Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 56, Issue 3, Pages 1313-1337Publisher
SIAM PUBLICATIONS
DOI: 10.1137/18M1175069
Keywords
characteristics MAC scheme; Navier-Stokes equations; superconvergence; nonuniform grids; lid-driven cavity
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Funding
- National Natural Science Foundation of China [11671233]
- China Scholarship Council
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In this paper, a characteristics marker and cell (C-MAC) scheme is established for the Navier-Stokes equations on nonuniform grids. Error estimates for the pressure and velocity in different discrete norms are established rigorously and carefully. We obtain the second order superconvergence in the discrete L-2 norm for both velocity and pressure and the second order super-convergence for some terms of the H-1 norm of the velocity for the C-MAC scheme on nonuniform grids, which have not been reported before. Finally, some numerical experiments are presented to show the correctness and accuracy of the C-MAC scheme and the robustness and efficiency of the overall solution technique has been demonstrated using the lid-driven cavity model.
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