ALL-FEM: Agentic Large Language models Fine-tuned for Finite Element Methods

Motivation

• Finite-element analysis underpins engineering simulation, but implementing, testing, and validating FEniCS or Firedrake codes remains time-consuming and requires specialized numerical expertise.This expertise includes variational formulations, time integration, and linear algebra.Source: §1 · p. 1
• Duplicated code development burdens research, while commercial software offers reliability at high licensing and operational cost and limits non-standard problem solving.Researchers repeatedly modify similar codes, whereas black-box commercial tools reduce user-induced errors but constrain flexibility.Source: §1 · p. 2
• Off-the-shelf LLMs can hallucinate syntactic or semantic errors, motivating domain-specific fine-tuning and agentic workflows that verify intermediate steps and interact with tools.Fine-tuning constrains outputs toward valid FEM syntax and formulations, while agents replace single zero-shot generation with sequential reasoning and verification.Source: §1 · p. 2

Contributions

• ALL-FEM fine-tunes open-weight 3B–120B LLMs on over 1000 FEniCS codes expanded from expert-curated seeds through sequential multi-LLM data augmentation.The verified synthetic dataset targets mapping PDE boundary-value problems to reliable FEniCS implementations in a data-scarce domain.Source: §1 · p. 2

Framework

• Its LLM-orchestrated multi-agent workflow formulates weak problems and boundary conditions, generates and debugs FEniCS code, checks formulation consistency, and plots results.The pipeline links data generation, model specialization, and simulation automation while adapting agent selection across computational mechanics challenges.Source: §1 · p. 3

Evaluation

• 71.79% of 39 benchmark problems produced correct code with the best fine-tuned LLM in a multi-agent framework, outperforming non-agentic GPT-5 Thinking.The benchmarks span elasticity, plasticity, Newtonian and non-Newtonian flow, thermofluids, fluid-structure interaction, multiphase models, and moving-domain diffusion-reaction systems.Source: §1 · p. 3

2.1 LLM Selection

• The study fine-tunes Llama 3.2 3B, Qwen3 32B, Llama 3.3 70B, and GPT-OSS 120B, while using proprietary GPT-5 Thinking as a non-fine-tuned reference baseline.The selected open-source models span different scales and architectures; GPT-5 Thinking cannot be fine-tuned but provides a state-of-the-art comparison reference.Source: §2.1 · pp. 3–4

2.2.1 Dataset Creation · Seed Data Collection

• The fine-tuning corpus contains 1004 executable FEniCS codes, created from a 503-entry curated seed dataset and 501 synthetically generated additions.Seed sources include tutorials, lecture notes, official DOLFIN demos, expert materials, public archives, and approximately 40 in-house scripts, covering solid, fluid, multiphysics, heat-transfer, diffusion, and foundational PDE tasks.Source: §2.2.1 · p. 4, Seed Data Collection · pp. 4–5

Synthetic Data Generation Pipeline

• The augmentation pipeline uses RAG and multiple models to vary seven PDE problems across ten geometric or topological domains and ten boundary-condition sets, generating 700 codes that are executed, corrected once, discarded if still erroneous, and expert-verified.OpenAI o3 handles problem design and code generation, o4-mini produces systematic variants, Gemini 2.5 Pro performs one-shot debugging, and reviewers check prompt-to-code compatibility and ParaView outputs.Source: Synthetic Data Generation Pipeline · p. 5, Figure 1 · p. 5

2.2.2 Low-Rank Adaptation (LoRA) and Quantized LoRA (QLoRA)

• LoRA freezes pretrained weights and learns low-rank updates, reducing trainable parameters and adaptation costs without adding inference latency; QLoRA additionally stores base weights at 4-bit precision.Llama 3.2 3B and Qwen 3 32B use LoRA, whereas Llama 3.3 70B and GPT-OSS 120B use QLoRA because of hardware memory constraints.Source: §2.2.2 · p. 6

LoRA Settings

• Each LoRA adapter uses rank r = 8, scaling factor α = 2r, dropout 0.15, and adapters on all attention and feed-forward projection layers.The scaling factor controls update strength, rank controls adaptation capacity, and larger rank increases memory and computational overhead.Source: LoRA Settings · pp. 6–7, §2.2.2 · p. 6

Learning Optimizer Settings · Hardware

• Supervised fine-tuning uses HuggingFace SFTTrainer with AdamW, a learning-rate warm-up to 3 × 10^-5 followed by linear decay, 16-sample effective batches, and 210 update steps averaging 3.3 epochs.Models run on NVIDIA H100 GPUs through Purdue’s Anvil/Gautschi infrastructure; merged adapters are converted to GGUF for Ollama deployment, with larger models quantized for single-H100 inference.Source: Learning Optimizer Settings · p. 7, Hardware · p. 7

2.2.4 Validation

• Training loss decreased by approximately 1.7× to 2.4×, while final mean token-level evaluation accuracy increased with model parameter count across the validated models.Figure 2 reports five-fold cross-validation for Llama 3.2 3B, Qwen 3 32B, and Llama 3.3 70B; GPT-OSS 120B was not cross-validated because of computational constraints.Source: §2.2.4 · p. 7, Figure 2 · p. 8
• Five-fold cross-validation trains on four dataset folds and validates on the fifth, with training loss dropping fastest during the first approximately 50 steps and flattening after approximately 150 steps.The small differences across folds indicate a homogeneous, consistent dataset without a disproportionately influential fold.Source: §2.2.4 · p. 8

2.3 Agentic AI

• AutoGen agents automate knowledge retrieval, PDE formulation, FEniCS code generation and execution, result analysis, and iterative refinement using runtime feedback.The framework uses Assistant Agents for language-model responses, User Proxy Agents for execution and feedback, and a Group Chat Manager for coordination.Source: §2.3 · p. 8

2.3.1 Two-agent Framework

• The two-agent framework uses a FEniCS Coder and Executor in a fixed, autonomous loop that revises code from runtime errors until execution succeeds or the token limit is reached.Fine-tuned and non-fine-tuned LLMs serve as the Assistant Agent, enabling assessment of model scale and fine-tuning effects.Source: §2.3.1 · p. 9, Figure 3 · p. 9

2.3.2 Multi-Agent Framework

• The multi-agent framework addresses context overload, hallucination, and executable-but-incorrect code by assigning planning, formulation, coding, execution, correction, evaluation, and coordination to specialized agents.A flexible Coordinator can revisit earlier outputs, while an Admin provides manual termination because the Coordinator otherwise may continue indefinitely; separate LLMs and prompts reinforce agent roles.Source: §2.3.2 · pp. 9–10

3.1 Evaluation Methodology

• Frameworks are compared with GPT-5 Thinking in a non-agentic two-attempt setup that retains only the second fresh-session result when the first code is non-executable.This baseline emulates computational mechanicians without agentic-AI training.Source: §3.1 · p. 11

Test set

• The benchmark contains 39 expert-designed problems spanning solid, fluid, and multiphysics mechanics, divided evenly into easy, medium, and hard subsets.Problems specify geometry, mathematical model, boundary conditions, and expected outputs, and are separate from the 1005-problem training dataset.Source: Test set · p. 11
• The test distribution targets generalization through coupled and higher-complexity systems, including five problems involving PDE families or couplings absent from training.Examples include Allen-Cahn, Boussinesq Navier-Stokes–temperature, Brinkman/free-flow, and Stokes/Darcy couplings, plus novel combinations of familiar PDEs.Source: Test set · p. 11
• Representative test cases cover easy linear elasticity, medium Boussinesq-coupled flow and temperature, and hard fluid-structure interaction with moving-domain Navier-Stokes.The fluid-structure case uses an Arbitrary Lagrangian Eulerian fluid model, a St. Venant-Kirchhoff solid, interface no-slip, and traction balance.Source: Test set · pp. 12–13

Code correctness evaluation

• Correctness requires executable code whose solution matches a reference through visual comparison, characteristic-line checks, LLM-judge code analysis, and manual verification.The procedure rejects physically incorrect formulations even when their plotted outputs appear indistinguishable, as illustrated by a plane-strain versus plane-stress error.Source: Code correctness evaluation · p. 14
• Relative L2 error is not the primary metric because frameworks may use different meshes, although its agreement with the adopted criterion was tested on five representative problems.A common finite-element space would require difficult mesh transfer and could introduce projection errors; threshold sensitivity is reported in Appendix A.Source: Code correctness evaluation · p. 14

Performance metric

• Accuracy is defined as correctly solved questions divided by total questions, with results reported across difficulty levels and grouped by physics category.Figures distinguish two-agent frameworks, the multi-agent framework, and GPT-5 Thinking, while identifying agentic systems by their code-generating LLM.Source: Figure 5 · p. 13, Performance metric · p. 14

Model Size Improves Performance in a Two-agent Framework

• 71.79% overall accuracy makes GPT-OSS 120B FT the strongest reported two-agent model, outperforming Llama 3.3 70B FT at 20.51% and Qwen 3 32B FT at 12.82%.Non-fine-tuned GPT-OSS 120B reaches 58.97% across all 39 problems.Source: Model Size Improves Performance in a… · p. 14
• Increasing model size improves performance as difficulty and physics breadth increase: GPT-OSS 120B FT solves 15 solid, 11 fluid, and 2 multiphysics questions, versus Llama 3.3 70B’s 6, 2, and 0.Llama 3.3 70B FT and Qwen 3 32B FT solve no medium or hard problems, while GPT-OSS models perform substantially better.Source: Model Size Improves Performance in a… · pp. 14–15, Figure 6 · p. 15

Fine-tuning Improves Performance in a Two-agent Framework

• Fine-tuning consistently improves two-agent results, raising Llama 3.3 70B from zero solved problems to 8 and enabling Qwen 3 32B FT to surpass larger non-fine-tuned Llama 3.3 70B.Fine-tuning also improves GPT-OSS across easy, medium, and hard sets and helps it solve more solid and fluid problems.Source: Fine-tuning Improves Performance in a… · p. 15

GPT-OSS FT in a Two-agent Framework Outperforms a non-agentic GPT-5 Thinking Deployment

• GPT-OSS FT outperforms GPT-5 Thinking across all difficulty levels despite fewer parameters and lower inference cost, combining domain-specific fine-tuning with an execution-feedback loop.The comparison positions GPT-OSS FT as a lower-cost open-source alternative for FEniCS computational mechanics problems.Source: GPT-OSS FT in a Two-agent Framework… · p. 16

Multi-agent Framework Performs Better than Two-agent Framework

• The multi-agent framework solves two more medium-difficulty questions than two-agent GPT-OSS FT, matches it on easy and hard sets, and produces a more accurate ALE formulation despite both failing the sample problem.Its implementation captures the moving-domain transport formulation more accurately but still imposes boundary conditions incorrectly.Source: Multi-agent Framework Performs Better… · p. 16

Limitations of the framework

• The evaluation lacks uniform error metrics because prompts omit mesh specifications, relies on domain-expert comparison, and retains a human termination step after evaluator acceptance.The benchmark’s simple 2D geometries and solver-focused fine-tuning underrepresent 3D meshing, tagging, and real-world CAD-to-mesh complexity.Source: Limitations of the framework · pp. 17–18

System

• ALL-FEM was built from over 500 expert-generated FEniCS codes expanded into over 1000 entries, then used to fine-tune 3B–120B models with LoRA/QLoRA.The models were embedded in both a minimal two-agent Coder-Executor loop and a richer multi-agent system.Source: §4 · p. 18

Results

• Across 39 problems spanning solid mechanics, fluids, thermofluids, multiphysics, phase separation, and moving-domain transport, runtime feedback improved performance and fine-tuning improved code correctness.The study reports substantial gains despite relatively small training data, suggesting that scaling the dataset could further improve robustness and accuracy.Source: §4 · p. 18
• Fine-tuned GPT-OSS 120B in a multi-agent framework achieved the highest performance and surpassed non-agentic GPT-5 Thinking within the study’s setup.The result indicates that fine-tuned smaller models can rival or outperform larger proprietary systems when agentically orchestrated.Source: §4 · p. 18

Limitations and future work

• Reliable fully automatic simulation remains unresolved, requiring larger community-built code databases and additional agents, including visual result analyzers for error correction.The authors identify these directions as necessary for more robust engineering-workflow automation.Source: §4 · p. 18

Broader implications

• The combination of curated domain data, parameter-efficient fine-tuning, and agentic orchestration may extend to other scientific and engineering workflows that are intricate and software-dependent.The conclusion presents this combination as a feasible approach for autonomous simulation systems in computational mechanics.Source: §4 · p. 18

Validation design

• Across five representative problems, L2-based validation tests compare pass/fail outcomes with the multi-step solution comparison process.The tests assess robustness and accuracy using quantitative relative L2 errors.Source: Appendix A · p. 18

Test 1: Interpolated reference

• With finer-mesh reference solutions interpolated onto generated meshes, a 4% relative L2-error threshold produces almost consistent pass/fail decisions with multi-step evaluation.Test 1 sweeps thresholds from 1% to 4% and reports pass counts and average errors in Table A1.Source: Appendix A · p. 19, Table A1 · p. 19

Test 2: Same-mesh reference

• Using matched generated meshes and finite-element spaces, a 0.001% relative L2-error threshold yields identical labels to multi-step evaluation across all cases.Although Test 2 is the cleanest quantitative assessment, it requires extensive manual intervention; therefore, the scalable multi-step process remains the evaluation criterion.Source: Appendix A · p. 19, Table A2 · p. 20

• Mesh statistics report elements, hmax, hmin, and degrees of freedom for every benchmark, contextualizing performance variations and discretization scale.These data complement Sec. 3.2 and clarify the discretizations under which the agentic workflow produced solutions.Source: Appendix B · p. 20

Solid mechanics

• Table B1 covers mesh statistics for the solid mechanics benchmark set comprising Problems 1–16.Source: Table B1 · p. 20

Fluid and multiphysics

• Tables B2 and B3 cover mesh statistics for the fluid mechanics Problems 1–15 and multiphysics Problems 1–8 benchmark sets.Source: Table B2 · p. 21, Table B3 · p. 21

Cost metrics and scope

• Computational cost is measured by API calls, prompt/completion/total token usage, and wall-clock time across representative fine-tuned GPT-OSS runs.Table C1 compares these costs for two-agent and multi-agent workflows on three example problems rather than the full benchmark set.Source: Appendix C · p. 21, Table C1 · p. 21

Measurement caveats

• Wall-clock time combines LLM latency with FEniCS runtime, including repeated executions during debugging, so cross-machine comparisons require caution.The reported duration can vary substantially with hardware and system configuration.Source: Appendix C · p. 21

Solid mechanics

• All frameworks produce displacement fields visually identical to the reference for Solid Q1, as shown in Figure D1.The problem is a rectangular plate, and the plotted field is displacement magnitude.Source: Figure D1 · p. 22, Appendix D · p. 22
• For Solid Q4, most frameworks match the reference displacement pattern, but Llama 3.3 70B misses the circular holes and produces a different result.The problem is a rectangular plate with two circular holes.Source: Appendix D · p. 22, Figure D2 · p. 23
• For Solid Q15, the Multi-agent framework, GPT-OSS 120B, and GPT-5 Thinking match the reference, whereas GPT-OSS 120B Finetuned differs despite producing executable output.The plotted quantity is displacement magnitude for a rectangular plate with three circular holes.Source: Appendix D · p. 22, Figure D3 · p. 23

Fluid mechanics

• For Fluid Q7, the Multi-agent framework and both GPT-OSS 120B variants align closely with the reference velocity field, unlike GPT-5 Thinking’s weaker obstacle-region variation.The matching outputs preserve similar high-velocity regions around and downstream of a circular obstacle in a rectangular channel.Source: Appendix D · p. 22, Figure D4 · p. 24
• For Fluid Q10, GPT-5 Thinking matches the reference cavity-flow structure, while the Multi-agent framework and GPT-OSS 120B variants share a different identical pattern.The plotted quantity is velocity magnitude in a unit-square cavity.Source: Appendix D · p. 22, Figure D5 · p. 24

Appendix E Benchmark Problems

• The benchmark comprises 39 computational mechanics problems, displayed in LaTeX fonts for readability but prompted to systems as plain text with Unicode symbols.Source: Appendix E · p. 25

Baseline flow benchmarks

• Problems 1–5 cover rectangular-channel and cavity Stokes/Navier–Stokes flows with pressure, body-force, lid-driven, prescribed-inlet, and pressure-gauge conditions.They include Taylor–Hood P2-P1 elements for the lid-driven Stokes cavity and request velocity, pressure, speed, or streamwise-velocity outputs.Source: Fluid Mechanics Problems · pp. 25–27

Complex geometries

• For steady incompressible Navier–Stokes models, outputs include top-wall shear stress τw(x,H)=µ(∂ux/∂y) to identify re-attachment where τw(x,H)=0, and circle drag coefficient CD=2FD/(ρ ¯U 2D).Source: Fluid Mechanics Problems · p. 27

Transport and thermal coupling

• Problems 8–10 extend fluid benchmarks to periodic body-force flow, advection–diffusion transport, and Boussinesq natural convection with temperature coupling.The formulations prescribe periodicity and a pressure gauge, transport concentration with inlet, outlet, and impermeable-wall conditions, or couple buoyancy to temperature and report Nusselt number.Source: Fluid Mechanics Problems · pp. 28–29

Non-Newtonian flow

• Problem 11 models steady non-Newtonian channel flow using a power-law effective viscosity with flow behavior index n = 0.5.The benchmark requires velocity-profile extraction, maximum mid-channel velocity, and export of velocity, pressure, and effective-viscosity fields.Source: Fluid Mechanics Problems · pp. 29–30

Temperature-dependent viscosity

• Problem 12 couples Navier–Stokes and temperature advection–diffusion through viscosity µ(T) = µrefe^−β(T −Tref), with heated and adiabatic walls.It requires viscosity visualization, a mid-length velocity profile, and export of u, p, T, and µ fields.Source: Fluid Mechanics Problems · p. 30

Scalar transport

• Problem 13 isolates steady scalar advection–diffusion in a channel with a prescribed parabolic velocity, concentration boundary values, and zero diffusive wall flux.The benchmark uses Umax = 0.75 m s−1 and D = 1.0 × 10−5 m2 s−1, exporting the concentration field in XDMF format.Source: Fluid Mechanics Problems · pp. 30–31

Fluid Mechanics Problem 14

• Problem 14 models turbulent flow past a diameter-D cylinder in a square domain using residual-based VMS with SUPG, PSPG, and grad-div stabilization.The domain is Ω = [−30D, +30D] × [−30D, +30D], with the cylinder centered at (0, 0).Source: Fluid Mechanics Problems · p. 31
• Problem 14 imposes uniform inflow, traction-free outflow, no-slip walls and cylinder boundaries, and initially stationary fields with optional perturbation for vortex shedding.Parameters are U = 1.0 m/s, ν = 2.56 × 10−5 m2/s, ρ = 1.0 kg/m3, and D = 1 m.Source: Fluid Mechanics Problems · p. 31
• Problem 14 reports mean drag over t ∈ [8.0 s, 10.0 s] and saves velocity and pressure fields at t = 10.0 s in XDMF format.The saved file is vms solution.xdmf.Source: Fluid Mechanics Problems · p. 31

Fluid Mechanics Problem 15

• Problem 15 solves unsteady incompressible Navier–Stokes flow in a unit square with periodic boundaries and a prescribed sinusoidal initial velocity.The density is ρ = 1, viscosity is ν = 1×10−3, and the simulation runs to t = 1 with a timestep chosen for stability across advection and viscous scales.Source: Fluid Mechanics Problems · pp. 31–32
• Problem 15 saves velocity fields at representative times, including t = 0, 0.25, 0.5, and 1.0, in XDMF format.The outputs are intended to track the evolving numerical solution over the simulation interval.Source: Fluid Mechanics Problems · p. 32

Easy problems

• The easy benchmarks cover rectangular plates with prescribed displacement or traction, holes, notches, and a bonded aluminum–steel interface under plane-stress linear elasticity.The geometries include centered single or double circular holes, rectangular and semicircular notches, and two material subdomains with perfect displacement and traction continuity.Source: Solid Mechanics Problems · pp. 32–34
• The easy cases require displacement or von Mises-stress fields, color-map outputs, XDMF exports, and, for holed plates, maximum hole-boundary stress and Kt = σmax/2 MPa.The aluminum–steel case instead outputs displacement magnitude, while the single- and double-hole cases explicitly request stress-concentration measurements.Source: Solid Mechanics Problems · pp. 33–34

Medium problems

• Medium benchmarks extend linear elasticity to orthotropic stiffness rotated by θ = 30 degrees, height-varying Young’s modulus, plane strain, and nearly incompressible materials with circular holes.The orthotropic case uses E1 = 40 GPa, E2 = 10 GPa, G12 = 5 GPa, and ν12 = 0.25; the graded case uses E(y) = 100 GPa + 100 GPa × (y/0.20).Source: Solid Mechanics Problems · pp. 35–36
• For ν ≈ 0.5, pure displacement elements over-stiffen because of volumetric locking, so mixed displacement–pressure formulations are standard practice for nearly incompressible solids.The material uses E = 5 MPa and ν = 0.5 with a mixed (u, p) formulation imposing J = 1; the hole carries Phole = 0.10 MPa follower pressure.Source: Solid Mechanics Problems · pp. 36–37

Hard problems

• The hard benchmarks model plane-strain large-deformation quasi-incompressible Neo-Hookean strips with two circular holes and follower pressure, requesting pressure, von Mises-stress, and displacement outputs.The prescribed right-edge displacement is +0.060 m, and each hole receives uniform follower pressure Phole = 0.10 MPa.Source: Solid Mechanics Problems · pp. 37–38
• The final hard benchmark uses finite-strain Saint-Venant–Kirchhoff plane-strain elasticity for a strip with three circular holes and exports deformed geometry, maximum principal Green–Lagrange strain, and deviatoric-stress measures.It defines F, E, S, J, and Cauchy stress σ, applies ux = +0.012 m at the right edge, and saves Emax and σvm(s) fields.Source: Solid Mechanics Problems · p. 38

Solution procedure and output

• Load stepping uses Newton iterations and advances only while the maximum principal Green–Lagrange strain satisfies Emax ≤ 0.03; the displacement is saved in XDMF format.The material parameters are λ = 19.44 GPa, µ = 29.17 GPa, and σY = 243 MPa.Source: Solid Mechanics Problems · pp. 38–39

Problem geometry

• The benchmark analyzes a plane-strain quarter plate domain [0, 100] × [0, 180] mm containing a quarter hole of radius 50 mm at the origin.Source: Solid Mechanics Problems · p. 38

Constitutive model

• The model uses small-strain von Mises elastoplasticity with associative flow, perfect plasticity, deviatoric plastic strain, and Kuhn–Tucker loading conditions.The yield condition is F = q − σY ≤ 0, with initially zero plastic strain.Source: Solid Mechanics Problems · pp. 38–39

Boundary conditions

• Symmetry constrains ux = 0 on x = 0 and uy = 0 on y = 0, while the top edge receives u = (0, 1) mm and the hole is traction-free.The x = 100 mm edge also has prescribed traction conditions as specified in the problem statement.Source: Solid Mechanics Problems · p. 39

Benchmark scope

• The benchmarks cover moving-domain diffusion-reaction, Allen-Cahn curvature flow, Cahn-Hilliard spinodal decomposition, Stokes-Darcy coupling, two fluid–structure interaction cases, and free-fluid/porous-flow coupling.The problems collectively test ALE formulations, phase-field methods, coupled subdomain physics, and interface conditions across diverse geometries and material models.Source: Multiphysics Problems · pp. 39–42

Multiphysics Problem 1

• The moving-domain transport benchmark solves an ALE diffusion-reaction equation on an expanding circular disk with zero total flux and first-order decay.The radius follows R(t) = R0 + s · t with R0 = 0.05 m and s = 1.0 × 10−4 m s−1; D = 1.0 × 10−5 m2 s−1, κ = 1.0 × 10−4 s−1, and ∆t = 0.01 s through 10 seconds.Source: Multiphysics Problems · p. 39

Multiphysics Problems 2–3

• The phase-field benchmarks use implicit Allen-Cahn curvature flow with homogeneous Neumann conditions and backward-Euler Cahn-Hilliard dynamics with degenerate mobility and periodic conditions.Allen-Cahn evolution uses ε = 0.01, M = 1.0, T = 0.20, and ∆t = 1.0e −3; Cahn-Hilliard evolution uses θ = 1.5, α = 3000, adaptive stepping, and a split mixed formulation.Source: Multiphysics Problems · pp. 39–40

Multiphysics Problems 4, 7–8

• The coupled flow benchmarks formulate Stokes-Darcy exchange through mass continuity, traction balance, and interface conditions, while porous-flow cases couple free-fluid equations to Brinkman or Darcy models.The setups prescribe distinct subdomain geometries, inlet and outlet conditions, and outputs including velocity, pressure, pressure drop, and interface profiles.Source: Multiphysics Problems · pp. 40, 42, 43

Multiphysics Problems 5–6

• The fluid–structure interaction benchmarks solve incompressible ALE flow coupled respectively to plane-strain linear elasticity in an elastic tube and a St. Venant-Kirchhoff flag.Both enforce no-slip and traction balance at fluid-solid interfaces, with outputs comprising velocity, pressure, displacement, and time-dependent flag-point motion.Source: Multiphysics Problems · pp. 41–42