A bounded-interval multiwavelet formulation with conservative finite-volume transport for one-dimensional Buckley–Leverett waterflooding

arXiv:2603.28981v1 Announce Type: new
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.