Sloshing (Liquid Surface Fluctuation)
Sloshing (Liquid Surface Fluctuation): Theoretical Foundations
Overview
Teacher! Today's topic is sloshing (liquid surface oscillation), right? What exactly is it?
Liquid surface oscillation inside LNG ship tanks. Evaluation of impact pressure.
Governing Equations
After hearing this, I finally understand why sloshing is so important!
Discretization Methods
How do you actually solve these equations on a computer?
We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix and construct the global stiffness equation.
We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. higher-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.
Matrix Solution Algorithms
What exactly are matrix solution algorithms?
Solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.
| Solver | Classification | Memory Usage | Applicable Scale |
|---|---|---|---|
| LU decomposition | Direct Method | O(n²) | Small to Medium Scale |
| Cholesky decomposition | Direct Method (Symmetric Positive Definite) | O(n²) | Small to Medium Scale |
| PCG Method | Iterative Method | O(n) | Large Scale |
| GMRES Method | Iterative Method | O(n·m) | Large Scale / Non-symmetric |
| AMG Preconditioner | Preprocessing | O(n) | Very Large Scale |
So, if you cut corners on the finite element method part, you'll pay for it later. I'll keep that in mind!
Implementation in Commercial Tools
So, what software can be used for sloshing (liquid surface oscillation)?
| Tool Name | Developer/Current | Main File Formats |
|---|---|---|
| Simcenter STAR-CCM+ | Siemens Digital Industries Software | .sim, .java, .csv |
| Ansys Fluent | Ansys Inc. | .cas, .dat, .msh, .jou |
| OpenFOAM | Open Source (OpenCFD/ESI, OpenFOAM Foundation) | Dictionary files (blockMeshDict, etc.), .foam |
| Ansys CFX | Ansys Inc. | .cfx, .def, .res, .ccl |
Vendor Lineage and Product Integration History
Do the origins of each software have dramatic stories?
Simcenter STAR-CCM+
Next is the story about Simcenter STAR. What's it about?
Developed by CD-adapco. Acquired by Siemens in 2016 and integrated into the Simcenter brand. Features polyhedral meshes.
Current Affiliation: Siemens Digital Industries Software
Ansys Fluent
Next is the story about Ansys Fluent. What's it about?
Developed by Fluent Inc. Acquired by Ansys in 2006. A general-purpose CFD solver based on unstructured grids.
Current Affiliation: Ansys Inc.
After hearing this, I finally understand why development is so important!
OpenFOAM
What exactly is OpenFOAM?
Open-source CFD originating from Imperial College London. Parallel development by OpenCFD Ltd (under ESI Group) and The OpenFOAM Foundation.
Current Affiliation: Open Source (OpenCFD/ESI, OpenFOAM Foundation)
Wow, the story about development is incredibly interesting! Tell me more.
File Formats and Interoperability
Are there any points to note when transferring data between different software?
| Format | Extension | Type | Overview |
|---|---|---|---|
| CGNS | .cgns | CFD Data | CFD General Notation System. Standard exchange format for CFD results. |
| VTK | .vtk/.vtu | Visualization | Visualization Toolkit format. Used by ParaView, etc. |
When converting models between different solvers, attention is needed regarding the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Particularly, higher-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.
I see... Formats may seem simple at first glance, but they're actually quite profound.
Practical Considerations
Are there any "field wisdom" things not found in textbooks?
Related Topics
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