LLM agents are increasingly used for code generation, but physics-based simulation poses a deeper challenge: natural-language descriptions of simulation models are inherently underspecified, and different admissible resolutions of implicit choices produce physically valid but scientifically distinct configurations. Without explicit detection and resolution of these ambiguities, neither the correctness of the result nor its reproducibility from the original description can be assured. This paper investigates agentic scientific simulation, where model construction is organized as an execution-grounded interpret-act-validate loop and the simulator serves as the authoritative arbiter of physical validity rather than merely a runtime. We present JutulGPT, a reference implementation built on the fully differentiable Julia-based reservoir simulator JutulDarcy. The agent combines structured retrieval of documentation and examples with code synthesis, static analysis, execution, and systematic interpretation of solver diagnostics. Underspecified modelling choices are detected explicitly and resolved either autonomously (with logged assumptions) or through targeted user queries. The results demonstrate that agent-mediated model construction can be grounded in simulator validation, while also revealing a structural limitation: choices resolved tacitly through simulator defaults are invisible to the assumption log and to any downstream representation. A secondary experiment with autonomous reconstruction of a reference model from progressively abstract textual descriptions shows that reconstruction variability exposes latent degrees of freedom in simulation descriptions and provides a practical methodology for auditing reproducibility. All code, prompts, and agent logs are publicly available.