• Coupled systems mechanics
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• 제8권2호
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• pp.129-146
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• 2019

The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

• 방사성폐기물학회지
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• 제21권1호
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• pp.175-182
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• 2023

APro, a modularized process-based total system performance assessment framework, was developed at the Korea Atomic Energy Research Institute (KAERI) to simulate radionuclide transport considering coupled thermal-hydraulic-mechanical-chemical processes occurring in a geological disposal system. For reactive transport simulation considering geochemical reactions, COMSOL and PHREEQC are coupled with MATLAB in APro using an operator splitting scheme. Conventionally, coupling is performed within a MATLAB interface so that COMSOL stops the calculation to deliver the solution to PHREEQC and restarts to continue the simulation after receiving the solution from PHREEQC at every time step. This is inefficient when the solution is frequently interchanged because restarting the simulation in COMSOL requires an unnecessary setup process. To overcome this issue, a coupling scheme that calls PHREEQC inside COMSOL was developed. In this technique, PHREEQC is called through the "MATLAB function" feature, and PHREEQC results are updated using the COMSOL "Pointwise Constraint" feature. For the one-dimensional advection-reaction-dispersion problem, the proposed coupling technique was verified by comparison with the conventional coupling technique, and it improved the computation time for all test cases. Specifically, the more frequent the link between COMSOL and PHREEQC, the more pronounced was the performance improvement using the proposed technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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• pp.201-210
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• 2010

We propose a new robust and accurate method for the numerical solution of medical image segmentation. The modified Allen-Cahn equation is used to model the boundaries of the image regions. Its numerical algorithm is based on operator splitting techniques. In the first step of the splitting scheme, we implicitly solve the heat equation with the variable diffusive coefficient and a source term. Then, in the second step, using a closed-form solution for the nonlinear equation, we get an analytic solution. We overcome the time step constraint associated with most numerical implementations of geometric active contours. We demonstrate performance of the proposed image segmentation algorithm on several artificial as well as real image examples.

• East Asian mathematical journal
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• 제27권5호
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• pp.545-555
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• 2011

Based on the A-maximal(m)-relaxed monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems using the relaxed proximal point algorithm is explored, while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modified version of the relaxed proximal point algorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong convergence results on proximal point algorithms in real Hilbert space settings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of variational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to first- order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for finding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1996년도 춘계 학술대회논문집
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• pp.131-136
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• 1996

The numerical method for the flow field of a gas atomization process is presented. For the analysis of the compressible supersonic jet flow of a gas. an axisymmetric Navier-Stokes equations are solved using a LU-factored upwind method. The MUSCL type TVD scheme is used for the discretization of inviscid flux, whereas Steger-Warming splitting and LU factorization is applied to the implicit operator. For the validation of the present method, we computed the flow field around the simple gas atomizer proposed by Issac. The numerical results has shown excellent agreement with the experimental data.

• 한국정밀공학회지
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• 제13권3호
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• pp.158-164
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• 1996

In this paper, the CNC cutting planning module for product with three dimensional solid shape is realized to develop a smart CAD/CAM system which performs systematically from the shape design of procuct by the B-Rep solid modeler to the CNC cutting of product by a machining center. The three dimensional solid shape of product can be easily designed and constructed by the Euler operators and Boolean operators of the solid modeler. And the various functions such as the automatic generation of tool path for the rough and finish cutting processes, the automatic elimination of overcut, the automatic generation of CNC code for the machining center and do on, are established. Especially, the overcut-free tool paths are obtained by splitting the CL solid which is composed of the offset surfaces of the solid shape of product.

• Korean Journal of Hydrosciences
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• 제6권
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• 대한기계학회논문집A
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• 제24권1호
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• pp.196-205
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• 2000

Computed Tomography (CT), Nuclear Magnetic Resonance Imaging (MR1) and some ultrasound techniques make it possible to obtain cross sections of human body or mechanical parts. In CAD system, a series of sectional surfaces can also be obtained from solid models of 3D objects. In this paper we introduce a tetrahedral meshing algorithm from these series of general sections using basic operators. In this scheme. general sections of three-dimensional object are triangulated first and side surfaces between two sections are triangulated by the use of tiling process. Finally tetrahedral meshing process is performed on each layer of 3D objects, which is composed of two general sections and one side surface.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2006년도 학술발표회 논문집
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• pp.22-27
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• 2006

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third-order QUICKEST explicit finite difference schemes respectively to solve the pure advection equation in order to prevent the occurrence of numerical oscillations. Due to various limiters owning different features, the numerical tests for 1D pure advection and 2D dispersion are conducted to evaluate the performance of different TVD schemes firstly, then the TVD schemes are applied to experimental data for simulating the 2D mixing in a straight trapezoidal channel to test the model capability. Both the numerical tests and model application show that the TVD schemes are very competent for solving the advection-dominated transport problems.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 춘계 학술대회논문집
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• pp.161-165
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• 2004

In the vortex particle method based on the vorticity-velocity formulation for solving the Wavier-Stokes equations, the unsteady, incompressible, viscous laminar flow over a NACA 0012 foil is simulated. By applying an operator-splitting method, the 'convection' and 'diffusion' equations are solved sequentially at each time step. The convection equation is solved using the vortex particle method, and the diffusion equation using the particle strength exchange(PSE) scheme which is modified to avoid a spurious vorticity flux. The scheme is improved for variety body shape using one image layer scheme. For a validation of the present method, we illustrate the early development of the viscous flow about an impulsively started NACA 0012 foil for Reynolds number 550.