Minor flux adjustment near mixing ratio extremes for simplified yet highly accurate monotonic calculation of tracer advection

American Geophysical Union (AGU) - Tập 105 Số D7 - Trang 9335-9348 - 2000
Chris J. Walcek1
1Atmospheric Sciences Research Center, State University of New York, at Albany

Tóm tắt

A simplified but very accurate method for calculating advection of mixing ratios in a mass conservative and absolutely monotonic manner in divergent or nondivergent multidimensional flows is presented. This scheme uses a second‐order‐accurate, upstream approximation with monotone limiters and additionally adjusts fluxes at two cell edges around local extremes of a tracer distribution to significantly improve overall advection calculations. The minor flux adjustment slightly aggregates mass around local peaks in a manner which counters the inherent numerical diffusion associated with most numerical advection algorithms when advecting poorly resolved features. When advecting tracer shapes which are resolved by fewer than 10–20 grid cells, this scheme is significantly more accurate than higher‐order algorithms for a wide range of test problems. For well‐resolved tracer distributions this algorithm is very accurate and usually preserves local peak and minimum values almost perfectly. The scheme is positive‐definite, but negative values can be advected with no modifications. A generalized algorithm and FORTRAN subroutine is presented for advecting mixing ratios or other conservative quantities through variable‐spaced grids of one to three dimensions, including deformational flows. One‐ and two‐dimensional tests are presented and compared with other higher‐order algorithms. The computational requirements of this algorithm are significantly lower than those of other higher‐order and less accurate schemes.

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Tài liệu tham khảo

10.1175/1520-0493(1989)117<1006:APDASO>2.0.CO;2

10.1175/1520-0493(1989)117<2633:R>2.0.CO;2

10.1175/1520-0493(1992)120<2592:MFLITA>2.0.CO;2

10.1175/1520-0493(1993)121<2637:TMAPFF>2.0.CO;2

10.1175/1520-0493(1990)118<0586:AOTPPM>2.0.CO;2

10.1175/1520-0493(1994)122<0111:LMVOBA>2.0.CO;2

10.1016/0960-1686(91)90128-T

10.1175/1520-0493(1998)126<0232:ACMFUI>2.0.CO;2

10.1016/0021-9991(84)90143-8

10.1175/1520-0493(1997)125<1983:BSAPFF>2.0.CO;2

10.1016/1352-2310(94)00124-4

10.1175/1520-0493(1993)121<0297:TMVOBP>2.0.CO;2

10.1016/0021-9991(73)90128-9

10.1137/0724022

10.1006/jcph.1995.1125

10.1175/1520-0450(1996)035<1897:AMCPDA>2.0.CO;2

10.1175/1520-0493(1996)124<2046:MFFSLT>2.0.CO;2

10.1175/1520-0493(1994)122<1575:ACOTVL>2.0.CO;2

10.1175/1520-0493(1998)126<0812:TUOTLF>2.0.CO;2

10.1029/JD091iD06p06671

10.1175/1520-0493(1994)122<1337:CSPTDT>2.0.CO;2

10.1029/RG025i001p00071

10.1175/1520-0450(1981)020<1483:ANFDSF>2.0.CO;2

10.1175/1520-0493(1984)112<1206:ANTSWA>2.0.CO;2

10.1175/1520-0493(1983)111<0479:ASPDAS>2.0.CO;2

10.1016/0021-9991(90)90105-A

Staniforth A., 1987, Comments on “Smolarkiewicz's deformational flow”, SIAM J. Numer. Anal., 115, 894

Sweby P. K., 1984, High resolution schemes using flux limiters for hyperbolic conservation laws, Mon. Weather Rev., 21, 995

10.1175/1520-0493(1985)113<1050:ATSSFT>2.0.CO;2

10.1006/jcph.1996.0006

10.1175/1520-0493(1997)125<1990:TSPSAT>2.0.CO;2

10.1175/1520-0469(1988)045<2123:AMMFAD>2.0.CO;2

10.1175/1520-0493(1987)115<0540:TFTUAS>2.0.CO;2

10.1016/0021-9991(77)90095-X

10.1016/S1352-2310(98)00099-5

10.1175/1520-0493(1993)121<0753:NCSTUG>2.0.CO;2

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American Geophysical Union (AGU)

Tập 105 Số D7

9335-9348

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