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<p>In this paper, we solve the velocity-pressure formulation of the incompressible Navier-Stokes equations by utilizing high-order finite difference operators that satisfy a summation-by-parts property on multi-block curvilinear domain discretizations. We apply the projection method to connect the interior multi-block interfaces, and we show the stability of the discretization through a discrete version of the energy method. Analytical test cases reveal that the discretization achieves good accuracy and high-order convergence. We also explore the efficiency of increasing the discretization order, showing that, in certain instances, a higher-order discretization provides greater accuracy while using fewer degrees of freedom. Additionally, our method reaches a good agreement with benchmark data for a well-studied benchmark problem.</p>

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Provably Stable and High-Order Accurate Multi-Block Finite Difference Discretisation for Incompressible Flow

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月18日

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  • David Niemelä,
  • Gustav Eriksson,
  • Ken Mattsson

摘要

In this paper, we solve the velocity-pressure formulation of the incompressible Navier-Stokes equations by utilizing high-order finite difference operators that satisfy a summation-by-parts property on multi-block curvilinear domain discretizations. We apply the projection method to connect the interior multi-block interfaces, and we show the stability of the discretization through a discrete version of the energy method. Analytical test cases reveal that the discretization achieves good accuracy and high-order convergence. We also explore the efficiency of increasing the discretization order, showing that, in certain instances, a higher-order discretization provides greater accuracy while using fewer degrees of freedom. Additionally, our method reaches a good agreement with benchmark data for a well-studied benchmark problem.