ASTR 474 Problem Set 04: Hydrodynamics and Resolution

Objectives and instructions

Practice computational reasoning, quantitative analysis, validation, and scientific communication for lectures 05-06.

Use SI or explicitly stated astronomical units consistently; show conversions and significant figures.
Cite all data, software, and adapted code. Distinguish supplied measured data from synthetic records.
Include runnable code and record environment, command, and seed where used.
Collaboration on concepts is permitted; each submitted derivation, code, and interpretation must be the student's own and contributors must be named.

Revisions and resubmissions are encouraged to improve mastery and grade under the course policy.

Problem 4.1

Derive the conserved variables and physical flux for one-dimensional ideal-gas Euler flow from mass, momentum, and total-energy conservation.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Problem 4.2

Using the generated resolution table, compute successive L1 error ratios and describe whether they support an asymptotic first-order trend. Include the 512-zone reference limitation.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Problem 4.3

Audit the Rusanov teaching solver: identify one positivity test, one integral conservation test, one boundary-condition test, and two missing requirements for production astrophysical hydrodynamics.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Reproducibility check

Use this generated reference result as one consistency check, not as a substitute for showing reasoning: The density L1 discrepancy against the 512-zone reference decreases from 0.03066 at 32 cells to 0.00521 at 256; measured mass errors are listed independently.

No textbook exercise is adopted for this course; problems are original and cite the primary software/data sources in the reference log.

Submission

Submit a readable PDF report, source code, environment/version record, and any generated tables/figures. The assignment is complete only when another student can rerun the command and identify the inputs and validation test.