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<p>In this paper, an efficient algorithm is presented for wormhole propagation under the Darcy-Brinkman-Forchheimer (DBF) framework. A modified-upwind scheme is provided for the solute transport equation in the model to avoid the numerical oscillation. The marker and cell (MAC) method is devoted for spatial discretization to reach second-order error estimates in space. The second-order backward difference formula (BDF2) is proposed to improve time accuracy to second-order. In order to handle nonlinear terms and improve computational efficiency, the modified two-grid algorithm is applied. A small positive parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2443_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> </InlineEquation> is presented to transform a non-differentiable nonlinear term into a quadratic continuous differentiable term. The modified two-grid algorithm is used to achieve second-order error estimates of the pressure, velocity, porosity, concentration and auxiliary flux. The effectiveness of the second-order modified two-grid algorithm is verified through some numerical experiments. By comparing with traditional algorithm upon MAC scheme with the BDF2 method, the efficiency and accuracy of the algorithm is illustrated.</p>

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An efficient modified two-grid algorithm upon MAC scheme for simulating wormhole propagation with the Darcy-Brinkman-Forchheimer framework

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Huishan Wang,
  • Wei Liu,
  • Pengshan Wang

摘要

In this paper, an efficient algorithm is presented for wormhole propagation under the Darcy-Brinkman-Forchheimer (DBF) framework. A modified-upwind scheme is provided for the solute transport equation in the model to avoid the numerical oscillation. The marker and cell (MAC) method is devoted for spatial discretization to reach second-order error estimates in space. The second-order backward difference formula (BDF2) is proposed to improve time accuracy to second-order. In order to handle nonlinear terms and improve computational efficiency, the modified two-grid algorithm is applied. A small positive parameter \(\varepsilon \) is presented to transform a non-differentiable nonlinear term into a quadratic continuous differentiable term. The modified two-grid algorithm is used to achieve second-order error estimates of the pressure, velocity, porosity, concentration and auxiliary flux. The effectiveness of the second-order modified two-grid algorithm is verified through some numerical experiments. By comparing with traditional algorithm upon MAC scheme with the BDF2 method, the efficiency and accuracy of the algorithm is illustrated.