Generalized theory for numerical instability of the Gaussian-filtered Navier-Stokes equations as a model system for large eddy simulation of turbulence
| dc.creator | Ida, Masato | |
| dc.creator | Oshima, Nobuyuki | |
| dc.date | 2006-06-22 | |
| dc.date.accessioned | 2026-07-07T07:18:49Z | |
| dc.date.available | 2026-07-07T07:18:49Z | |
| dc.description | The Gaussian-filtered Navier-Stokes equations are examined theoretically and a generalized theory of their numerical stability is proposed. Using the exact expansion series of subfilter-scale stresses or integration by parts, the terms describing the interaction between the mean and fluctuation portions in a statistically steady state are theoretically rewritten into a closed form in terms of the known filtered quantities. This process involves high-order derivatives with time-independent coefficients. Detailed stability analyses of the closed formulas are presented for determining whether a filtered system is numerically stable when finite difference schemes or others are used to solve it. It is shown that by the Gaussian filtering operation, second and higher even-order derivatives are derived that always exhibit numerical instability in a fixed range of directions; hence, if the filter widths are unsuitably large, the filtered Navier-Stokes equations can in certain cases be unconditionally unstable even though there is no error in modeling the subfilter-scale stress terms. As is proved by a simple example, the essence of the present discussion can be applied to any other smooth filters; that is, such a numerical instability problem can arise whenever the dependent variables are smoothed out by a filter. | |
| dc.description | 24 pages, 2 figures, REVTEX4 | |
| dc.identifier | https://arxiv.org/abs/physics/0606196 | |
| dc.identifier | http://arxiv.org/abs/physics/0606196 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114439 | |
| dc.subject | Fluid Dynamics | |
| dc.subject | Computational Physics | |
| dc.title | Generalized theory for numerical instability of the Gaussian-filtered Navier-Stokes equations as a model system for large eddy simulation of turbulence | |
| dc.type | text |