Thermal Via
Thermal Via: Theoretical Foundations
Overview
Teacher! Today's topic is about thermal vias, right? What are they?
Thermal conduction paths in the thickness direction of a PCB. Reduction of thermal resistance via copper vias.
I understand now what my senior meant when he said, "At least do the thermal conduction path in the thickness direction properly."
Governing Equations
I understand now what my senior meant when he said, "At least describe the thermal vias properly."
Discretization Method
How do you actually solve this equation 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 a 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 by 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(nยฒ) | Small to Medium Scale |
| Cholesky decomposition | Direct Method (Symmetric Positive Definite) | O(nยฒ) | Small to Medium Scale |
| PCG Method | Iterative Method | O(n) | Large Scale |
| GMRES method | Iterative Method | O(nยทm) | 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 to handle thermal vias?
| Tool Name | Developer/Current | Main File Formats |
|---|---|---|
| Ansys Mechanical (formerly ANSYS Structural) | Ansys Inc. | .cdb, .rst, .db, .ans, .mac |
| Ansys Fluent | Ansys Inc. | .cas, .dat, .msh, .jou |
| Simcenter STAR-CCM+ | Siemens Digital Industries Software | .sim, .java, .csv |
| COMSOL Multiphysics | COMSOL AB | .mph |
Vendor Lineage and Product Integration History
Do the origins of each software have dramatic stories?
Ansys Mechanical (formerly ANSYS Structural)
Tell me about "Ansys Mechanical"!
Developed in 1970 by Swanson Analysis Systems Inc. (SASI). APDL (Ansys Parametric Design Language) based.
Current Affiliation: Ansys Inc.
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 its development is important!
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
Wow, the story of its development is super interesting! Tell me more.
File Formats and Interoperability
Are there any points to note when transferring data between different software?
| Format | Extension | Type | Overview |
|---|---|---|---|
| STEP | .stp/.step | Neutral CAD | 3D CAD data exchange format compliant with ISO 10303. Supports geometry + PMI. |
| IGES | .igs/.iges | Neutral CAD | Early CAD data exchange standard. Has issues with surface data compatibility. Transition to STEP is progressing. |
When converting models between different solvers, attention must be paid to 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 seem simple at first glance, but they're actually very deep.
Practical Considerations
Are there things like "field wisdom" that aren't in textbooks?
Verification of mesh convergence, validation of boundary condition reasonableness, and sensitivity analysis of material parameters are extremely important.
- Mesh Dependency Verification: Confirm convergence with at least 3 levels of mesh density.
- Boundary Condition Reasonableness: Setting physically meaningful constraint conditions.
- Result Verification: Theoretical solutions, experimental data
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators