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We investigate the stability of the modified difference scheme of Kim and Moin for numerical integration of two-dimensional
incompressible Navier–Stokes equations by the Fourier method and by the method of discrete perturbations. The obtained analytic-form
stability condition gives the maximum time steps allowed by stability, which are by factors f...
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Citations
... Проекционные конечно-разностные методы [5][6][7] получили широкое распространение при численном решении уравнений Навье-Стокса несжимаемых жидкостей. Одной из проблем этих методов является правильный выбор граничных условий для вспомогательных переменных для того, чтобы получить вычислительные методы и программирование. ...
... The immersed boundary method has extended significantly the scope of applicability of the rectangular Cartesian grids at the numerical solution of applied problems of the incompressible fluid dynamics. The projection finite difference methods [12,27,4] have gained widespread acceptance at the numerical solution of the incompressible Navier–Stokes equations . A recurring difficulty in these methods is the proper choice of boundary conditions for the auxiliary variables in order to obtain at least second order accuracy in the computed solution. ...
The method of collocations and least squares, which was previously proposed for the numerical solution of the two-dimensional Navier---Stokes equations governing steady incompressible viscous flows, is extended here for the three-dimensional case. The derivation of the collocation and matching conditions is carried out in symbolic form using the CAS Mathematica. The numerical stages are implemented in a Fortran code, into which the left-hand sides of the collocation and matching equations have been imported from the Mathematica program. The results of numerical tests confirm the second order of convergence of the presented method.
Modern CFD applications require the treatment of general complex domains to accurately model the emerging flow patterns. In the present work, a new low order finite difference scheme is employed and tested for the numerical solution of the incompressible Navier-Stokes equations in a complex domain described in curvilinear coordinates. A staggered grid discretization is used on both the physical and computational domains. A subgrid based computation of the Jacobian and the metric coefficients of the transformation is used. The incompressibility condition, properly transformed in curvilinear coordinates, is enforced by an iterative procedure employing either a modified local pressure correction technique or the globally defined numerical solution of a general elliptic BVP. Results obtained by the proposed overall solution technique, exhibit very good agreement with other experimental and numerical calculations for a variety of domains and grid configurations. The overall numerical solver effectively treats the general complex domains.
