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Volume 18, Issue 5
Numerical Solution of the Unsteady Incompressible Navier-Stokes Equations on the Curvilinear Half-Staggered Mesh

Lan-Chieh Huang

J. Comp. Math., 18 (2000), pp. 521-540.

Published online: 2000-10

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In this paper, the Crank-Nicholson+component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-staggered mesh has been extended to the curvilinear half-staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in $Δt$) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an out flow boundary, the half-staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.

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@Article{JCM-18-521, author = {Huang , Lan-Chieh}, title = {Numerical Solution of the Unsteady Incompressible Navier-Stokes Equations on the Curvilinear Half-Staggered Mesh}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {5}, pages = {521--540}, abstract = {

In this paper, the Crank-Nicholson+component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-staggered mesh has been extended to the curvilinear half-staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in $Δt$) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an out flow boundary, the half-staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9063.html} }
TY - JOUR T1 - Numerical Solution of the Unsteady Incompressible Navier-Stokes Equations on the Curvilinear Half-Staggered Mesh AU - Huang , Lan-Chieh JO - Journal of Computational Mathematics VL - 5 SP - 521 EP - 540 PY - 2000 DA - 2000/10 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9063.html KW - Unsteady incompressible Navier-Stokes equations, Curvilinear half- staggered mesh, Discrete projection. AB -

In this paper, the Crank-Nicholson+component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-staggered mesh has been extended to the curvilinear half-staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in $Δt$) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an out flow boundary, the half-staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.

Lan-Chieh Huang. (1970). Numerical Solution of the Unsteady Incompressible Navier-Stokes Equations on the Curvilinear Half-Staggered Mesh. Journal of Computational Mathematics. 18 (5). 521-540. doi:
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