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3D finite volume groundwater and heat transport modeling with non-orthogonal grids, using a coordinate transformation method

Rühaak, W. and Rath, V. and Wolf, A. and Clauser, C. (2008):
3D finite volume groundwater and heat transport modeling with non-orthogonal grids, using a coordinate transformation method.
In: Advances in Water Resources, pp. 513-524, 31, (3), [Online-Edition: http://www.sciencedirect.com/science/article/B6VCF-4R53WJ9-1...],
[Article]

Abstract

Many popular groundwater modeling codes are based on the finite differences or finite volume method for orthogonal grids. In cases of complex subsurface geometries this type of grid either leads to coarse geometric representations or to extremely fine meshes. We use a coordinate transformation method (CTM) to circumvent this shortcoming. In computational fluid dynamics (CFD), this method has been applied successfully to the general Navier-Stokes equation. The method is based on tensor analysis and performs a transformation of a curvilinear into a rectangular unit grid, on which a modified formulation of the differential equations is applied. Therefore, it is not necessary to reformulate the code in total. We applied the CTM to an existing three-dimensional code (SHEMAT), a simulator for heat conduction and advection in porous media. The finite volume discretization scheme for the non-orthogonal, structured, hexahedral grid leads to a 19-point stencil and a correspondingly banded system matrix. The implementation is straightforward and it is possible to use some existing routines without modification. The accuracy of the modified code is demonstrated for single phase flow on a two-dimensional analytical solution for flow and heat transport. Additionally, a simple case of potential flow is shown for a two-dimensional grid which is increasingly deformed. The result reveals that the corresponding error increases only slightly. Finally, a thermal free-convection benchmark is discussed. The result shows, that the solution obtained with the new code is in good agreement with the ones obtained by other codes.

Item Type: Article
Erschienen: 2008
Creators: Rühaak, W. and Rath, V. and Wolf, A. and Clauser, C.
Title: 3D finite volume groundwater and heat transport modeling with non-orthogonal grids, using a coordinate transformation method
Language: English
Abstract:

Many popular groundwater modeling codes are based on the finite differences or finite volume method for orthogonal grids. In cases of complex subsurface geometries this type of grid either leads to coarse geometric representations or to extremely fine meshes. We use a coordinate transformation method (CTM) to circumvent this shortcoming. In computational fluid dynamics (CFD), this method has been applied successfully to the general Navier-Stokes equation. The method is based on tensor analysis and performs a transformation of a curvilinear into a rectangular unit grid, on which a modified formulation of the differential equations is applied. Therefore, it is not necessary to reformulate the code in total. We applied the CTM to an existing three-dimensional code (SHEMAT), a simulator for heat conduction and advection in porous media. The finite volume discretization scheme for the non-orthogonal, structured, hexahedral grid leads to a 19-point stencil and a correspondingly banded system matrix. The implementation is straightforward and it is possible to use some existing routines without modification. The accuracy of the modified code is demonstrated for single phase flow on a two-dimensional analytical solution for flow and heat transport. Additionally, a simple case of potential flow is shown for a two-dimensional grid which is increasingly deformed. The result reveals that the corresponding error increases only slightly. Finally, a thermal free-convection benchmark is discussed. The result shows, that the solution obtained with the new code is in good agreement with the ones obtained by other codes.

Journal or Publication Title: Advances in Water Resources
Volume: 31
Number: 3
Uncontrolled Keywords: Finite volume method;Groundwater flow;Heat transport;Non-orthogonal grid;Finite difference method;Verification;Benchmark
Divisions: 11 Department of Materials and Earth Sciences
11 Department of Materials and Earth Sciences > Earth Science
11 Department of Materials and Earth Sciences > Earth Science > Geothermal Science and Technology
Date Deposited: 06 Nov 2014 13:25
Official URL: http://www.sciencedirect.com/science/article/B6VCF-4R53WJ9-1...
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