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An efficient second-order accurate finite-volume method is developed
for a solution of the incompressible Navier-Stokes equations on complex
multi-block structured curvilinear grids. Unlike in the finite-volume or
finite-difference-based alternating-direction-implicit (ADI) methods, where
factorization of the coordinate transformed governing equations is
performed along generalized coordinate directions, in the proposed method,
the discretized Cartesian form Navier-Stokes equations are factored along
curvilinear grid lines. The new ADI finite-volume method is also extended
for simulations on multi-block structured curvilinear grids with which
complex geometries can be efficiently resolved. The numerical method is
first developed for an unsteady convection-diffusion equation, then is
extended for the incompressible Navier-Stokes equations. The order of
accuracy and stability characteristics of the present method are analyzed
in simulations of an unsteady convection-diffusion problem, decaying
vortices, flow in a lid-driven cavity, flow over a circular cylinder, and
turbulent flow through a planar channel. Numerical solutions predicted by
the proposed ADI finite-volume method are found to be in good agreement
with experimental and other numerical data, while the solutions are
obtained at much lower computational cost than those required by other
iterative methods without factorization. For a simulation on a grid with
O(10^5) cells, the computational time required by the present ADI-based
method for a solution of momentum equations is found to be less than 20% of
that required by a method employing a biconjugate-gradient-stabilized
scheme.
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