Moment-based approximation of cell and face integrals in THINC/QQ reconstruction on unstructured grids
Abstract
On unstructured grids, the tangent of hyperbola for interface capturing (THINC) method with quadratic surface representation and Gaussian quadrature (THINC/QQ) requires topology-dependent numerical quadrature for cell and face integrals and Newton iteration for the surface constant. This study introduces a quadratic moment-matched sigmoid (QMMS) approximation that evaluates these quantities from the mean and variance of the quadratic field while retaining the hyperbolic-tangent reconstruction profile and the boundary variation diminishing (BVD) formulation. A slope-matched Gaussian cumulative distribution function and a moment-matched Gaussian model provide closed form approximations for the surface constant and face averages, eliminating Newton iteration and topology-dependent runtime quadrature from these evaluations. Single-cell tests and nine two- and three-dimensional benchmarks assess reconstruction accuracy, flow-field differences, and computational cost. Across the tested cases, the principal transported and shock structures remain closely aligned with those obtained using THINC/QQ, with local differences concentrated mainly near discontinuities, contact regions, and developed shear layers. Reconstruction-stage profiling gives mean THINC/QQ-to-QMMS time ratios of 2.12 in two dimensions and 1.85 in three dimensions. QMMS therefore reduces reconstruction-stage cost while replacing topology-dependent runtime integral evaluation with a common moment-based formulation
Related
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BibTeX
@misc{yoo2026momentbased,
title = {{Moment-based approximation of cell and face integrals in THINC/QQ reconstruction on unstructured grids}},
author = {Young-Lin Yoo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38215},
eprint = {2609.38215},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38215},
}
RIS
TY - UNPB
TI - Moment-based approximation of cell and face integrals in THINC/QQ reconstruction on unstructured grids
AU - Young-Lin Yoo
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.38215
UR - https://arxiv.org/abs/2609.38215
AB - On unstructured grids, the tangent of hyperbola for interface capturing (THINC) method with quadratic surface representation and Gaussian quadrature (THINC/QQ) requires topology-dependent numerical quadrature for cell and face integrals and Newton iteration for the surface constant. This study introduces a quadratic moment-matched sigmoid (QMMS) approximation that evaluates these quantities from the mean and variance of the quadratic field while retaining the hyperbolic-tangent reconstruction profile and the boundary variation diminishing (BVD) formulation. A slope-matched Gaussian cumulative distribution function and a moment-matched Gaussian model provide closed form approximations for the surface constant and face averages, eliminating Newton iteration and topology-dependent runtime quadrature from these evaluations. Single-cell tests and nine two- and three-dimensional benchmarks assess reconstruction accuracy, flow-field differences, and computational cost. Across the tested cases, the principal transported and shock structures remain closely aligned with those obtained using THINC/QQ, with local differences concentrated mainly near discontinuities, contact regions, and developed shear layers. Reconstruction-stage profiling gives mean THINC/QQ-to-QMMS time ratios of 2.12 in two dimensions and 1.85 in three dimensions. QMMS therefore reduces reconstruction-stage cost while replacing topology-dependent runtime integral evaluation with a common moment-based formulation
ER -