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Finite-Volume Groundwater Modeling With Non-Orthogonal Grids, Using A Coordinate Transformation Method

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 leads either to coarse geometric representations or to extreme large meshes. We use a coordinate transformation method (CTM) to circumvent this shortcoming. In computational fluid dynamics (CFD), this method has been successfully applied 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 have 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 hexahedral grid leads to a 19-point stencil and a corresponding banded system matrix. The implementation is straightforward and it is possible to use some existing routines without modification. The accuracy of the modified code was demonstrated on a two-dimensional analytical solution for coupled flow and heat transport.

Item Type: Article 2006 Rühaak, W. and Clauser, C. and Wolf, A. and Rath, V. Finite-Volume Groundwater Modeling With Non-Orthogonal Grids, Using A Coordinate Transformation Method English 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 leads either to coarse geometric representations or to extreme large meshes. We use a coordinate transformation method (CTM) to circumvent this shortcoming. In computational fluid dynamics (CFD), this method has been successfully applied 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 have 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 hexahedral grid leads to a 19-point stencil and a corresponding banded system matrix. The implementation is straightforward and it is possible to use some existing routines without modification. The accuracy of the modified code was demonstrated on a two-dimensional analytical solution for coupled flow and heat transport. Proceedings of the conference Modflow and More 2006: Managing Ground-Water Systems. International Ground Water Modeling Center (IGWMC), May 22-24, Colorado School of Mines, Golden Colorado. 11 Department of Materials and Earth Sciences > Earth Science > Geothermal Science and Technology11 Department of Materials and Earth Sciences > Earth Science11 Department of Materials and Earth Sciences 16 Nov 2015 08:59 Dublin CoreMultiline CSVAtomEP3 XMLJSONEndNoteReference ManagerT2T_XMLBibTeXASCII CitationSimple MetadataMODSHTML CitationRDF+XML TUfind oder in Google

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