A discussion of artificial compressibility
The artificial compressibility method for solving the unsteady Navier–Stokes equations is discussed. Typically, this method is combined with a dual time stepping procedure which involves an iteration in pseudo-time within each physical time step, and which guarantees a convergence towards the soluti...
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| Published in | Coastal engineering (Amsterdam) Vol. 53; no. 1; pp. 93 - 98 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
2006
Elsevier |
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| Abstract | The artificial compressibility method for solving the unsteady Navier–Stokes equations is discussed. Typically, this method is combined with a dual time stepping procedure which involves an iteration in pseudo-time within each physical time step, and which guarantees a convergence towards the solution for the incompressible flow problem. Numerous examples from the literature, however, ignore the pseudo-time iteration, in which case the choice of artificial compressibility becomes a tradeoff between accuracy and numerical efficiency. In this case it becomes important to establish thresholds for the artificial compressibility. In order to establish such thresholds, we derive linear wave solutions for progressive and standing waves under the influence of artificial compressibility. Thresholds are given in terms of the Mach number and the Courant number. |
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| AbstractList | The artificial compressibility method for solving the unsteady Navier-Stokes equations is discussed. Typically, this method is combined with a dual time stepping procedure which involves an iteration in pseudo-time within each physical time step, and which guarantees a convergence towards the solution for the incompressible flow problem. Numerous examples from the literature, however, ignore the pseudo-time iteration, in which case the choice of artificial compressibility becomes a tradeoff between accuracy and numerical efficiency. In this case it becomes important to establish thresholds for the artificial compressibility. In order to establish such thresholds, we derive linear wave solutions for progressive and standing waves under the influence of artificial compressibility. Thresholds are given in terms of the Mach number and the Courant number. |
| Author | Schäffer, H.A. Madsen, P.A. |
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| Cites_doi | 10.1017/S0022112085001264 10.1016/0045-7930(90)90027-U 10.1016/0021-9991(67)90037-X 10.1002/fld.1650190506 10.1006/jcph.1994.1034 10.1016/0378-3839(87)90032-9 10.1016/0021-9991(88)90007-1 10.1061/(ASCE)0733-950X(2004)130:2(63) 10.1175/1520-0493(1996)124<1272:AROBWI>2.0.CO;2 10.1016/0377-0265(89)90066-3 10.2514/3.60663 10.1016/S0167-8191(01)00113-2 10.1016/0307-904X(87)90182-X 10.1016/S0045-7930(01)00068-8 10.1006/jsvi.1994.1427 10.1016/S0278-4343(00)00007-8 10.1017/S0022112076002322 10.1016/S0141-1187(98)00014-5 10.2514/3.10382 10.2514/3.9119 10.1175/1520-0485(1996)026<1868:ANMOMP>2.0.CO;2 10.1175/1520-0469(1987)044<1180:NSOTOD>2.0.CO;2 |
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| Keywords | Artificial compressibility Linear wave solutions Navier–Stokes equations compressibility waves efficiency solution accuracy Navier-Stokes equations |
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| SubjectTerms | Artificial compressibility Earth sciences Earth, ocean, space Exact sciences and technology Geomorphology, landform evolution Linear wave solutions Marine and continental quaternary Navier–Stokes equations Surficial geology |
| Title | A discussion of artificial compressibility |
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