SIMUG – finite element model of sea ice dynamics on triangular grid in local Cartesian basis
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Sergey S. Petrov
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Nikolay G. Iakovlev
Abstract
The paper presents the dynamical core of the new sea ice model SIMUG (Sea Ice Model on Unstructured Grid) on the A- and CD-types of unstructured triangular grids in the local-element basis on sphere. Three standardized box tests to reproduce the Linear Kinematic Features (LKFs), and the short-term forecast in the real Arctic Ocean geometry with the realistic atmosphere and ocean forcing demonstrate the model quality compared to other sea ice models like CICE, FESOM, MITgcm, and ICON-O. The distinctive features of the model presented are a wide choice of transport schemes, and the new numerical implementation with the serial and parallel C++ coding and INMOST, Ani2D, and Ani3D packages to deal with unstructured grids. Code profiling and scalability assessment are carried out. In general, the A-version of the ice drift model works faster, but has fewer degrees of freedom on the same grid. Due to the increase in the degrees of freedom, the model on the CD grid gives ultra-resolution of LKFs, but requires more strict conditions for stability.
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Funding: The study was carried out at the Marchuk Institute of Numerical Mathematics (INM RAS), Moscow, Russia. The work of Sergey S. Petrov (investigation of numerical methods on CD-grid, writing, coding, interpretation of results) was supported by the Moscow Center of Fundamental and Applied Mathematics at INM RAS (Agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2022-286). The work of Nikolay G. Iakovlev (investigation of numerical methods on A-grid, writing, reviewing, editing) was supported by the Russian Science Foundation (project 21-71-30023).
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A Appendix. Preudocode for main procedures
Algorithm 1
Pseudocode of mEVP method for A-grid
| for i = 0, Nits do | ▹ subiterations |
| ComputeStrainRateTensor() | |
| UpdateStressTensorMevp() | ▹ Update sigma (22) |
| AssembleForceVector() | ▹ calculate (σ, ∇ φ) |
| UpdateVelocityMevp() | ▹ Update velocity (23) |
| end for |
Algorithm 2
Pseudocode of nodal force assembling for A-grid. Part 1
| Force[NumberOfNotBndNodes][2] = 0 | ▹ prepare force array |
| procedure AssembleForceVector() | |
| for triangle Ti in Triangles do | ▹ iterate over triangles |
| AdjNodes = Ti → GetNodes() | ▹ get the adjacent nodes for triangle |
| TrianGradientInNodeBasis[3][2] | ▹ prepare the 2D array for basis function gradients |
| TrianSigmaInNodeBasis[3][2][2] | ▹ prepare the 2D array for stress tensor components |
| for node Nj in AdjNodes do | ▹ iterate over trian nodes |
| TrianGradientInNodeBasis[j] = | ▹ move gradient of basis function to node basis |
| TransferVectorToTriangleBasis(Ti → GetTrianGradientInTrianBasis()[j]) | |
| TrianSigmaInNodeBasis[j] = | ▹ move stress tensor to node basis |
| TransferTensorToTriangleBasis(Ti → GetTrianSigmaInTrianBasis()) | |
| if (Nj is not BndNode) then | |
| Force[GlobalIndexOfLocalNode(Nj)] += | ▹ Here * stands for scalar product |
| TrianSigmaInNodeBasis[j]*TrianGradientInNodeBasis[j] | |
| end if | |
| end for | |
| end for | |
| end procedure | |
Algorithm 3
Pseudocode for assembling the stabilization term on CD-grid
| Stabilization[NumberOfEdges][2] = 0 | ▹ prepare stabilization array |
| StabilizationSum[NumberOfEdges][2] = 0 | ▹ prepare stabilization sum array |
| procedure AssembleStabilization() | |
| for triangle Ti in Triangles do | ▹ iterate over triangles |
| AdjEdges = Ti → GetEdges() | ▹ get the adjacent edges for triangle |
| EdgeVelocities[3][2] | ▹ prepare the 2D array for edge velocities in trian basis |
| for edge Ej in AdjEdges do | ▹ iterate over trian edges |
| EdgeVelocities[j] = | ▹ move velocity to trian basis |
| TransferVectorToTriangleBasis(Ej → GetVelocity()) | |
| end for | |
| for edge Ej in AdjEdges do | ▹ iterate over trian edges |
| StabilizationSum[GlobalIndexOfLocalEdge(Ej)] += | ▹ compute stab sum |
| #x2003; TransferVectorToEdgeBasis(EdgeVelocities[(j + 1) mod 3]), (j + 1) mod 3) - | |
| TransferVectorToEdgeBasis(EdgeVelocities[(j + 2) mod 3]), (j + 2) mod 3) | |
| end for | |
| SatbSumTrian[3][2] | ▹ prepare the 2D array for stab sum in trian basis |
| for edge Ej in AdjEdges do | ▹ iterate over trian edges |
| SatbSumTrian[j] = | ▹ move stabilization sum to trian basis |
| TransferVectorToTrianBasis(StabilizationSum[j]) | |
| end for | |
| for edge Ej in AdjEdges do | ▹ iterate over trian edges |
| Stabilization[GlobalIndexOfLocalEdge(Ej)] += | ▹ compute stabilization in edge basis |
| -TransferVectorToEdgeBasis(StabSumTrian[(j+1) mod 3], (j + 1) mod 3))* | |
| EtaEdge[(j+1) mod 3] | |
| +TransferVectorToEdgeBasis(StabSumTrian[(j+2) mod 3], (j + 2) mod 3))* | |
| EtaEdge[(j+2) mod 3] | |
| end for | |
| end for | |
| end procedure | |
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Particle tracking for face-based flux data on general polyhedral grids with applications to groundwater flow modelling
- CarNum: parallel numerical framework for computational cardiac electromechanics
- SIMUG – finite element model of sea ice dynamics on triangular grid in local Cartesian basis
- Validation of boundary conditions for coronary circulation model based on a lumped parameter approach
- Ensemble-based statistical verification of INM RAS Earth system model
- Neural networks singular evolutive interpolated Kalman filter and its application to data assimilation for 2D water pollution model
Artikel in diesem Heft
- Frontmatter
- Particle tracking for face-based flux data on general polyhedral grids with applications to groundwater flow modelling
- CarNum: parallel numerical framework for computational cardiac electromechanics
- SIMUG – finite element model of sea ice dynamics on triangular grid in local Cartesian basis
- Validation of boundary conditions for coronary circulation model based on a lumped parameter approach
- Ensemble-based statistical verification of INM RAS Earth system model
- Neural networks singular evolutive interpolated Kalman filter and its application to data assimilation for 2D water pollution model
