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 - <p style="text-align: justify;">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.</p>