Pith Number

pith:IKTWKNEN

pith:2026:IKTWKNENUDFZ2TM7G5NUGVGVVA

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Fully Discrete Active Flux Method based on Transported Acoustic Increments for the Compressible Euler Equations

Karthik Duraisamy

Reconstructing acoustic increments as cellwise quadratic fields and evaluating them at convective feet yields the exact unsplit frozen evolution for the compressible Euler equations.

arxiv:2605.12915 v1 · 2026-05-13 · math.NA · cs.NA · physics.flu-dyn

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Claims

C1strongest claim

For constant frozen coefficients, the resulting point update reduces to the transported composition, eliminating the additive split defect and yielding the exact unsplit frozen evolution when the acoustic and advective generators commute.

C2weakest assumption

Reconstructing the acoustic increment as a cellwise Q2 field and evaluating it at the convective foot accurately captures the unsplit evolution operator even for the full nonlinear Euler equations.

C3one line summary

A new transported acoustic increment reconstruction in the Active Flux framework yields third-order accuracy and exact unsplit frozen evolution for the compressible Euler equations.

References

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[1] Roe, Philip L. , title =. Proceedings of the. 2025 , doi = 2025

[2] Roe, Philip L. , title =. Computers & Fluids , volume =

[3] Roe, Philip L. , title =. Handbook of Numerical Analysis , volume =

[4] Journal of Computational Physics , volume =

[5] and Roe, Philip L

Formal links

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Receipt and verification

First computed	2026-05-18T03:09:10.379694Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42a765348da0cb9d4d9f375b4354d5a813266408afe1060eef2f963e976b967b

Aliases

arxiv: 2605.12915 · arxiv_version: 2605.12915v1 · doi: 10.48550/arxiv.2605.12915 · pith_short_12: IKTWKNENUDFZ · pith_short_16: IKTWKNENUDFZ2TM7 · pith_short_8: IKTWKNEN

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/IKTWKNENUDFZ2TM7G5NUGVGVVA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 42a765348da0cb9d4d9f375b4354d5a813266408afe1060eef2f963e976b967b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37dc2df47fa8b9c9573e3bd6b44cd511cebffce9eeec220744a39adb383249d7",
    "cross_cats_sorted": [
      "cs.NA",
      "physics.flu-dyn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T02:41:43Z",
    "title_canon_sha256": "11102bd1ea928a856085e6b3a4d64b6a6d3f67575f5268b4d40c76571f1a551d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12915",
    "kind": "arxiv",
    "version": 1
  }
}