A bounded-interval multiwavelet formulation with conservative finite-volume transport for one-dimensional Buckley--Leverett waterflooding
Abstract
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.
Keywords
Cite
@article{arxiv.2603.28981,
title = {A bounded-interval multiwavelet formulation with conservative finite-volume transport for one-dimensional Buckley--Leverett waterflooding},
author = {Christian Tantardini},
journal= {arXiv preprint arXiv:2603.28981},
year = {2026}
}