A Cartesian Grid Finite-Volume Method for the Advection-Diffusion Equation in Irregular Geometries
We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a “capacity function” to model the fact that so...
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| Vydáno v: | Journal of computational physics Ročník 157; číslo 1; s. 143 - 180 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
01.01.2000
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| ISSN: | 0021-9991, 1090-2716 |
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| Abstract | We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a “capacity function” to model the fact that some cells are only partially available to the fluid. The advection portion then uses the explicit wave-propagation methods implemented in CLAWPACK, and is stable for Courant numbers up to 1. Diffusion is modelled with an implicit finite-volume algorithm. Results are shown for several geometries. Convergence is verified and the 1-norm order of accuracy is found to between 1.2 and 2 depending on the geometry and Peclet number. Software is available on the web. |
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| AbstractList | We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a “capacity function” to model the fact that some cells are only partially available to the fluid. The advection portion then uses the explicit wave-propagation methods implemented in CLAWPACK, and is stable for Courant numbers up to 1. Diffusion is modelled with an implicit finite-volume algorithm. Results are shown for several geometries. Convergence is verified and the 1-norm order of accuracy is found to between 1.2 and 2 depending on the geometry and Peclet number. Software is available on the web. A finite volume method is developed which is essentially second class accurate for smooth q (density or concentration) in very general geometries and which can also handle steep gradients (and, in certain cases, discontinuities) in q. This is accomplished by the high resolution shock capturing methods of CLAWPACK for the advection portion of the method, coupled with an implicit finite volume discretization of the diffusion equation. (AIAA) The authors present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a capacity function to model the fact that some cells are only partially available to the fluid. The advection portion then uses the explicit wave-propagation methods implemented in CLAWPACK, and is stable for Courant numbers up to 1. Diffusion is modeled with an implicit finite-volume algorithm. Results are shown for several geometries. Convergence is verified and the 1-norm order of accuracy is found to between 1.2 and 2 depending on the geometry and Peclet number. Software is available on the web. |
| Author | LeVeque, Randall J. Calhoun, Donna |
| Author_xml | – sequence: 1 givenname: Donna surname: Calhoun fullname: Calhoun, Donna organization: Department of Applied Mathematics, f1calhoun@amath.washington.eduf1 – sequence: 2 givenname: Randall J. surname: LeVeque fullname: LeVeque, Randall J. organization: Department of Applied Mathematics, f1calhoun@amath.washington.eduf1 |
| BackLink | https://www.osti.gov/biblio/20014347$$D View this record in Osti.gov |
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| Cites_doi | 10.1016/0045-7825(94)90135-X 10.1016/0045-7825(94)90022-1 10.1137/S0036142997315974 10.1137/0913006 10.1006/jcph.1993.1007 10.1006/jcph.1998.5965 10.1016/0021-9991(84)90086-X 10.2172/771633 10.1016/0021-9991(88)90036-8 10.1016/0045-7930(94)90031-0 10.1016/0956-0521(90)90016-E 10.1006/jcph.1996.5603 10.1137/0733033 10.1137/S1064827594273730 10.1137/S1064827595282532 10.1016/0021-9991(77)90100-0 10.1137/0731054 10.1090/psapm/048/1314863 10.1137/0721021 10.2514/6.1989-1930 10.1137/0913035 10.1006/jcph.1998.5891 |
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| Keywords | Finite-volume advection-diffusion Cartesian grid software embedded boundary high-resolution |
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| Snippet | We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a... A finite volume method is developed which is essentially second class accurate for smooth q (density or concentration) in very general geometries and which can... The authors present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm... |
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| SubjectTerms | ADVECTION ALGORITHMS CARTESIAN COORDINATES CONVERGENCE DIFFUSION ENGINEERING FINITE ELEMENT METHOD GEOMETRY MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE MESH GENERATION |
| Title | A Cartesian Grid Finite-Volume Method for the Advection-Diffusion Equation in Irregular Geometries |
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