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The implicit line-by-line recurrence method in application to the solution of problems of incompressible viscous fluid dynamics

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In the paper the results of applying the implicit line-by-line recurrence method for solving of systems of elliptic difference equations, arising, in particular, at numerical simulation of dynamics of incompressible viscous fluid are considered. Research is conducted on the example of the problem about a steady-state two-dimensional lid-driven cavity flow formulated in primitive variables ($u,\, v,\, p$) for large Re (up to 20 000) and grids (up to 2049×2049). High efficiency of the method at calculation of a pressure correction fields is demonstrated. The difficulties of constructing a solution of the problem for large Rе are analyzed.

Keywords: a lid-driven cavity flow, Navier–Stokes equations, numerical methods for SLAE sol
Citation in English: Fomin A.A., Fomina L.N. The implicit line-by-line recurrence method in application to the solution of problems of incompressible viscous fluid dynamics // Computer Research and Modeling, 2015, vol. 7, no. 1, pp. 35-50
Citation in English: Fomin A.A., Fomina L.N. The implicit line-by-line recurrence method in application to the solution of problems of incompressible viscous fluid dynamics // Computer Research and Modeling, 2015, vol. 7, no. 1, pp. 35-50
DOI: 10.20537/2076-7633-2015-7-1-35-50
• , . On the convergence of the implicit iterative line-by-line recurrence method for solving difference elliptical equations. // Computer Research and Modeling. 2017. — V. 9, no. 6. — P. 857.
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