What is data transfer between non-matching meshes?

When coupling separate solvers, such as fluid and structural, the nodes and elements of each mesh usually don't line up at the interface. Moving one side's results (temperature, heat flux, pressure, displacement) onto the other mesh by interpolation or averaging is called mapping, and its error affects the accuracy of the whole coupled analysis.

How do conservative and consistent mapping differ?

Consistent mapping interpolates values at the receiving points, suiting field values like temperature and displacement. Conservative mapping averages weighted by overlapping area so totals such as heat or force are unchanged by the transfer, suiting fluxes and forces. Transferring heat flux consistently can create or destroy energy.

Does conservative mapping solve everything?

It preserves totals, but fine detail can only be represented down to the receiving mesh's resolution. Conservatively mapping flux with a sharp peak (max 4,571 W/m²) onto 10 elements gave zero total error but flattened the peak to 2,317 W/m². If local temperatures matter, the receiving mesh must also be fine enough.

Data Transfer Between Non-Matching Meshes

Category: Coupled Analysis – Multiphysics | Revised 2026-10-01

CAE visualization for mapping dissimilar meshes theory - technical simulation diagram

Data Transfer Between Non-Conformal Meshes

Theory: transferring values or quantities

Overview

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After passing CFD heat flux to the structural model, temperatures no longer match. Is the mesh mismatch to blame?

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Quite possibly. The fluid side is usually fine near walls to resolve boundary layers while the structure is coarse, so the meshes don't match at the interface, and how flux is transferred changes the result. Reading values at the receiving points (consistent) is simple, but with sharp peaks in the flux distribution it misses them and changes the total heat transferred. Heat must be conserved, so a changed total shifts structural temperatures overall. Averaging by overlapping area (conservative) preserves the total, though a coarse mesh flattens peaks. Choose according to the nature of the quantity transferred.

Consistent and conservative mapping

$$ \text{consistent: } q_j^{T} = \sum_i N_i(x_j)\,q_i^{S},\qquad \text{conservative: } q_j^{T} = \frac{1}{|\Gamma_j|}\sum_i |\Gamma_j \cap \Gamma_i|\,q_i^{S} $$

S is the source (fluid) and T the target (structure); N are source shape functions (interpolation); |Γⱼ ∩ Γᵢ| is the overlap area (length in 1D) between elements.

Conservation of totals

$$ P = \int_\Gamma q\,d\Gamma,\qquad \sum_j q_j^T |\Gamma_j| = \sum_i q_i^S |\Gamma_i|\ \ (\text{conservative}) $$

Example: a 1 m interface. The source has 97 elements with heat flux q(x) = 1000·(1 + 0.8 sin 2πx + 3 exp(−((x − 0.3)/0.02)²)) W/m² (a sharp peak at x = 0.3). Targets have 10 and 40 elements.

Coffee Break Trivia

Joining meshes that don't match

As coupled analysis spread in the 1990s, making interface meshes match was laborious and often impossible, so mapping methods between non-matching meshes were researched. In aeroelasticity the idea emerged of pairing force and displacement mappings so that virtual work is preserved. Today's coupling libraries such as preCICE let users choose consistent or conservative mapping per quantity.

Worked examples

Example 1: coarse target (10 elements)

Method	Total heat	Total error	Peak flux
Nearest value	1,003.5 W/m	−9.30%	1,813 W/m²
Linear interpolation (consistent)	1,002.3 W/m	−9.41%	1,810 W/m²
Overlap average (conservative)	1,106.4 W/m	0.00%	2,317 W/m²

Example 2: finer target (40 elements)

Method	Total error	Peak flux
Nearest value	−1.52%	3,518 W/m²
Linear interpolation (consistent)	−0.16%	3,753 W/m²
Overlap average (conservative)	0.00%	3,699 W/m²

The source total is 1,106.35 W/m and its maximum element value 4,571 W/m².

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With 10 elements, consistent mapping loses nearly 10% of the heat.

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If no target element centre falls on the peak, point-sampling misses it. The peak width (about 0.04 m) is narrower than the target element length (0.1 m), so almost none of its heat transfers. Quantities whose totals matter, like heat flux and force, should be mapped conservatively; field values like temperature and displacement consistently. In fluid–structure coupling, mapping displacement consistently from structure to fluid and force conservatively from fluid to structure also keeps energy exchange at the interface correct. Even conservative mapping flattens the peak on the receiving mesh, so to get local peak temperatures right, the receiving mesh must resolve the peak width. With 40 elements, every method recovered much of the peak height.

Choosing and checking mappings

Classify quantities as field values (temperature, displacement) or totals-matter quantities (flux, force).
Map field values consistently and fluxes/forces conservatively.
Compare total heat, net force and moment before and after transfer.
Check interface geometry matches on both sides (no gaps or overlaps).
Where local values matter, refine the receiving mesh to the distribution's detail.

Coffee Break Trivia

“An over-cooled component”

In one component's thermal analysis, mapping CFD heat-transfer results onto a coarse structural mesh gave temperatures over 10 °C below measurement. The total transferred flux was about 8% below the fluid side, missing heat from a narrow zone struck by hot gas. Switching to conservative mapping and refining the structural mesh there removed the heat discrepancy and brought temperatures within a few degrees of measurement. Comparing total heat before and after mapping then became a standard check.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Mapping heat flux consistently	Heat created or lost	Use conservative
Not checking totals	Errors unnoticed	Compare totals
Target too coarse	Peaks flattened	Refine locally
Geometry mismatch	Values extrapolated	Match geometry
Choosing force/displacement maps independently	Energy not conserved	Pair to preserve virtual work

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