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<p>In this paper, a V-cycle two-grid decoupled method is devised and studied for the mixed dual-permeability-Navier-Stokes system which depicts a dual-porosity flow and a free flow coupled through certain interface conditions. The crucial idea is firstly solving a mixed system on relatively coarse grid, then solving a linearized Navier-Stokes system and two Darcy systems on a fine grid, finally carrying out a linear correction on the coarse grid. Since the linearized Navier-Stokes system and two Darcy systems on the fine grid are independent with each other, they could be solved in parallel and legacy codes could be utilized in this step. The optimal error estimates are established both in the sense of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> norm and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> norm. Some numerical experiments are reported to verify the effectiveness and efficiency for the proposed V-cycle two-grid decoupled method.</p>

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V-Cycle Two-Grid Decoupled Method for a Mixed Dual-Permeability-Navier-Stokes System

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Liyun Zuo,
  • Guangzhi Du

摘要

In this paper, a V-cycle two-grid decoupled method is devised and studied for the mixed dual-permeability-Navier-Stokes system which depicts a dual-porosity flow and a free flow coupled through certain interface conditions. The crucial idea is firstly solving a mixed system on relatively coarse grid, then solving a linearized Navier-Stokes system and two Darcy systems on a fine grid, finally carrying out a linear correction on the coarse grid. Since the linearized Navier-Stokes system and two Darcy systems on the fine grid are independent with each other, they could be solved in parallel and legacy codes could be utilized in this step. The optimal error estimates are established both in the sense of \(H^1\) H 1 norm and \(L^2\) L 2 norm. Some numerical experiments are reported to verify the effectiveness and efficiency for the proposed V-cycle two-grid decoupled method.