A generalized MAC scheme on curvilinear domains

Yin-Liang Huang National University of Tainan Jian-Guo Liu Duke University Wei-Cheng Wang National Tsing Hua University

Numerical Analysis and Scientific Computing mathscidoc:1702.25025

Siam Journal on Scientific Computing, 35, (5), 953-986, 2013.5
We propose a simple finite difference scheme for Navier--Stokes equations in primitive formulation on curvilinear domains. With proper boundary treatment and interplay between covariant and contravariant components, the spatial discretization admits exact Hodge decomposition and energy identity. As a result, the pressure can be decoupled from the momentum equation with explicit time stepping. No artificial pressure boundary condition is needed. In addition, it can be shown that this spatially compatible discretization leads to uniform inf-sup condition, which plays a crucial role in the pressure approximation of both dynamic and steady state calculations. Numerical experiments demonstrate the robustness and efficiency of our scheme.
Navier–Stokes equations, inf-sup condition, mark-and-cell scheme, incompressible flow, pressure boundary condition, pressure Poisson equation
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  title={A generalized MAC scheme on curvilinear domains},
  author={Yin-Liang Huang, Jian-Guo Liu, and Wei-Cheng Wang},
  booktitle={Siam Journal on Scientific Computing},
Yin-Liang Huang, Jian-Guo Liu, and Wei-Cheng Wang. A generalized MAC scheme on curvilinear domains. 2013. Vol. 35. In Siam Journal on Scientific Computing. pp.953-986. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208214503499309317.
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