An asymptotic-and curl-preserving finite volume scheme for a novel hyperbolic barotropic Navier-Stokes model
Abstract
We introduce a first-order hyperbolic and thermodynamically compatible formulation of the barotropic Navier-Stokes equations. This new model is asymptotically consistent with the Stokes model for compressible viscous fluids, provided that suitable relaxation terms and evolution equations for two auxiliary vector and tensor fields are added. The tensor field is endowed with a curl-free constraint. A novel second-order finite volume scheme is designed to solve the governing equations: a semi-implicit time discretization allows the scheme to be asymptotic preserving with respect to the low Reynolds and low Mach number limits of the original hyperbolic Navier-Stokes model. Nonlinear equations of state are handled by means of a nested Newton algorithm, which includes the pressure sub-system arising from the implicit treatment of the pressure terms. Convective fluxes are discretized explicitly, ensuring stability and shock-capturing properties in the case of high Mach number flows. The scheme is proven to be curl-free thanks to compatible differential operators defined on a vertex-staggered spatial discretization. A large suite of test cases in multiple space dimensions demonstrates the accuracy, robustness, and effectiveness of the new numerical method across multiple stiffness regimes for both Mach and Reynolds numbers.
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BibTeX
@misc{guines2026asymptoticand,
title = {{An asymptotic-and curl-preserving finite volume scheme for a novel hyperbolic barotropic Navier-Stokes model}},
author = {Antoine Guines and Walter Boscheri and Sergey Gavrilyuk and Barbara Re},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05745343v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - An asymptotic-and curl-preserving finite volume scheme for a novel hyperbolic barotropic Navier-Stokes model
AU - Antoine Guines
AU - Walter Boscheri
AU - Sergey Gavrilyuk
AU - Barbara Re
PY - 2026
DA - 2026/09/10
PB - HAL
UR - https://hal.science/hal-05745343v1
AB - We introduce a first-order hyperbolic and thermodynamically compatible formulation of the barotropic Navier-Stokes equations. This new model is asymptotically consistent with the Stokes model for compressible viscous fluids, provided that suitable relaxation terms and evolution equations for two auxiliary vector and tensor fields are added. The tensor field is endowed with a curl-free constraint. A novel second-order finite volume scheme is designed to solve the governing equations: a semi-implicit time discretization allows the scheme to be asymptotic preserving with respect to the low Reynolds and low Mach number limits of the original hyperbolic Navier-Stokes model. Nonlinear equations of state are handled by means of a nested Newton algorithm, which includes the pressure sub-system arising from the implicit treatment of the pressure terms. Convective fluxes are discretized explicitly, ensuring stability and shock-capturing properties in the case of high Mach number flows. The scheme is proven to be curl-free thanks to compatible differential operators defined on a vertex-staggered spatial discretization. A large suite of test cases in multiple space dimensions demonstrates the accuracy, robustness, and effectiveness of the new numerical method across multiple stiffness regimes for both Mach and Reynolds numbers.
ER -