CFD Applicability Evaluation System

• CFD Applicability Evaluation Systems are comprehensive frameworks that integrate methodologies, metrics, and software to assess simulation accuracy and experimental fidelity.
• They employ modular pipelines covering geometry, solver settings, and statistical analysis to ensure models are fit-for-purpose through reproducible criteria.
• Quantitative measures such as overlap coefficients, rank correlations, and CFD-Applicability Scores provide actionable insights for validating performance and reliability.

A Computational Fluid Dynamics (CFD) Applicability Evaluation System is a coordinated set of methodologies, metrics, and software tools for systematically quantifying the scientific validity, engineering relevance, experimental fidelity, and computational performance of CFD workflows. Its purpose is to establish whether a given CFD model or workflow is “fit for purpose” across diverse scientific, clinical, or engineering scenarios—ranging from biomedical validation, surrogate modeling, uncertainty quantification, and segmentation-to-simulation benchmarking, to large-scale code testing and hardware performance assessment. Drawing from recent literature (Kudlaty et al., 2020, Luo et al., 2023, Wilfong et al., 16 Sep 2025, Rezaeiravesh et al., 2020, Xiao et al., 1 Dec 2025, Peravali et al., 2024, Lawenda et al., 23 May 2025), such systems define rigorous pipelines and reproducible criteria for evaluating the reliability, robustness, and hardware efficiency of CFD-driven analyses.

1. Modular Pipeline Architecture

A general CFD Applicability Evaluation System follows a modular, extensible pipeline that maps domain-specific input (geometry, parameters, initial conditions) to actionable outputs (validation metrics, performance numbers, decision criteria). Canonical modules include:

• Geometry & Mesh Module: Segmentation, surface clean-up, expert review, mesh generation with strict element quality metrics, and mesh-independence checks (Kudlaty et al., 2020, Xiao et al., 1 Dec 2025).
• Physics & Solver Module: Selection of flow regime (laminar, RANS, LES), physical model fidelity, boundary/initial condition application, convergence enforcement (Luo et al., 2023).
• Experimental/Bench Module: Physical replica construction, measurement modality specification (e.g., γ-scintigraphy, PIV, MRI), compartmentalization for region-wise analysis (Kudlaty et al., 2020).
• Post-Processing & Metrics Module: Data registration/alignment, computation of overlap and rank-correlation coefficients, global and local error fields, grid-independence (Kudlaty et al., 2020, Xiao et al., 1 Dec 2025).
• Statistical & Decision Module: Statistical hypothesis testing with p-value controls, multiple comparison corrections (e.g., FDR, Bonferroni), acceptance thresholds, and iterative refinement procedures.
• Performance & Hardware Module: Automated regression/benchmark testing, grindtime/FVOPS computation, HW characteristic probing, and cross-platform normalization (Wilfong et al., 16 Sep 2025, Lawenda et al., 23 May 2025).

This modular construction allows rapid adaptation of the evaluation system to any CFD context by substituting domain-specific workflows into each module.

2. Quantitative Agreement and Applicability Metrics

Applicability is rigorously measured using a suite of scalar, vector, and distributional metrics designed for inter-model, inter-method, and cross-hardware comparison:

• Overlap Coefficient (OC):

$$\mathrm{OC} = \frac{\sum_{i=1}^n \min(M_i^{\rm CFD},\,M_i^{\rm exp})}{\sum_{i=1}^n M_i^{\rm exp}}$$

OC quantifies distributional overlap between CFD and experimental or reference results across superimposed spatial grids. OC ≥ 0.6 is recommended for complex fields, ≥ 0.8 for regular cases (Kudlaty et al., 2020).

• Rank Correlation (Kendall’s $\tau$):

$\tau = \frac{C-D}{\frac{1}{2} n(n-1)}$

Assesses monotonic agreement in compartmental rankings. $\tau \geq 0.7$ is considered strong (Kudlaty et al., 2020).

• Statistical Hypothesis Testing:

Post hoc corrections for multiple hypothesis testing (e.g., Benjamini-Hochberg) ensure metrics' significance is not inflated by multiple comparisons (Kudlaty et al., 2020).

• CFD-Applicability Score (CFD-AS):

$$AS_{\mathrm{CFD}} = \frac{\widehat{TP}}{TP + FP + FN}$$

Combines geometric availability, meshing success, and solver convergence into a binary or scalar diagnostic for segmentation-to-simulation chains (Xiao et al., 1 Dec 2025).

• Error Norms:

Relative $L_2$, $L_1$, $L_\infty$ errors and maximum pointwise deviations provide fieldwise and aggregate accuracy assessments; time-accumulation error $E_{\mathrm{acc}}(k)$ captures long-term surrogate drift (Luo et al., 2023, Peravali et al., 2024).

• Uncertainty Quantification:

Surrogate-based statistical descriptors (e.g., GPR mean/variance, Polynomial Chaos Expansion coefficients, Sobol indices) yield parametric coverage of robustness and sensitivity (Rezaeiravesh et al., 2020).

3. Validation Protocols and Experimental Integration

Applicability evaluation systems implement validation loops that require close agreement between simulation and experimental or in vitro data:

• Model-Experiment Linkage: Physical models (e.g., 3D-printed airways, vessel phantoms) are constructed for direct comparison with simulated velocity/pressure or scalar transport fields. Compartmental statistics are extracted with precisely defined registration and alignment rules (Kudlaty et al., 2020).
• Surrogate Model Validation: ML surrogates and neural operators must be benchmarked on true out-of-distribution generalization using established train/val/test splits, held-out parameters, and auto-regressive rollouts to quantify error growth (Luo et al., 2023).
• Segmentations for CFD: In biomedicine, pipeline steps from voxel mask to mesh to flow solution are flagged for topology, mesh, and solver convergence failures; statistics (such as CFD-AS) allow head-to-head ranking of segmentation algorithms for CFD-readiness (Xiao et al., 1 Dec 2025).

Stage	Metric(s)	Acceptance Threshold
Geometry/Mesh	OC	≥ 0.6 (complex), ≥ 0.8 (simple)
Compartmental/Field	τ	≥ 0.7
Surrogate/ML	$E_{L_2}$, $E_{acc}$	≤ 5% (engineering), ≤ 1% (scientific)
Biomedical CFD	CFD-AS	As high as achievable

4. Hardware, Solver, and Performance Evaluation

Modern systems integrate automated hardware benchmarking, regression testing, and code correctness checking as intrinsic aspects of CFD applicability.

• Correctness Regression: Automated suites (e.g., ≈500 tests per hardware target) verify kernel output against “golden” reference files to $\leq 10^{-12}$ tolerance, revealing compiler and hardware bugs (Wilfong et al., 16 Sep 2025).
• Performance Metrics: Figures of merit such as grindtime

$$\mathrm{grindtime} = \frac{T_{\mathrm{wall}} \times 10^9}{N_{\mathrm{pts}}\,N_{\mathrm{eq}}}$$

and FVOPS

$$\mathrm{FVOPS} = \frac{N_{\rm cells}}{t_{\rm iter}}$$

enable architecture‐agnostic comparisons and detection of device-specific efficiency regimes (Wilfong et al., 16 Sep 2025, Lawenda et al., 23 May 2025).

• Profiling and Optimization: Hardware counters (L1/L2/L3 cache hits/misses, memory stalls, CPI, IPC, Backend_Bound.MEMORY) correlate with FVOPS and guide mesh-size tuning for peak throughput. L3 cache “knee” points and memory-bandwidth effects are mapped directly onto CFD throughput (Lawenda et al., 23 May 2025).
• Strong/Weak Scaling: Systems are benchmarked from single node to leadership scale (e.g., up to 65,536 GCDs), with grindtime scalability and efficiency reported (Wilfong et al., 16 Sep 2025).

5. Applicability Classification and Decision Logic

Systems implement explicit rules for making go/no-go or method-selection decisions:

• Physical Regime Discrimination: Regime thresholds such as Knudsen number demarcate domain-of-validity for continuum CFD versus kinetic DSMC; breakdown criteria (e.g., $Kn_B>0.05$) trigger hybridization (Peravali et al., 2024).
• Metric-Guided Acceptance: Simulations are accepted if all core metrics (OC, $\tau$, CFD-AS, $L_2$ error) meet prescribed acceptance thresholds. If not, iterative refinement (e.g., mesh, boundary conditions, surrogate architecture) is mandated (Kudlaty et al., 2020, Luo et al., 2023).
• Robustness and Sensitivity: Uncertainty propagation and sensitivity analysis partition error/variance across model parameters and noise sources, informing design or refinement priorities (Rezaeiravesh et al., 2020).

6. Extensions and Best Practice Recommendations

• Parameter Space Coverage: Use of Latin Hypercube, Sobol’ sequences, or full grids enables comprehensive exploration of design and noise-variable impacts on model applicability (Rezaeiravesh et al., 2020).
• Surrogate Stabilization: Multi-fidelity approaches, physics-constrained losses, and hybridize ML with PDE correctors to limit long-horizon drift (Luo et al., 2023).
• Region-specific Metrics: Hybrid methods (e.g., CFD-DSMC) allocate regions of computational effort according to physical regime and error/cost tradeoffs, ensuring $\epsilon<5\%$ at minimized energy/time (Peravali et al., 2024).
• Benchmarking for Scheduling: FVOPS-based performance curves inform mesh partitioning and node allocation, matching computational kernels to architectural sweet spots for maximal throughput (Lawenda et al., 23 May 2025).

7. Comparative Evaluation and Benchmarking

Applicability frameworks enable systematic cross-comparison:

• Segmentation Framework Benchmarking: Case-local and global CFD-AS facilitate direct rank-ordering of segmentation networks by their ability to yield CFD-ready models, providing a scalar performance measure that is robust to failure at any pipeline stage (Xiao et al., 1 Dec 2025).
• Cross-hardware and Cross-code Comparisons: Grindtime and FVOPS standardization allow universal benchmarking across CPUs, GPUs, and APUs, detecting regressions, bugs, or breakthrough optimizations (Wilfong et al., 16 Sep 2025, Lawenda et al., 23 May 2025).
• Utility Across Application Domains: Although specific in technical workflow, the outlined systems are portable to biomedical, surrogacy, uncertainty quantification, engineering, and hardware benchmarking domains alike.

The CFD Applicability Evaluation System provides the scientific and computational foundation for establishing quantitative, reproducible, and actionable criteria for the deployment and validation of CFD in any high-stakes context where accuracy, robustness, and computational performance are non-negotiable.