• Title/Summary/Keyword: boundary condition

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NOTE ON LOCAL ESTIMATES FOR WEAK SOLUTION OF BOUNDARY VALUE PROBLEM FOR SECOND ORDER PARABOLIC EQUATION

  • Choi, Jongkeun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1123-1148
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    • 2016
  • The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.

Boundary conditions for Time-Domain Finite-Difference Elastic Wave Modeling in Anisotropic Media (이방성을 고려한 시간영역 유한차분법 탄성파 모델링에서의 경계조건)

  • Lee, Ho-Yong;Min, Dong-Joo;Kwoon, Byung-Doo;Lim, Seung-Chul;Yoo, Hai-Soo
    • Geophysics and Geophysical Exploration
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    • v.11 no.2
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    • pp.153-160
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    • 2008
  • Seismic modeling is used to simulate wave propagation in the earth. Although the earth's subsurface is usually semi-infinite, we cannot handle the semi-infinite model in seismic modeling because of limited computational resources. For this reason, we usually assume a finite-sized model in seismic modeling. In that case, we need to eliminate the edge reflections arising from the artificial boundaries introducing a proper boundary condition. In this study, we changed three kinds of boundary conditions (sponge boundary condition, Clayton and Engquist's absorbing boundary condition, and Higdon's transparent boundary condition) so that they can be applied in elastic wave modeling for anisotropic media. We then apply them to several models whose Poisson's ratios are different. Clayton and Engquist's absorbing boundary condition is unstable in both isotropic and anisotropic media, when Poisson's ratio is large. This indicates that the absorbing boundary condition can be applied in anisotropic media restrictively. Although the sponge boundary condition yields good results for both isotropic and anisotropic media, it requires too much computational memory and time. On the other hand, Higdon's transparent boundary condition is not only inexpensive, but also reduce reflections over a wide range of incident angles. We think that Higdon's transparent boundary condition can be a method of choice for anisotropic media, where Poisson's ratio is large.

Development of internal inflow/outflow steady mean flow boundary condition using Perfectly Matched Layer for the prediction of turbulence-cascade interaction noise (난류-캐스케이드 상호작용 소음 예측을 위한 Perfectly Matched Layer 을 이용한 내부 입/출구 정상유동 경계조건의 개발)

  • Kim, Dae-Hwan;Cheong, Cheol-Ung
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2012.04a
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    • pp.521-526
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    • 2012
  • It is essential for the accurate time-domain prediction of broadband noise due to turbulence-cascade interaction to develop inflow/outflow boundary conditions to satisfy the following three requirements: to maintain the back ground mean flow, to nonreflect the outgoing disturbances and to generate the specified input gust. The preceding study(1) showed that Perfectly Matched Layer (PML) boundary condition was successfully applied to absorb the outgoing disturbances and to generate the specified gust in the time-domain computations of broadband noise due to interaction of incident gust with a cascade of flat-plates. In present study, PML boundary condition is extended in order to predict steady mean flow that is needed for the computation of noise due to interaction of incident gust with a cascade of airfoils. PML boundary condition is originally designed to absorb flow disturbances superimposed on the steady meanflow in the buffer zone. However, the steady meanflow must be computed before PML boundary condition is applied on the flow computation. In the present paper, PML equations are extended by introducing source term to maintain desired mean flow conditions. The extended boundary condition is applied to the benchmark problem where the meanflow around a cascade of airfoils is predicted. These illustrative computations reveal that the extended PML equations can effectively provide and maintain the target meanflow.

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Development of Internal Inflow/outflow Steady Mean Flow Boundary Condition Using Perfectly Matched Layer for the Prediction of Turbulence-cascade Interaction Noise (난류-캐스케이드 상호작용 소음 예측을 위한 Perfectly Matched Layer을 이용한 내부 입/출구 정상유동 경계조건의 개발)

  • Kim, Dae-Hwan;Cheong, Cheol-Ung
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.22 no.7
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    • pp.685-691
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    • 2012
  • It is essential for the accurate time-domain prediction of broadband noise due to turbulence-cascade interaction to develop inflow/outflow boundary conditions to satisfy the following three requirements: to maintain the back ground mean flow, to nonreflect the outgoing disturbances and to generate the specified input gust. The preceding study showed that perfectly matched layer(PML) boundary condition was successfully applied to absorb the outgoing disturbances and to generate the specified gust in the time-domain computations of broadband noise due to interaction of incident gust with a cascade of flat-plates. In present study, PML boundary condition is extended in order to predict steady mean flow that is needed for the computation of noise due to interaction of incident gust with a cascade of airfoils. PML boundary condition is originally designed to absorb flow disturbances superimposed on the steady meanflow in the buffer zone. However, the steady meanflow must be computed before PML boundary condition is applied on the flow computation. In the present paper, PML equations are extended by introducing source term to maintain desired mean flow conditions. The extended boundary condition is applied to the benchmark problem where the meanflow around a cascade of airfoils is predicted. These illustrative computations reveal that the extended PML equations can effectively provide and maintain the target meanflow.

Pressure Correction Method and Slip Boundary Conditions for Microflows (미소유동 해석을 위한 압력수정기법 및 미끄럼 경계조건)

  • Choi, Hyung-Il;Maeng, Joo-Sung;Lee, Do-Hyung
    • Proceedings of the KSME Conference
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    • 2001.06e
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    • pp.430-435
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    • 2001
  • This paper introduces a pressure correction method for microflow computation. Conventional CFD methods with no slip boundary condition fail to predict the rarefaction effect of the wall when simulating gas microflows in the slip-flow regime. Pressure correction method with an appropriate slip boundary condition is an efficient tool in analyzing microscale flows. The present unstructured SIMPLE algorithm adopts both the classical Maxwell boundary condition and Langmuir boundary condition proposed by Myong. The simulation results of microchannel flows show that the proposed method has an effective predictive capability for microscale flows.

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Comparison of Temperature Distribution Between Two Different Fin Tip Boundary Conditions for a Pin Fin (Pin fin의 다른 두 핀 끝 경계조건 사이의 온도분포 비교)

  • Kang, Hyung-Suk
    • Journal of Industrial Technology
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    • v.31 no.A
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    • pp.21-25
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    • 2011
  • A comparison of temperature distributions along the fin length coordinate between two different fin tip boundary conditions for a circular pin fin is made by using the one-dimensional analytic method. One tip boundary condition is the actual fin tip boundary condition and fin tip temperature is arbitrarily given for another fin tip boundary condition. The value of the fin base temperature is depend on the fin base thickness and fin radius. One of the results shows that the temperature distribution along the fin length coordinate for the actual fin tip boundary condition and that for the arbitrarily given fin tip temperature are the same if the arbitrarily given fin tip temperature and the fin tip temperature for the actual fin tip boundary condition are the same.

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