An Unstructured Grid, Finite-Volume, Three-Dimensional, Primitive Equations Ocean Model: Application to Coastal Ocean and Estuaries
Citations
514 citations
Cites background from "An Unstructured Grid, Finite-Volume..."
...Werner, 1991); UnTRIM (Casulli and Walters, 2000); ELCIRC (Zhang et al., 2004); SEOM (Iskandarani et al., 2003); FVCOM (Chen et al., 2003)) and are typically based on finite differences (POM, TRIM, ROMS, NCOM), finite elements (SEOM, ADCIRC, QUODDY), or hybrid approaches involving finite volumes (UnTRIM, ELCIRC, FVCOM)....
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...Models based on the explicit mode splitting technique (POM, ROMS, FVCOM, ADCIRC, QUODDY, SEOM), in addition to having errors associated with the splitting of the internal and external modes (Shchepetkin and McWilliams, 2005), suffer from numerical stability constraints (e.g., the Courant–Friedrich–Lewy (CFL) condition) that restrict the maximum allowable time step and thus the size of the problem....
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...Werner, 1991); UnTRIM (Casulli and Walters, 2000); ELCIRC (Zhang et al., 2004); SEOM (Iskandarani et al., 2003); FVCOM (Chen et al., 2003)) and are typically based on finite differences (POM, TRIM, ROMS, NCOM), finite elements (SEOM, ADCIRC, QUODDY), or hybrid approaches involving finite volumes…...
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399 citations
Cites methods from "An Unstructured Grid, Finite-Volume..."
...The horizontal and vertical eddy viscosities are given by mH and mV, respectively, and the horizontal gradient operator is given by rH ¼ ex o ox þ ey o oy : ð5Þ Following the work of Casulli (1999), the pressure is split into its hydrostatic ph and nonhydrostatic q components with p = ph + q, where the hydrostatic pressure is defined by oph oz ¼ q0 þ qð Þg: ð6Þ Integrating this equation from z to the free surface, h, and substitution into the momentum equations (1)–(3) yields ou ot þr ðuuÞ fvþ bw ¼ 1 q0 oq ox 1 q0 ops ox g o ox ðhþ rÞ þ rH ðmHrHuÞ þ o oz mV ou oz ; ð7Þ ov ot þr ðuvÞ þ fu ¼ 1 q0 oq oy 1 q0 ops oy g o oy ðhþ rÞ þ rH ðmHrHvÞ þ o oz mV ov oz ; ð8Þ ow ot þr ðuwÞ bu ¼ 1 q0 oq oz þrH ðmHrHwÞ þ o oz mV ow oz ; ð9Þ where ps is the pressure at the free surface, and the baroclinic pressure head is given by r ¼ 1 q0 Z h z qdz: ð10Þ Integrating the continuity equation (4) from the bottom, defined by z = d(x,y), to the free-surface at z = h(x,y, t) yields the depth-averaged continuity equation oh ot þ o ox Z h d udz þ o oy Z h d vdz ¼ 0; ð11Þ where we have employed the kinematic boundary conditions at z = h and z = d, viz., oh ot þ uHjz¼h rHh ¼ wjz¼h; ð12Þ uHjz¼ d rHd ¼ wjz¼ d ; ð13Þ and the horizontal velocity vector is given by uH ¼ uex þ vey : ð14Þ Eqs....
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...However, as described by Armfield and Street (2000), because qc ¼ OðDtÞ in the pressure correction algorithm, an iteration is not required in order to attain second-order accuracy....
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...…2Dt qci;k qci;k 1 Dzi;k þ Dzi;k 1 ; ð76Þ followed by an update of the nonhydrostatic pressure field with qnþ1=2i;k ¼ q n 1=2 i;k þ qci;k: ð77Þ Following Armfield and Street (2000), the time level of the nonhydrostatic pressure field is specified at the halftime steps in order to maintain…...
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...Following the limitations derived by Fletcher (1997) when explicit central differencing is employed for advection of momentum and horizontal diffusion is treated explicitly, the time step is limited by jU jDt Dj þ jwjDt Dz 2 6 2mHDt D2j 6 1: ð83Þ Assuming a stable interpolation scheme is employed for horizontal advection of scalars, stability for the scalar advection equations is determined by Dt 6 min DjjU j ; D2j maxðcH;jHÞ !...
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...However, because the nonhydrostatic pressure is staggered in time with respect to the velocity (qn±1/2 about Un), the second-order Adams–Bashforth extrapolation scheme is used to compute the pressure at the final time step (Armfield and Street, 2000)....
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305 citations
Cites background from "An Unstructured Grid, Finite-Volume..."
...New multi-resolution approaches, both structured and unstructured, are emerging with applications focused on regional and coastal ocean modeling (Chen et al., 2003; Danilov et al., 2004; Shchepetkin and McWilliams, 2005; White et al., 2008)....
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288 citations
250 citations
Additional excerpts
...[7] Numerical models used in this study consist of seven primitive ocean governing equations (three for momentum, one for incompressible continuity, two for temperature and salinity, and one for density) [Blumberg and Mellor, 1987; Chen et al., 2003a ]....
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...FVCOM is solved numerically using an integrated form of the momentum equations with an approach of flux calculation with a second-order accurate upwind scheme for advection and the modified fourth-order Runge-Kutta time stepping for time integration [ Chen et al., 2003a ]....
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...estuarine circulation by Chen et al. (2003a) ....
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...[65] The comparison results described here are consistent with those found in the Bohai Sea by Chen et al. [2003a] , Figure 23. Comparison of FVCOM and POM surface current vectors at the end of the 10th model day from the runs shown in Figure 20. The vectors for POM were plotted at every fourth grid point....
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...D) primitive equation coastal ocean model (FVCOM) has been developed for the study of coastal ocean and estuarine circulation by Chen et al. (2003a)....
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References
6,488 citations
"An Unstructured Grid, Finite-Volume..." refers background or methods in this paper
...Here Km and Kh are parameterized using the Mellor and Yamada (1982) level-2....
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...5 turbulent closure model (Mellor and Yamada 1974, 1982), Sm and Sh are functions of the gradient Richardson number....
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3,074 citations
2,410 citations
"An Unstructured Grid, Finite-Volume..." refers background or methods in this paper
...5 turbulent closure model (Mellor and Yamada 1974, 1982), Sm and Sh are functions of the gradient Richardson number....
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...where Gh 5 (l 2 g/q 2r o )r z . In the original MY level- 2.5 turbulent closure model ( Mellor and Yamada 1974, 1982 ), S m and S h are functions of the gradient Richardson number....
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2,315 citations
2,119 citations