Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier–Stokes equations
| Autor: | Yuri A. Blinkov, Vladimir P. Gerdt, Pierluigi Amodio, Roberto La Scala |
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| Rok vydání: | 2017 |
| Předmět: |
Independent equation
Applied Mathematics 010102 general mathematics Mathematical analysis Finite difference method Finite difference 02 engineering and technology Non-dimensionalization and scaling of the Navier–Stokes equations 01 natural sciences Euler equations Physics::Fluid Dynamics Computational Mathematics symbols.namesake Pressure-correction method Hagen–Poiseuille flow from the Navier–Stokes equations 0202 electrical engineering electronic engineering information engineering symbols 020201 artificial intelligence & image processing 0101 mathematics Navier–Stokes equations Mathematics |
| Zdroj: | Applied Mathematics and Computation. 314:408-421 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2017.06.037 |
| Popis: | In this paper, we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier–Stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the system of three equations: the continuity equation and the proper Navier–Stokes equations. Then, we compute the canonical Grobner basis form for the obtained discrete system. It gives one more difference equation which is equivalent to the pressure Poisson equation modulo difference ideal generated by the Navier–Stokes equations, and thereby comprises a new finite difference approximation (scheme). We show that the new scheme is strongly consistent. Besides, our computational experiments demonstrate much better numerical behavior of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and with the scheme which is not strongly consistent. |
| Databáze: | OpenAIRE |
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