Update-Magnitude State Redistribution (UM-SRD): A Shut-off Extension of Weighted SRD for Cut-Cell Methods
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913159113080832 |
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| author | Karell, Justo E. |
| author_facet | Karell, Justo E. |
| contents | Berger & Giuliani (2024) developed a provably stable weighted state redistribution (SRD) algorithm for cut-cell meshes. A key limitation of their method is that, although flux redistribution naturally vanishes when updates are small, SRD continuously applies redistribution even when the flux balance is zero, preventing exact steady-state preservation and potentially introducing unnecessary dissipation in smooth regions. This work introduces Update-Magnitude State Redistribution (UM-SRD), which blends the SRD operator with the identity operator via a smooth, locally-defined scalar indicator of the finite-volume update magnitude. UM-SRD preserves conservation and reduces exactly to the base scheme when the finite-volume update is exactly zero in a small-cell neighborhood. For a one-dimensional model problem with a single small cut cell, we prove UM-SRD is total variation diminishing under the same CFL condition as the base upwind scheme, show the local truncation error modification is higher-order in smooth regions with the unnormalized indicator, and show that the normalized implementation preserves first-order accuracy. Numerical experiments demonstrate convergence toward first order on smooth 1D and 2D advection tests, confirm shut-off behaviour, verify non-oscillatory properties, provide numerical evidence that UM-SRD stabilizes the base scheme near a small cut cell where the base scheme diverges, and confirm exact steady-state preservation. The algorithm reuses existing weighted SRD infrastructure, adding only a local blending mechanism, making it practical for cut-cell finite-volume codes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Update-Magnitude State Redistribution (UM-SRD): A Shut-off Extension of Weighted SRD for Cut-Cell Methods Karell, Justo E. Numerical Analysis 65M08 Berger & Giuliani (2024) developed a provably stable weighted state redistribution (SRD) algorithm for cut-cell meshes. A key limitation of their method is that, although flux redistribution naturally vanishes when updates are small, SRD continuously applies redistribution even when the flux balance is zero, preventing exact steady-state preservation and potentially introducing unnecessary dissipation in smooth regions. This work introduces Update-Magnitude State Redistribution (UM-SRD), which blends the SRD operator with the identity operator via a smooth, locally-defined scalar indicator of the finite-volume update magnitude. UM-SRD preserves conservation and reduces exactly to the base scheme when the finite-volume update is exactly zero in a small-cell neighborhood. For a one-dimensional model problem with a single small cut cell, we prove UM-SRD is total variation diminishing under the same CFL condition as the base upwind scheme, show the local truncation error modification is higher-order in smooth regions with the unnormalized indicator, and show that the normalized implementation preserves first-order accuracy. Numerical experiments demonstrate convergence toward first order on smooth 1D and 2D advection tests, confirm shut-off behaviour, verify non-oscillatory properties, provide numerical evidence that UM-SRD stabilizes the base scheme near a small cut cell where the base scheme diverges, and confirm exact steady-state preservation. The algorithm reuses existing weighted SRD infrastructure, adding only a local blending mechanism, making it practical for cut-cell finite-volume codes. |
| title | Update-Magnitude State Redistribution (UM-SRD): A Shut-off Extension of Weighted SRD for Cut-Cell Methods |
| topic | Numerical Analysis 65M08 |
| url | https://arxiv.org/abs/2605.04863 |