrate that the multiscale model not only captures large scale features accurately, but also reflects kinetic interactions between the large and small scale of the incompressible flow of a linear viscoelastic fluid.

• Membrane and Water Treatment
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• v.13 no.4
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• pp.167-172
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• 2022

The analytical results are presented for the mass transfer in a cylindrical pore covering from the macroscale, multiscale to nanoscale owing to the variation of the inner diameter of the pore. When the thickness h_bf of the physically adsorbed layer potentially fully formed on the pore wall is comparable to but less than the inner radius R₀ of the pore, the multiscale flow occurs consisting of both the nanoscale non-continuum adsorbed layer flow and the macroscopic continuum liquid flow; When R₀ ≤ h_bf, the flow in the whole pore is essentially non-continuum; When R₀ is far greater than h_bf, the flow in the whole pore can be considered as macroscopic and continuum and the adsorbed layer effect is negligible.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.65-84
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• 2012

We present an application of the variational multiscale methodology to the computation of concentric annular pipe flow. Isogeometric analysis is utilized for higher order approximation of the solution using Non-Uniform Rational B-Splines (NURBS) functions. The ability of NURBS to exactly represent curved geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through the curved channel.

• Membrane and Water Treatment
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• v.13 no.6
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• pp.313-320
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• 2022

Theoretical calculation results are presented for the enhancement of the water mass flow rate through the hydrophobic micro/nano pores in the membrane respectively on the micrometer and nanometer scales. The water-pore wall interfacial slippage is considered. When the pore diameter is critically low (less than 1.82nm), the water flow in the nanopore is non-continuum and described by the nanoscale flow equation; Otherwise, the water flow is essentially multiscale consisting of both the adsorbed boundary layer flow and the intermediate continuum water flow, and it is described by the multiscale flow equation. For no wall slippage, the calculated water flow rate through the pore is very close to the classical hydrodynamic theory calculation if the pore diameter (d) is larger than 1.0nm, however it is considerably smaller than the conventional calculation if d is less than 1.0nm because of the non-continuum effect of the water film. When the driving power loss on the pore is larger than the critical value, the wall slippage occurs, and it results in the different scales of the enhancement of the water flow rate through the pore which are strongly dependent on both the pore diameter and the driving power loss on the pore. Both the pressure drop and the critical power loss on the pore for starting the wall slippage are also strongly dependent on the pore diameter.

• Wind and Structures
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• v.17 no.1
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• pp.1-19
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• 2013

A multiscale finite element method is applied to the Spalart-Allmaras turbulence model based detached-eddy simulation (DES). The multiscale arises from a decomposition of the scalar field into coarse (resolved) and fine (unresolved) scales. It corrects the lack of stability of the standard Galerkin formulation by modeling the scales that cannot be resolved by a given spatial discretization. The stabilization terms appear naturally and the resulting formulation provides effective stabilization in turbulent computations, where reaction-dominated effects strongly influence near-wall predictions. The multiscale DES is applied in the context of high-Reynolds flow over the Commonwealth Advisory Aeronautical Council (CAARC) standard tall building model, for both uniform and turbulent inflows. Time-averaged pressure coefficients on the exterior walls are compared with experiments and it is demonstrated that DES is able to resolve the turbulent features of the flow and accurately predict the surface pressure distributions under atmospheric boundary layer flows.

• Journal of computational fluids engineering
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• v.15 no.2
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• pp.35-40
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• 2010

In the present work, LES with new variational multiscale method is conducted on the fully developed channel flow with Reynolds number, 180 based on the friction velocity and the channel half width. Incompressible Navier-Stokes equations are integrated using finite element method with the basis function of NURBS. To solve space-time equations, Newton's method with two stage predictor multicorrector algorithm is employed. The code is parallelized using MPI. The computational domain is a rectangular box of size $2{\pi}{\times}2{\times}4/3{\pi}$ in the streamwise, wall normal and spanwise direction. Mean velocity profiles and velocity fluctuations are compared with the data of DNS. The results agree well with those of DNS and other traditional LES.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.56-59
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• 2009

In the present work, LES with new variational multiscale method is conducted on the fully developed channel flow with Reynolds number is 180 based on the friction velocity and the channel half width. Incompressible Navier-Stokes equations are integrated using finite element method with the basis function of NURBS. To solve space-time equations, Newton's method with two stage predictor multicorretor algorithm is employed. The code is parallelized using MPI. The computational domain is a rectangular box of size $2{\pi}{\times}2{\times}4/3{\pi}$ in the streamwise, wall normal and spanwise direction. Mean velocity profiles and velocity fluctuations are compared with the data of DNS. The results agree well with those of DNS and other traditional LES.

• Prospectives of Industrial Chemistry
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• v.24 no.3
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• pp.28-41
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• 2021

고분자 시스템의 경우 매우 상이한 시간 및 길이 스케일(time and length scale)에 연관된 복잡한 내부 구조(internal structure)를 가지고 있기 때문에 전통적인 실험 방법만으로는 체계적이고 종합적인 연구가 쉽지 않다. 최근 다양한 시간 및 길이 스케일에 연관된 연구를 진행할 수 있는 다중 스케일 전산 모사(multiscale computer simulation) 방법은 이러한 고분자 시스템 연구에 있어서 새로운 대안으로 각광받고 있다. 본 논문에서는 최근 급격한 발전을 이룬 고분자 용액(polymeric liquid) 시스템에 대한 평형(equilibrium) 및 비평형(nonequilibrium) 전산 모사(computer simulation) 방법들에 관해 소개하고 이를 통합적으로 해석할 수 있는 다중 스케일 전산 모사 방법에 대해 여러 가지 사례를 들어 살펴보았다.

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.46.4-46.4
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• 2008

• Interaction and multiscale mechanics
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• v.3 no.1
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• pp.1-22
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• 2010

In this paper one introduces a method of multiscale modelling called collection of dynamical systems with dimensional reduction. The method is suggested to be an appropriate approach to theoretical modelling of phenomena in mechanics of materials having in mind especially dynamics of processes. Within this method one formalizes scale of averaging of processes during modelling. To this end a collection of dynamical systems is distinguished within an elementary dynamical system. One introduces a dimensional reduction procedure which is designed to be a method of transition between various scales. In order to consider continuum models as obtained by means of the dimensional reduction one introduces continuum with finite-dimensional fields. Owing to geometrical elements associated with the elementary dynamical system we can formalize scale of averaging within continuum mechanics approach. In general presented here approach is viewed as a continuation of the rational mechanics.