Treatment of Solid-Fluid Interfaces (CHT Analysis)

Good question. In CHT (Conjugate Heat Transfer) analysis, we simultaneously solve for heat conduction in solids and convection in fluids. However, at the "interface" where these two domains meet, temperature and heat flux must be correctly transferred. This is the most critical point that determines the accuracy of CHT analysis.

For example, in gas turbine blade cooling analysis, elements of a few mm are sufficient inside the blade (solid), but elements of tens of micrometers are needed on the outside high-temperature gas (fluid) side to resolve the boundary layer. This causes the solid and fluid meshes to not match at the interface. Whether you choose a "matching mesh" or a "non-matching mesh" at this point significantly changes both the effort required and the accuracy.

There are two conditions that must be satisfied at the interface $\Gamma$. First, the Temperature Continuity Condition (Dirichlet condition):

Next, the Heat Flux Continuity Condition (Neumann condition):

Here, $k_s$, $k_f$ are the thermal conductivities of the solid and fluid respectively, and $n$ is the normal direction of the interface. Satisfying these two conditions simultaneously ensures energy conservation at the interface.

Exactly. If only temperature is matched and heat flux is not, an "artificial heat source" that generates or absorbs energy at the interface is created. In practice, this can be the cause of issues where the temperature distribution looks reasonable but the overall heat balance is off by 2-3%.

It can be summarized like this.

In practice, for analyses with complex solid shapes like automotive engine block cooling, it's standard practice to create solid and fluid meshes separately and connect them non-conformally.

That's a valid concern. That's precisely why "which interpolation method to use" is the lifeline of non-matching mesh CHT.

Let me introduce four typical methods.

1. Nearest Neighbor Interpolation
Uses the value from the closest node directly. Implementation is simple, but stair-step artifacts appear when the mesh size difference is large. Accuracy is around $O(h)$.

2. Linear Interpolation
Linearly interpolates from surrounding nodes. Accuracy improves to $O(h^2)$, but energy conservation is not strictly guaranteed.

3. RBF Interpolation (Radial Basis Function)
Constructs a smooth interpolation surface using radial basis functions. High accuracy but computational cost is $O(N^2)$, which may not scale well for large-scale models.

4. Conservative Interpolation
Also called GGI (General Grid Interface) or AMI (Arbitrary Mesh Interface). Distributes heat flux using area weighting, strictly satisfying energy conservation. This is the first choice for CHT analysis.

The concept is simple. Geometrically calculate the overlapping area $A_{ij}$ between the solid-side mesh face $A_s^i$ and the fluid-side mesh face $A_f^j$ at the interface. Then create a weight coefficient:

Use this weight to calculate the interface temperature for fluid-side cell $j$ as follows:

Since it's area-based weighting, all heat quantities are conserved without leakage. Think of it like "dividing a pizza and deciding the flavor distribution based on how many slices you received."

Right. In OpenFOAM it's AMI, in STAR-CCM+ it's In-place Interface, in Ansys Fluent it's Coupled Wall, in COMSOL it's Identity Pair. The names are different, but the underlying concept is the same: "area-based conservative mapping."

Let me list five insights accumulated in the field.

• Keep the mesh size ratio within 1:5 — If the interface element size ratio between the solid and fluid sides is too large, many fluid cells correspond to one large solid cell, degrading interpolation accuracy. Empirically, 1:5 is the borderline.
• Always include a boundary layer mesh on the fluid side — The temperature gradient near the interface is dominated by the fluid side. Along with y+ management, provide at least 10 layers of inflation.
• Simplify the interface shape as much as possible — Complex curved surfaces reduce the accuracy of overlap area calculation. Simplifications like removing fillets at the CAD stage are effective.
• Unify the normal direction of the interface — Always check that the normals on the solid and fluid sides are not opposite. Accidents where heat flux reverses due to sign errors are quite common.
• Explicitly model contact thermal resistance — Actual interfaces have grease or air gaps. Ignoring them leads to underestimation of temperature differences and mismatch with measurements.

It's true the hurdle is high, but the tutorials/heatTransfer/chtMultiRegionFoam is well-organized, so starting from there is recommended. Understanding the inter-region boundary condition definition (compressible::turbulentTemperatureCoupledBaffleMixed) is the most critical part; once you grasp that, the rest goes smoothly.

Each has its strengths and weaknesses, so choosing based on the application is best.

The common principle across all solvers is to "always verify the energy balance at the interface." In post-processing, generate a Flux Report and check that the difference between solid heat input and fluid heat received is within 0.1%.

Let me introduce three notable trends.

1. CHT Application of Overset Mesh (Chimera)
For rotating machinery where solids move, methods using overset meshes for interface handling are becoming practical. They are more robust against large displacements/deformations than traditional sliding meshes.

2. Interpolation Acceleration via Machine Learning
Research on "data-driven interpolation" that predicts interface temperature fields using neural networks is advancing. It has the potential to eliminate the need to redo GGI calculations every time the mesh changes within shape optimization loops.

3. Immersed Boundary Method (IBM)
A method that does not explicitly mesh the interface but handles it as a penalty term on a background mesh. Mesh generation is drastically reduced, but achieving high accuracy near the interface is still at the research stage, and practical deployment is yet to come.

Symptom 1: Temperature jumps discontinuously at the interface
Cause: Reversed interface normal direction, or undefined Shadow face.
Remedy: Visualize normal vectors in a mesh viewer and confirm correspondence between both sides.

Symptom 2: Overall heat balance is off by several percent or more
Cause: Use of non-conservative interpolation, or mesh size ratio exceeding 1:10.
Remedy: Switch to conservative interpolation (GGI/AMI) and adjust size ratio to within 1:5.

Symptom 3: Oscillatory temperature distribution appears near the interface
Cause: In partitioned coupling with explicit method, interface data update is one step delayed.
Remedy: Set interface relaxation factor to 0.5–0.7, or change to implicit coupling.

Symptom 4: Calculation diverges
Cause: Extreme difference in thermal conductivity between solid and fluid (e.g., copper 400 W/(m·K) vs. air 0.026 W/(m·K) is 15,000x).
Remedy: Set initial values from analytical solution and gradually increase coupling relaxation factor.

That's the correct approach. Even if the temperature contour plot looks beautiful, if the heat balance error is above 0.5%, always investigate the cause. Especially, always check the interface flux report every time. This alone can prevent 80% of troubles beforehand.