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Numerical Discretization (numerical + discretization)

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Selected Abstracts

Unstructured finite volume discretization of two-dimensional depth-averaged shallow water equations with porosity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010
L. Cea
Abstract This paper deals with the numerical discretization of two-dimensional depth-averaged models with porosity. The equations solved by these models are similar to the classic shallow water equations, but include additional terms to account for the effect of small-scale impervious obstructions which are not resolved by the numerical mesh because their size is smaller or similar to the average mesh size. These small-scale obstructions diminish the available storage volume on a given region, reduce the effective cross section for the water to flow, and increase the head losses due to additional drag forces and turbulence. In shallow water models with porosity these effects are modelled introducing an effective porosity parameter in the mass and momentum conservation equations, and including an additional drag source term in the momentum equations. This paper presents and compares two different numerical discretizations for the two-dimensional shallow water equations with porosity, both of them are high-order schemes. The numerical schemes proposed are well-balanced, in the sense that they preserve naturally the exact hydrostatic solution without the need of high-order corrections in the source terms. At the same time they are able to deal accurately with regions of zero porosity, where the water cannot flow. Several numerical test cases are used in order to verify the properties of the discretization schemes proposed. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Turbulence model and numerical scheme assessment for buffet computations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2004
Eric Goncalves
Abstract The prediction of shock-induced oscillations over transonic rigid airfoils is important for a better understanding of the buffeting phenomenon. The unsteady resolution of the Navier,Stokes equations is performed with various transport-equation turbulence models in which corrections are added for non-equilibrium flows. The lack of numerical efficiency due to the CFL stability condition is circumvented by the use of a wall law approach and a dual time stepping method. Moreover, various numerical schemes are used to try and be independent of the numerical discretization. Comparisons are made with the experimental results obtained for the supercritical RA16SC1 airfoil. They show the interest in using the SST correction or realizability conditions to get correct predictions of the frequency, amplitude and pressure fluctuations over the airfoil. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Validation of simplified PN models for radiative transfer in combustion systems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2008
E. Schneider
Abstract This paper illustrates the use of simplified PN approximations as a tools of achieving verification of codes and simulations of radiative transfer in combustion systems. The main advantage of considering these models is the fact that the integro-differential equation for radiative transfer can be replaced by a set of differential equations which are independent of angle variable, compatible to the partial differential equations of flow and combustion, and easy to solve using standard numerical discretizations. Validation of these models is then performed by comparing predictions to measurements for a three-dimensional diffusion flame. The good agreement between measurements and predictions indicates that the simplified PN models can be used to incorporate radiation transfer in combustion systems at very low computational cost without relying on discrete ordinates or Monte Carlo methods. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Unstructured finite volume discretization of two-dimensional depth-averaged shallow water equations with porosity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010
L. Cea
Abstract This paper deals with the numerical discretization of two-dimensional depth-averaged models with porosity. The equations solved by these models are similar to the classic shallow water equations, but include additional terms to account for the effect of small-scale impervious obstructions which are not resolved by the numerical mesh because their size is smaller or similar to the average mesh size. These small-scale obstructions diminish the available storage volume on a given region, reduce the effective cross section for the water to flow, and increase the head losses due to additional drag forces and turbulence. In shallow water models with porosity these effects are modelled introducing an effective porosity parameter in the mass and momentum conservation equations, and including an additional drag source term in the momentum equations. This paper presents and compares two different numerical discretizations for the two-dimensional shallow water equations with porosity, both of them are high-order schemes. The numerical schemes proposed are well-balanced, in the sense that they preserve naturally the exact hydrostatic solution without the need of high-order corrections in the source terms. At the same time they are able to deal accurately with regions of zero porosity, where the water cannot flow. Several numerical test cases are used in order to verify the properties of the discretization schemes proposed. Copyright © 2009 John Wiley & Sons, Ltd. [source]