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March 3, 2026

A strongly mass-conservative method for the coupled Navier-Stokes  and Darcy-Forchheimer equations

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Authors

JLJingyu LiuLZLina Zhao

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Overview

Proposes a mass-conservative scheme for coupled Navier-Stokes and Darcy-Forchheimer equations, highlighting robust behavior.

Key Points

  • To propose a mass-conservative numerical method for the coupled Navier-Stokes and Darcy-Forchheimer equations while ensuring stability and robustness.
  • Developed a staggered discontinuous Galerkin method for Navier-Stokes equations.
  • Utilized standard mixed finite elements for the Darcy-Forchheimer problem.
  • Implemented interface conditions directly without Lagrange multipliers or artificial fluxes.
  • Ensured that the velocity field is globally H(div)-conforming across the domain.
  • Analyzed the well-posedness of the nonlinear discrete system under small-data assumptions.
  • The proposed numerical scheme maintains exact mass conservation across the entire computational domain.
  • Numerical experiments demonstrate stability in regimes with small viscosity and large pressure.
  • The method shows pressure-robust behavior, maintaining accurate velocity approximations.

Cite This Study

Liu et al. (2026) studied this question.

synapsesocial.com/papers/69a67ed1f353c071a6f0a5e9https://doi.org/10.1051/m2an/2026021/pdf
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