A Fixed-Grid Affine-Constrained Multiwavelet Coefficient Method for Buckley--Leverett Shock Capturing
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916031097733120 |
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| author | Tantardini, Christian Dinvay, Evgueni |
| author_facet | Tantardini, Christian Dinvay, Evgueni |
| contents | We present a fixed-grid conservative affine-constrained modal/multiwavelet coefficient method for one-dimensional Buckley--Leverett saturation transport. The saturation is evolved directly in a local orthonormal coefficient basis with a mean/detail structure: the first mode carries the conservative cell average, whereas higher modes carry zero-mean local details. The hyperbolic inflow condition is imposed as a linear trace constraint on the coefficient vector and enforced by affine lifting. For $(p>1)$, the boundary reprojection is applied in the detail subspace of the inflow cell, so that the prescribed trace is restored without modifying the conservative cell-average update. The transport operator is discretized in conservative weak form with monotone numerical fluxes, and shock-induced oscillations are controlled by a troubled-cell limiter acting on modal details.
The method is validated on a Berea-core waterflood benchmark against an independent \texttt{pywaterflood} reference solution using the same Corey fractional-flow closure, physical parameters, and pore-volume-injected scaling. The affine-constrained coefficient solver reproduces the reference breakthrough curve and saturation profiles, preserves the imposed inflow trace to roundoff accuracy, controls saturation bounds through mean-preserving detail rescaling, and gives small accumulated global mass-balance defects. Mesh-refinement, flux-comparison, and modal-order studies show that $(p=2)$, corresponding to a piecewise-linear local representation, provides the most favorable accuracy--cost compromise among the tested orders for this shock-dominated benchmark. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Fixed-Grid Affine-Constrained Multiwavelet Coefficient Method for Buckley--Leverett Shock Capturing Tantardini, Christian Dinvay, Evgueni Fluid Dynamics Geophysics We present a fixed-grid conservative affine-constrained modal/multiwavelet coefficient method for one-dimensional Buckley--Leverett saturation transport. The saturation is evolved directly in a local orthonormal coefficient basis with a mean/detail structure: the first mode carries the conservative cell average, whereas higher modes carry zero-mean local details. The hyperbolic inflow condition is imposed as a linear trace constraint on the coefficient vector and enforced by affine lifting. For $(p>1)$, the boundary reprojection is applied in the detail subspace of the inflow cell, so that the prescribed trace is restored without modifying the conservative cell-average update. The transport operator is discretized in conservative weak form with monotone numerical fluxes, and shock-induced oscillations are controlled by a troubled-cell limiter acting on modal details. The method is validated on a Berea-core waterflood benchmark against an independent \texttt{pywaterflood} reference solution using the same Corey fractional-flow closure, physical parameters, and pore-volume-injected scaling. The affine-constrained coefficient solver reproduces the reference breakthrough curve and saturation profiles, preserves the imposed inflow trace to roundoff accuracy, controls saturation bounds through mean-preserving detail rescaling, and gives small accumulated global mass-balance defects. Mesh-refinement, flux-comparison, and modal-order studies show that $(p=2)$, corresponding to a piecewise-linear local representation, provides the most favorable accuracy--cost compromise among the tested orders for this shock-dominated benchmark. |
| title | A Fixed-Grid Affine-Constrained Multiwavelet Coefficient Method for Buckley--Leverett Shock Capturing |
| topic | Fluid Dynamics Geophysics |
| url | https://arxiv.org/abs/2605.21030 |