Pith Number

pith:765MNNZL

pith:2026:765MNNZLNX44XFCTHFC5YTVLYX

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Update-Magnitude State Redistribution (UM-SRD): A Shut-off Extension of Weighted SRD for Cut-Cell Methods

Justo E. Karell

UM-SRD blends weighted state redistribution with the identity operator using an update-magnitude indicator to achieve exact steady-state preservation in cut-cell finite-volume methods.

arxiv:2605.04863 v2 · 2026-05-06 · math.NA · cs.NA

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4 Citations open

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Claims

C1strongest claim

For a one-dimensional model problem with a single small cut cell, UM-SRD is total variation diminishing under the same CFL condition as the base upwind scheme, the local truncation error modification is higher-order in smooth regions with the unnormalized indicator, and the normalized implementation preserves first-order accuracy; numerical experiments confirm exact steady-state preservation and stabilization of the base scheme near a small cut cell.

C2weakest assumption

The blending indicator is assumed to be smooth and locally defined such that the overall operator remains conservative and the TVD property holds under the base CFL; the paper does not specify how the indicator is constructed in multiple dimensions or when multiple small cells interact.

C3one line summary

UM-SRD adds a smooth update-magnitude blending factor to weighted SRD so that redistribution vanishes at exact steady state in small cut cells, preserving the base scheme's properties and enabling exact steady-state preservation.

Receipt and verification

First computed	2026-05-26T02:04:12.071581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffbac6b72b6df9cb94533945dc4eabc5e07ed0fc5fb880c6e1d91f64ec12f080

Aliases

arxiv: 2605.04863 · arxiv_version: 2605.04863v2 · doi: 10.48550/arxiv.2605.04863 · pith_short_12: 765MNNZLNX44 · pith_short_16: 765MNNZLNX44XFCT · pith_short_8: 765MNNZL

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/765MNNZLNX44XFCTHFC5YTVLYX \
  | 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: ffbac6b72b6df9cb94533945dc4eabc5e07ed0fc5fb880c6e1d91f64ec12f080

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "393b052f67fb6ba47f88918f2b75b5b5ab65850b97f570d20741be8ddb61c96d",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-06T12:59:20Z",
    "title_canon_sha256": "71221106028eb910418d6d7150f333052a964c2e55347e484dd98fb3b6b84701"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04863",
    "kind": "arxiv",
    "version": 2
  }
}