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<p>In this paper, we propose a fully discrete numerical scheme for the Navier–Stokes equations, which combines the variable time step Dahlquist, Liniger, and Nevanlinna method in time and the symmetric interior penalty discontinuous Galerkin method in space. The proposed fully discrete numerical scheme satisfies the unconditional energy stability. We derive the convergence rate in space and the second-order convergence rate in time. An adaptive time step technique which can greatly improve the computational efficiency is further presented. Numerical examples are given to verify the theoretical results and show the effectiveness of our proposed method.</p>

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A time variable stepping technique for solving the Navier–Stokes equations with an adaptive minimum dissipation criterion

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • Qiankun Zhang,
  • Wenju Zhao,
  • Guang-an Zou

摘要

In this paper, we propose a fully discrete numerical scheme for the Navier–Stokes equations, which combines the variable time step Dahlquist, Liniger, and Nevanlinna method in time and the symmetric interior penalty discontinuous Galerkin method in space. The proposed fully discrete numerical scheme satisfies the unconditional energy stability. We derive the convergence rate in space and the second-order convergence rate in time. An adaptive time step technique which can greatly improve the computational efficiency is further presented. Numerical examples are given to verify the theoretical results and show the effectiveness of our proposed method.