Velocity field calculation for nonorthogonal numerical grids
Abstract
Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porousmedium numerical simulations. Such grids are referred to in this study as nonorthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Nonorthogonal grids are routinely encountered at the Savannah River Site in porousmedium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation, and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porousmedium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces.more »
 Authors:
 Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
 Publication Date:
 Research Org.:
 Savannah River Site (SRS), Aiken, SC (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1172684
 Report Number(s):
 SRNLSTI201500115
 DOE Contract Number:
 AC0908SR22470
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
Citation Formats
Flach, G. P.. Velocity field calculation for nonorthogonal numerical grids. United States: N. p., 2015.
Web. doi:10.2172/1172684.
Flach, G. P.. Velocity field calculation for nonorthogonal numerical grids. United States. doi:10.2172/1172684.
Flach, G. P.. 2015.
"Velocity field calculation for nonorthogonal numerical grids". United States.
doi:10.2172/1172684. https://www.osti.gov/servlets/purl/1172684.
@article{osti_1172684,
title = {Velocity field calculation for nonorthogonal numerical grids},
author = {Flach, G. P.},
abstractNote = {Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porousmedium numerical simulations. Such grids are referred to in this study as nonorthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Nonorthogonal grids are routinely encountered at the Savannah River Site in porousmedium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation, and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porousmedium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a nonorthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a nonorthogonal grid, Darcy velocity components are rigorously derived in this study from normal fluxes to cell faces, which are assumed to be provided by or readily computed from porousmedium simulation code output. The normal fluxes are presumed to satisfy mass balances for every computational cell, and if so, the derived velocity fields are consistent with these mass balances. Derivations are provided for general twodimensional quadrilateral and threedimensional hexagonal systems, and for the commonly encountered special cases of perfectly vertical side faces in 2D and 3D and a rectangular footprint in 3D.},
doi = {10.2172/1172684},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2015,
month = 3
}

Numerical calculation of flashing from long pipes using a twofield model
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Numerical calculation of flashing from long pipes using a twofield model
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