A Unified Numerical Framework for Turbulent Convection and Phase-Change Dynamics in Coupled Fluid-Porous Systems

TL;DR

The paper develops a unified single-domain framework for simulating turbulent convection and phase-change dynamics in coupled fluid–porous systems with variable porosity and high solid–to–fluid conductivity contrasts. It combines a Darcy–Brinkman momentum model with a modified phase-field approach, augmented by a thermal-dispersion correction and a robust RK3 temporal scheme with operator factorization to achieve second-order accuracy efficiently. The framework is validated across diverse benchmarks—channel flow over permeable substrates, thermally driven fluid–porous convection, 1D Stefan and 2D pure-water freezing, double-diffusive convection in porous media, and seawater freezing with mushy-layer formation—showing excellent agreement with theory, experiments, and prior simulations. This unified, highly scalable approach enables accurate, computationally efficient simulation of complex multi-physics mushy-layer problems, with broad relevance to geothermal processes, sea-ice dynamics, and materials processing.

Abstract

We present a unified numerical framework for simulating turbulent thermal convection and phase-change dynamics in coupled fluid-porous media systems. The framework is designed to handle high solid-to-fluid thermal conductivity contrast and spatiotemporally varying porosity. It combines a Darcy-Brinkman formulation with a modified phase-field method to achieve smooth two-way coupling across transitioning interfaces. The model integrates momentum, energy, solute transport, and phase evolution equations. A factorized operator-splitting approach with second-order temporal accuracy is employed to ensure computational efficiency. The numerical method is rigorously validated using a range of benchmark problems. These include channel flow over permeable substrates, thermal convection in porous-fluid layers, 1D Stefan and 2D pure-water phase changing, double-diffusive convection in porous media, and seawater solidification. The results show good agreement with existing experiments and simulations.

Figures (12)

• Figure 1: Schematic illustration of the solidification problem involving a binary fluid. The mushy domain $\Omega_m$ is separated from the liquid domain $\Omega_l$ by the liquid-solid interface $\Gamma$. The temperature $T_{l,m}$ and the concentration $S_{l,m}$ are solved in the two domains.
• Figure 2: Schematic of the validation setup for turbulent channel flow over a permeable substrate, following Breugem06. The domain has a height of $2\delta$, bounded by an impermeable wall at the top and a permeable layer of thickness $h=2\delta$ and porosity $\phi$ at the bottom. An interfacial layer of thickness $\delta_i$ facilitates a smooth transition in porosity and permeability.
• Figure 3: Validation of the mean and fluctuating velocity profiles for channel flow over a permeable substrate with porosity $\phi=0.8$. (a) Mean velocity profile normalized by the bulk velocity $U_b$ as a function of dimensionless height $z/H$. (b) Root mean square velocity fluctuations in wall units. Symbols denote the reference data from Breugem06 obtained using the Volume-Averaged Navier-Stokes (VANS) equations.
• Figure 4: Schematic of the two-layer system for validating thermally driven convection, after Reun21. The domain of total height $2h$ consists of a fluid-saturated porous medium of depth $h$ in the lower half ($-h\le z<0$) and a free fluid layer of depth $h$ in the upper half ($0<z\le h$). The interface is at $z=0$. The system is driven by a temperature difference between the hot bottom ($T_b$) and cold top ($T_t$) boundaries.
• Figure 5: Numerical results for coupled convection in a fluid-porous layer. (a) Snapshot of the temperature field $\theta$. (b) Horizontally averaged temperature profile.