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<p>On a 2-D staggered mesh of rectangles, we derive a complete flux-based finite-volume scheme for the incompressible fluid flow under magnetic force. The spatial discretization of the momentum equations requires the numerical approximation of convective and viscous fluxes through the faces of the underlying control volume. The convective fluxes are approximated with the help of cell-face velocities which are obtained by solving local boundary value problems (BVP). The newly derived cell-face velocities are significantly influenced by the cross-flux flow gradient, magnetic force, and pressure gradient. The integral representation of the cell-face velocity is decomposed as a sum of <i>homogeneous</i> and <i>inhomogeneous</i> parts of the solutions of BVP to emphasize the importance of external forcing factors. Also, a new semi-implicit time evolution scheme has been proposed for time integration to get a time-dependent or steady-state solution for considered benchmark problems. In the end, the numerical validation of the scheme has been successfully done on Taylor–Green vortex problem and singly and doubly lid-driven magneto-hydrodynamic cavity flow problems for different magnetic intensities in vertical and horizontal directions.</p>

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A new finite-volume complete flux scheme for magneto-hydrodynamic flows

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Chitranjan Pandey,
  • B. V. Rathish Kumar

摘要

On a 2-D staggered mesh of rectangles, we derive a complete flux-based finite-volume scheme for the incompressible fluid flow under magnetic force. The spatial discretization of the momentum equations requires the numerical approximation of convective and viscous fluxes through the faces of the underlying control volume. The convective fluxes are approximated with the help of cell-face velocities which are obtained by solving local boundary value problems (BVP). The newly derived cell-face velocities are significantly influenced by the cross-flux flow gradient, magnetic force, and pressure gradient. The integral representation of the cell-face velocity is decomposed as a sum of homogeneous and inhomogeneous parts of the solutions of BVP to emphasize the importance of external forcing factors. Also, a new semi-implicit time evolution scheme has been proposed for time integration to get a time-dependent or steady-state solution for considered benchmark problems. In the end, the numerical validation of the scheme has been successfully done on Taylor–Green vortex problem and singly and doubly lid-driven magneto-hydrodynamic cavity flow problems for different magnetic intensities in vertical and horizontal directions.