Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A UNIFIED STABILIZED FINITE VOLUME METHOD FOR STOKES AND DARCY EQUATIONS

  • Received : 2018.09.20
  • Accepted : 2018.12.13
  • Published : 2019.07.01
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Abstract

In this paper, we present and analyze a cell-centered collocated finite volume scheme for incompressible flows to compute solutions simultaneous to Stokes and Darcy equations by applying a pressure jump stabilization term to avoid locking. We prove that the new stabilized FV formulation satisfies a discrete inf-sup condition and error estimates for both problems. Finally, we present some numerical examples confirming this analysis.

Keywords

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FIGURE 1. Approximate velocity vectors and pressure elevation for Stokes with µ = 0.1.

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FIGURE 2. Approximate velocity vectors and pressure elevation for Darcy with α = 100.

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FIGURE 3. Convergence history for Stokes (left) µ = 0.1 andfor Darcy (right) with α = 100.

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FIGURE 4. Approximate velocity vectors and pressure elevation for Stokes with µ = 1.

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FIGURE 5. Approximate velocity vectors and pressure eleva-tion for Darcy with α = 10.

DBSHBB_2019_v56n4_1083_f0006.png 이미지

FIGURE 6. Convergence history for Stokes (left) µ = 1 and forDarcy (right) with α = 10.

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