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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.28981 |
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| _version_ | 1866915925946531840 |
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| author | Tantardini, Christian |
| author_facet | Tantardini, Christian |
| contents | We develop a hybrid conservative finite-volume / bounded-interval multiwavelet formulation for the deterministic one-dimensional Buckley--Leverett equation. Because Buckley--Leverett transport is a nonlinear hyperbolic conservation law with entropy-admissible shocks, the saturation update is performed by a conservative finite-volume scheme with monotone numerical fluxes, while the evolving state is represented and reconstructed in a bounded-interval multiwavelet basis. This strategy preserves the correct shock-compatible transport mechanism and simultaneously provides a hierarchical multiresolution description of the solution. Validation against reference Buckley--Leverett profiles for a Berea benchmark shows excellent agreement in probe saturation histories, spatial profiles, front-location diagnostics, and global error measures. The multiwavelet reconstruction also tracks the internal finite-volume state with essentially exact fidelity. The resulting formulation provides a reliable first step toward more native multiwavelet transport solvers for porous-media flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28981 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A bounded-interval multiwavelet formulation with conservative finite-volume transport for one-dimensional Buckley--Leverett waterflooding Tantardini, Christian Numerical Analysis Fluid Dynamics We develop a hybrid conservative finite-volume / bounded-interval multiwavelet formulation for the deterministic one-dimensional Buckley--Leverett equation. Because Buckley--Leverett transport is a nonlinear hyperbolic conservation law with entropy-admissible shocks, the saturation update is performed by a conservative finite-volume scheme with monotone numerical fluxes, while the evolving state is represented and reconstructed in a bounded-interval multiwavelet basis. This strategy preserves the correct shock-compatible transport mechanism and simultaneously provides a hierarchical multiresolution description of the solution. Validation against reference Buckley--Leverett profiles for a Berea benchmark shows excellent agreement in probe saturation histories, spatial profiles, front-location diagnostics, and global error measures. The multiwavelet reconstruction also tracks the internal finite-volume state with essentially exact fidelity. The resulting formulation provides a reliable first step toward more native multiwavelet transport solvers for porous-media flow. |
| title | A bounded-interval multiwavelet formulation with conservative finite-volume transport for one-dimensional Buckley--Leverett waterflooding |
| topic | Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2603.28981 |