Journal of the Korean Society for Industrial and Applied Mathematics

  • 제14권1호
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  • Pages.43-56
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  • 2010
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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NUMERICAL PROPERTIES OF GAUGE METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

  • Pyo, Jae-Hong (DEPARTMENT OF MATHEMATICS, KANGWON NATIONAL UNIVERSITY)
  • 투고 : 2010.03.06
  • 심사 : 2010.03.09
  • 발행 : 2010.03.25
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초록

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

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참고문헌

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