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Main Author: Tantardini, Christian
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.28981
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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
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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