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<p>The implementation of the finite-difference method in curvilinear coordinates necessitates coordinate transformations, where violations of the Geometric Conservation Law (GCL) lead to loss of freestream preservation. This failure mechanism typically manifests as numerical instability or spurious physical artifacts in simulations. In this paper, we developed a freestream-preserving Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) to solve viscous problems on perturbed grids. The geometrically induced errors are eliminated with the satisfaction of GCL. The central difference method is used for the computation of viscous flux terms, and the least squares method is introduced to enhance the accuracy and robustness of this scheme for solving subsonic viscous problems. The results of several viscous numerical tests demonstrate the reliable freestream-preserving property of the new method compared to MUSCL.</p>

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Enhanced freestream-preserving finite difference method based on MUSCL for numerical computation of laminar flow

  • 期刊论文

  • 发表日期：

    2025年6月13日

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  • Tianen Guan,
  • Zijia Huang,
  • Chunguang Xu

摘要

The implementation of the finite-difference method in curvilinear coordinates necessitates coordinate transformations, where violations of the Geometric Conservation Law (GCL) lead to loss of freestream preservation. This failure mechanism typically manifests as numerical instability or spurious physical artifacts in simulations. In this paper, we developed a freestream-preserving Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) to solve viscous problems on perturbed grids. The geometrically induced errors are eliminated with the satisfaction of GCL. The central difference method is used for the computation of viscous flux terms, and the least squares method is introduced to enhance the accuracy and robustness of this scheme for solving subsonic viscous problems. The results of several viscous numerical tests demonstrate the reliable freestream-preserving property of the new method compared to MUSCL.