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High-order multirate explicit time-stepping schemes for the baroclinic-barotropic split dynamics in primitive equations

Journal Article · · Journal of Computational Physics
 [1];  [2];  [2];  [3];  [4]
  1. Univ. of South Carolina, Columbia, SC (United States); University of South Carolina
  2. Univ. of South Carolina, Columbia, SC (United States)
  3. Florida State Univ., Tallahassee, FL (United States)
  4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations

In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong stability-preserving Runge-Kutta approach, we propose two high-order multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in this paper. The proposed schemes allow for a large time step to be used for the three-dimensional baroclinic (slow) mode and a small time step for the two-dimensional barotropic (fast) mode, in which each of the two mode solves just need to satisfy their respective CFL conditions for numerical stability. Specifically, at each time step, the baroclinic velocity is first computed by advancing the baroclinic mode and fluid thickness of the system with the large time-step and the assistance of some intermediate approximations of the barotropicmode obtained by substepping with the small time step; then the barotropic velocity is corrected by using the small time step to re-advance the barotropic mode un-der an improved barotropic forcing produced by interpolation of the forcing terms from the preceding baroclinic mode solves; lastly, the fluid thickness is updated by coupling the baroclinic and barotropic velocities. Additionally, numerical inconsistencies on the discretized sea surface height caused by the mode splitting are relieved via a reconciliation process with carefully calculated flux deficits. Here, two benchmark tests from the “MPAS-Ocean” platform are carried out to numerically demonstrate the performance and parallel scalability of the proposed SSPRK-SE schemes.

Research Organization:
Univ. of South Carolina, Columbia, SC (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced ScientificComputing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Biological and Environmental Research (BER). Earth and Environmental Systems Science Division
Grant/Contract Number:
SC0020270
OSTI ID:
1865068
Alternate ID(s):
OSTI ID: 1845906
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 457; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (18)

Table 1(p. 5)table Table 1
Algorithm 1(p. 8)figure Algorithm 1
Algorithm 2(p. 8)figure Algorithm 2
Algorithm 3(p. 9)figure Algorithm 3
Algorithm 4(p. 11)figure Algorithm 4
Table 2(p. 18)table Table 2
Table 3(p. 20)table Table 3
Table 4(p. 21)table Table 4
Figure 1(p. 22)figure Figure 1
Figure 2(p. 22)figure Figure 2
Figure 3(p. 23)figure Figure 3
Table 5(p. 23)table Table 5
Table 6(p. 24)table Table 6
Figure 4(p. 25)figure Figure 4
Figure 5(p. 26)figure Figure 5
Figure 6(p. 27)figure Figure 6
Figure 7(p. 28)figure Figure 7
Figure 8(p. 28)figure Figure 8

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Related Subjects

54 ENVIRONMENTAL SCIENCES
58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
Baroclinic-barotropic splitting
Explicit time-stepping
Multirate
Primitive equations
SSH reconciliation
Strong stability preserving Runge-Kutta