• Title/Summary/Keyword: diffusion approximation

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A Study on Interaction of Estuarial Water and Sediment Transport (하구수와 표사의 상호작용에 관한 연구)

  • Lee, H.;Lee, J.W.
    • Journal of Korean Port Research
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    • v.14 no.4
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    • pp.451-461
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    • 2000
  • The design and maintenance of navigation channel and water facilities of an harbor which is located at the mouth of river or at the estuary area are difficult due to the complexity of estuarial water and sediment circulation. Effects of deepening navigable waterways, of changing coastline configurations, or of discharging dredged material to the open sea are necessary to be investigated and predicted in terms of water quality and possible physical changes to the coastal environment. A borad analysis of the transport mechanism in the estuary area was made in terms of sediment property, falling velocity, concentration and flow characteristics. In order to simulate the transport processes, a two-dimensional finite element model is developed, which includes erosion, transport and deposition mechanism of suspended sediments. Galerkin’s weighted residual method is used to solve the transient convection-diffusion equation. The fluid domain is subdivided into a series of triangular elements in which a quadratic approximation is made for suspended sediment concentration. Model could deal with a continuous aggregation by stipulating the settling velocity of the flocs in each element. The model provides suspended sediment concentration, bed shear stress, erosion versus deposition rate and bed profile at the given time step.

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Quantitative Label-free Terahertz Sensing of Transdermal Nicotine Delivered to Human Skin

  • Lee, Gyuseok;Namkung, Ho;Do, Youngwoong;Lee, Soonsung;Kang, Hyeona;Kim, Jin-Woo;Han, Haewook
    • Current Optics and Photonics
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    • v.4 no.4
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    • pp.368-372
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    • 2020
  • We report the terahertz time-domain spectroscopy (THz-TDS) of transdermal drug delivery in human skin. The time evolution of transdermal nicotine delivery in nicotine patches was assessed by detecting the transmission coefficient of sub-picosecond THz pulses and using a semi-analytic model based on the single-layer effective medium approximation. Using commercial nicotine patches (Nicoderm CQ®, 7 mg/24 h), THz transmission coefficients were measured to quantitatively analyze the cumulative amounts of nicotine released from the patches in the absence of their detailed specifications, including multilayer structures and optical properties at THz frequencies. The results agreed well with measurements by conventional in vitro and in vivo methods, using a diffusion cell with high-performance liquid chromatography and blood sampling respectively. Our study revealed the ability of the THz-TDS method to be an effective alternative to existing methods for noninvasive and label-free assessments of transdermal drug delivery, showing its high promise for biomedical, pharmaceutical, and cosmetic applications.

High accurate three-dimensional neutron noise simulator based on GFEM with unstructured hexahedral elements

  • Hosseini, Seyed Abolfazl
    • Nuclear Engineering and Technology
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    • v.51 no.6
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    • pp.1479-1486
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    • 2019
  • The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin Finite Element Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion and noise equations are discretized using the unstructured hexahedral by considering the linear approximation of the shape function in each element. The validation of the static calculation is performed via comparison between calculated results and reported data for the VVER-1000 benchmark problem. A sensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements) is done. Finally, the neutron noise calculation is performed for the neutron noise source of type of variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructured tetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution and neutron multiplication factor are appeared in the neutron noise equation, the more accurate calculation of these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigation of the changes of the neutron noise distribution in axial direction of the reactor core shows that the 3D neutron noise analysis is required instead of 2D.

Multigroup cross-sections generated using Monte-Carlo method with flux-moment homogenization technique for fast reactor analysis

  • Yiwei Wu;Qufei Song;Kuaiyuan Feng;Jean-Francois Vidal;Hanyang Gu;Hui Guo
    • Nuclear Engineering and Technology
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    • v.55 no.7
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    • pp.2474-2482
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    • 2023
  • The development of fast reactors with complex designs and operation status requires more accurate and effective simulation. The Monte-Carlo method can generate multi-group cross-sections in arbitrary geometry without approximation on resonances treatment and leads to good results in combination with diffusion codes. However, in previous studies, the coupling of Monte-Carlo generated multi-group cross-sections (MC-MGXS) and transport solvers has shown relatively large biases in fast reactor problems. In this paper, the main contribution to the biases is proved to be the neglect of the angle-dependence of the total cross-sections. The flux-moment homogenization technique (MHT) is proposed to take into account this dependence. In this method, the angular dependence is attributed to the transfer cross-sections, keeping an independent form for the total sections. For the MET-1000 benchmark, the multi-group transport simulation results with MC-MGXS generated with MHT are improved by 700 pcm and an additional 120 pcm with higher order scattering. The factors that cause the residual bias are discussed. The core power distribution bias is also significantly reduced when MHT is used. It proves that the MCMGXS with MHT can be applicable with transport solvers in fast reactor analysis.

Real-Time Hierarchical Techniques for Rendering of Translucent Materials and Screen-Space Interpolation (반투명 재질의 렌더링과 화면 보간을 위한 실시간 계층화 알고리즘)

  • Ki, Hyun-Woo;Oh, Kyoung-Su
    • Journal of Korea Game Society
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    • v.7 no.1
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    • pp.31-42
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    • 2007
  • In the natural world, most materials such as skin, marble and cloth are translucent. Their appearance is smooth and soft compared with metals or mirrors. In this paper, we propose a new GPU based hierarchical rendering technique for translucent materials, based on the dipole diffusion approximation, at interactive rates. Information of incident light, position, normal, and irradiance, on the surfaces are stored into 2D textures by rendering from a primary light view. Huge numbers of pixel photons are clustered into quad-tree image pyramids. Each pixel, we select clusters (sets of photons), and then we approximate multiple subsurface scattering term with the clusters. We also introduce a novel hierarchical screen-space interpolation technique by exploiting spatial coherence with early-z culling on the GPU. We also build image pyramids of the screen using mipmap and pixel shader. Each pixel of the pyramids is stores position, normal and spatial similarity of children pixels. If a pixel's the similarity is high, we render the pixel and interpolate the pixel to multiple pixels. Result images show that our method can interactively render deformable translucent objects by approximating hundreds of thousand photons with only hundreds clusters without any preprocessing. We use an image-space approach for entire process on the GPU, thus our method is less dependent to scene complexity.

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Fast GPU Implementation for the Solution of Tridiagonal Matrix Systems (삼중대각행렬 시스템 풀이의 빠른 GPU 구현)

  • Kim, Yong-Hee;Lee, Sung-Kee
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.11_12
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    • pp.692-704
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    • 2005
  • With the improvement of computer hardware, GPUs(Graphics Processor Units) have tremendous memory bandwidth and computation power. This leads GPUs to use in general purpose computation. Especially, GPU implementation of compute-intensive physics based simulations is actively studied. In the solution of differential equations which are base of physics simulations, tridiagonal matrix systems occur repeatedly by finite-difference approximation. From the point of view of physics based simulations, fast solution of tridiagonal matrix system is important research field. We propose a fast GPU implementation for the solution of tridiagonal matrix systems. In this paper, we implement the cyclic reduction(also known as odd-even reduction) algorithm which is a popular choice for vector processors. We obtained a considerable performance improvement for solving tridiagonal matrix systems over Thomas method and conjugate gradient method. Thomas method is well known as a method for solving tridiagonal matrix systems on CPU and conjugate gradient method has shown good results on GPU. We experimented our proposed method by applying it to heat conduction, advection-diffusion, and shallow water simulations. The results of these simulations have shown a remarkable performance of over 35 frame-per-second on the 1024x1024 grid.

Optimization of the growth of $CaF_2$ crystals by model experiments and numerical simulation

  • Molchanov, A.;Graebner, O.;Wehrhan, G.;Friedrich, J.;Mueller, G.
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.13 no.1
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    • pp.15-18
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    • 2003
  • High purity single crystalline calcium fluoride ($CaF_2$) has excellent optical transmission characteristics down to deep UV and is therefore selected as the main optical material for the next generation of lithography apparatus operating at wavelength of 157 nm. The growth of large sized $CaF_2$ single crystals with the required properties for this optical application can be achieved only by optimizing the crystal growth process by the aid of numerical simulation. This needs especially a precise calculation of the heat transport and temperature distribution in the solid and liquid $CaF_2$ under crystal growth conditions. As $CaF_2$ is considered to be semitransparent, the internal radiative heat transfer in $CaF_2$ plays an decisive role in the simulation of the heat transport. On the other hand it is very difficult to obtain quantitative experimental data for evaluating numerical models as $CaF_2$ is extremely corrosive at high temperatures. In this work we present a newly developed experimental technique to perform temperature measurements in $CaF_2$-crystal as well as in the melt under conditions of crystal growth process. These experimental results are compared to calculated temperature data, which were obtained by using different numerical models concerning the internal heat transfer in semitransparent $CaF_2$. It will be shown, that an advanced model, which was developed by the authors, gives a much better agreement with experimental data as a standard model, which was taken from the literature.

Development of a Flow Analysis Code Using an Unstructured Grid with the Cell-Centered Method

  • Myong, Hyon-Kook;Kim, Jong-Tae
    • Journal of Mechanical Science and Technology
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    • v.20 no.12
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    • pp.2218-2229
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    • 2006
  • A conservative finite-volume numerical method for unstructured grids with the cell-centered method has been developed for computing flow and heat transfer by combining the attractive features of the existing pressure-based procedures with the advances made in unstructured grid techniques. This method uses an integral form of governing equations for arbitrary convex polyhedra. Care is taken in the discretization and solution procedure to avoid formulations that are cell-shape-specific. A collocated variable arrangement formulation is developed, i.e. all dependent variables such as pressure and velocity are stored at cell centers. For both convective and diffusive fluxes the forms superior to both accuracy and stability are particularly adopted and formulated through a systematic study on the existing approximation ones. Gradients required for the evaluation of diffusion fluxes and for second-order-accurate convective operators are computed by using a linear reconstruction based on the divergence theorem. Momentum interpolation is used to prevent the pressure checkerboarding and a segregated solution strategy is adopted to minimize the storage requirements with the pressure-velocity coupling by the SIMPLE algorithm. An algebraic solver using iterative preconditioned conjugate gradient method is used for the solution of linearized equations. The flow analysis code (PowerCFD) developed by the present method is evaluated for its application to several 2-D structured-mesh benchmark problems using a variety of unstructured quadrilateral and triangular meshes. The present flow analysis code by using unstructured grids with the cell-centered method clearly demonstrate the same accuracy and robustness as that for a typical structured mesh.

Real-Time Simulation of Single and Multiple Scattering of Light (빛의 단일 산란과 다중 산란의 실시간 시뮬레이션 기법)

  • Ki, Hyun-Woo;Lyu, Ji-Hye;Oh, Kyoung-Su
    • Journal of Korea Game Society
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    • v.7 no.2
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    • pp.21-32
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    • 2007
  • It is significant to simulate scattering of light within media for realistic image synthesis; however, this requires costly computation. This paper introduces a practical image-space approximation technique for interactive subsurface scattering. We use a general two-pass approach, which creates transmitted irradiance samples onto shadow maps and computes illumination using the shadow maps. We estimate single scattering efficiently using a method similar to common shadow mapping with adaptive deterministic sampling. A hierarchical technique is applied to evaluate multiple scattering, based on a diffusion theory. We further accelerate rendering speed by tabulating complex functions and utilizing level of detail. We demonstrate that our technique produces high-quality images of animated scenes with blurred shadow at hundreds frames per second on graphics hardware. It can be integrated into existing interactive systems easily.

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Direct numerical simulations of viscoelastic turbulent channel flows at high drag reduction

  • Housiadas Kostas D.;Beris Antony N.
    • Korea-Australia Rheology Journal
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    • v.17 no.3
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    • pp.131-140
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    • 2005
  • In this work we show the results of our most recent Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flow using spectral spatial approximations and a stabilizing artificial diffusion in the viscoelastic constitutive model. The Finite-Elasticity Non-Linear Elastic Dumbbell model with the Peterlin approximation (FENE-P) is used to represent the effect of polymer molecules in solution, The corresponding rheological parameters are chosen so that to get closer to the conditions corresponding to maximum drag reduction: A high extensibility parameter (60) and a moderate solvent viscosity ratio (0.8) are used with two different friction Weissenberg numbers (50 and 100). We then first find that the corresponding achieved drag reduction, in the range of friction Reynolds numbers used in this work (180-590), is insensitive to the Reynolds number (in accordance to previous work). The obtained drag reduction is at the level of $49\%\;and\;63\%$, for the friction Weissenberg numbers 50 and 100, respectively. The largest value is substantially higher than any of our previous simulations, performed at more moderate levels of viscoelasticity (i.e. higher viscosity ratio and smaller extensibility parameter values). Therefore, the maximum extensional viscosity exhibited by the modeled system and the friction Weissenberg number can still be considered as the dominant factors determining the levels of drag reduction. These can reach high values, even for of dilute polymer solution (the system modeled by the FENE-P model), provided the flow viscoelasticity is high, corresponding to a high polymer molecular weight (which translates to a high extensibility parameter) and a high friction Weissenberg number. Based on that and the changes observed in the turbulent structure and in the most prevalent statistics, as presented in this work, we can still rationalize for an increasing extensional resistance-based drag reduction mechanism as the most prevalent mechanism for drag reduction, the same one evidenced in our previous work: As the polymer elasticity increases, so does the resistance offered to extensional deformation. That, in turn, changes the structure of the most energy-containing turbulent eddies (they become wider, more well correlated, and weaker in intensity) so that they become less efficient in transferring momentum, thus leading to drag reduction. Such a continuum, rheology-based, mechanism has first been proposed in the early 70s independently by Metzner and Lamley and is to be contrasted against any molecularly based explanations.