Approximation of the convective flux in the incompressible Navier-Stokes equations using local boundary-value problems

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We present the spatial discretization of the nonlinear convective flux in the incompressible Navier-Stokes equations using local boundary-value problems. The finite-volume discretization of the incompressible Navier-Stokes equations over staggered grids requires the approximation of the cell-face velocity components. In the proposed method, the cell-face velocity components are computed from local boundary-value problems, with the pressure gradient and the gradient of the transverse flux as source terms. The approximation is expressed as the sum of the homogeneous part, corresponding to the convection-diffusion operator, and the inhomogeneous part, corresponding to the source terms. The homogeneous part of the approximation is shown to be a weighted average of the central and the upwind approximation and thus, is first-order convergent over coarse grids and second-order over finer grids. We show that the inhomogeneous part of the approximation effectively removes the numerical diffusion introduced by the homogeneous part. The inclusion of the source terms in the local boundary-value problem results in a more accurate approximation that shows uniform second-order convergence and does not introduce any spurious oscillations.

Originele taal-2Engels
Pagina's (van-tot)523-536
Aantal pagina's14
TijdschriftJournal of Computational and Applied Mathematics
Volume340
DOI's
StatusGepubliceerd - 1 jan 2018

Vingerafdruk

Incompressible Navier-Stokes Equations
Navier Stokes equations
Boundary value problems
Boundary Value Problem
Fluxes
Approximation
Source Terms
Pressure gradient
Discretization
Face
Grid
Staggered Grid
Convection-diffusion
Cell
Weighted Average
Pressure Gradient
Finite Volume
Transverse
Inclusion
Oscillation

Citeer dit

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title = "Approximation of the convective flux in the incompressible Navier-Stokes equations using local boundary-value problems",
abstract = "We present the spatial discretization of the nonlinear convective flux in the incompressible Navier-Stokes equations using local boundary-value problems. The finite-volume discretization of the incompressible Navier-Stokes equations over staggered grids requires the approximation of the cell-face velocity components. In the proposed method, the cell-face velocity components are computed from local boundary-value problems, with the pressure gradient and the gradient of the transverse flux as source terms. The approximation is expressed as the sum of the homogeneous part, corresponding to the convection-diffusion operator, and the inhomogeneous part, corresponding to the source terms. The homogeneous part of the approximation is shown to be a weighted average of the central and the upwind approximation and thus, is first-order convergent over coarse grids and second-order over finer grids. We show that the inhomogeneous part of the approximation effectively removes the numerical diffusion introduced by the homogeneous part. The inclusion of the source terms in the local boundary-value problem results in a more accurate approximation that shows uniform second-order convergence and does not introduce any spurious oscillations.",
keywords = "Cell-face velocities, Convective terms, Finite-volume method, Incompressible Navier-Stokes equations",
author = "N. Kumar and {ten Thije Boonkkamp}, {J. H.M.} and B. Koren",
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Approximation of the convective flux in the incompressible Navier-Stokes equations using local boundary-value problems. / Kumar, N.; ten Thije Boonkkamp, J. H.M.; Koren, B.

In: Journal of Computational and Applied Mathematics, Vol. 340, 01.01.2018, blz. 523-536.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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AB - We present the spatial discretization of the nonlinear convective flux in the incompressible Navier-Stokes equations using local boundary-value problems. The finite-volume discretization of the incompressible Navier-Stokes equations over staggered grids requires the approximation of the cell-face velocity components. In the proposed method, the cell-face velocity components are computed from local boundary-value problems, with the pressure gradient and the gradient of the transverse flux as source terms. The approximation is expressed as the sum of the homogeneous part, corresponding to the convection-diffusion operator, and the inhomogeneous part, corresponding to the source terms. The homogeneous part of the approximation is shown to be a weighted average of the central and the upwind approximation and thus, is first-order convergent over coarse grids and second-order over finer grids. We show that the inhomogeneous part of the approximation effectively removes the numerical diffusion introduced by the homogeneous part. The inclusion of the source terms in the local boundary-value problem results in a more accurate approximation that shows uniform second-order convergence and does not introduce any spurious oscillations.

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