COMSOL Multiphysics Implementation of Pressure Formulation for Darcy-Convection-Diffusion-Reaction Flow

Project Description

This repository contains the numerical implementation and simulation data for a Darcy-scale model of reactive solute transport in a porous medium. To achieve high resolution and computational efficiency, the system is solved using a Pressure-Concentration ($p$-$c$) formulation in COMSOL Multiphysics®. This approach eliminates the velocity vector from the primary governing equations, reducing the system to two coupled scalar PDEs.

The model is used to investigate hydrodynamic instabilities (fingering), in which fluid density and viscosity are non-linearly coupled to the concentration field.

Technical Specifications

• Software: COMSOL Multiphysics® v6.3

• Interface: Weak Form PDE (Mathematics Module)

• Mesh Type: Quadrilateral (Mapped Mesh)

• Total Elements: 291,466 elements

• Boundary Elements: 2,400 elements

• Degrees of Freedom (DOFs): 2,336,310

• Element Size: Max: 0.262, Min: 5 × 10⁻⁴

• Solver: Time-dependent implicit BDF (orders 1–5) with a relative tolerance of 10⁻⁵

• Time Stepping: $t \in [0, 3000]$ with an output interval of 5.

Mathematical Model

The implementation transforms the Darcy-Incompressibility system into the following set of governing equations:

• Pressure Equation:

  $$\nabla \cdot \left( -\frac{K}{\mu(c)} \nabla p \right) = \nabla \cdot \left( \frac{K \rho(c)}{\mu(c)} \mathbf{g} \right)$$

• Transport Equation:

  $$(1+k) \frac{\partial c}{\partial t} + \nabla \cdot \left[ c \left( -\frac{K}{\mu(c)} (\nabla p + \rho(c)\mathbf{g}) \right) \right] = D \Delta c - \kappa c$$

• Constitutive Relations:

  $$\mu(c) = \exp(Rc) \quad \text{and} \quad \rho(c) = 1 + \alpha c$$

File Structure and Data Descriptions

The following files are included in this repository:

1. Darcy_Pressure_Formulation_COMSOL.mph: The master COMSOL model file containing the weak form implementation and solver configurations.

2. c_R_1_alpha_1_kappa_0_k_0.txt: Concentration ($c$) data for $R=1, \alpha=1, \kappa=0$ at $k=0$.

3. c_R_1_alpha_1_kappa_0_k_1.txt: Concentration ($c$) data for $R=1, \alpha=1, \kappa=0$ at $k=1$.

4. c_R_1_alpha_1_kappa_0_k_2.txt: Concentration ($c$) data for $R=1, \alpha=1, \kappa=0$ at $k=2$.

5. Interfical_length_Variance_Energy_R_1_alpha_1_k_1_kappa_0.txt: Extracted physical metrics for the case ($R=1, \alpha=1, k=1, \kappa=0$).

   • Column 1: Time ($T$)

   • Column 2: Interfacial Length ($L$)

   • Column 3: Concentration Variance ($\sigma^2$)

   • Column 4: Total Kinetic Energy ($E_k$)

Instructions for Use

1. Open the .mph file in COMSOL Multiphysics® 6.3.

2. Model Configuration: The model is defined for a $100 \times 200$ vertical domain with an initial interface at $y = 100$.

3. Execution: Right-click Study 1 and select Compute.

   • Note: Due to the 2.3 million+ DOFs, a system with at least 32 GB of RAM is required.

Citation

If you use these models or data in your research, please cite:

Kundu, S. and Mishra, M., "COMSOL Multiphysics® Implementation of Pressure Formulation for Darcy-Convection-Diffusion-Reaction Flow," Zenodo (2026). DOI: 10.5281/zenodo.18891897

Contact Information

Sahil Kundu (PhD Student) & Prof. Manoranjan Mishra (Advisor)

Department of Mathematics, Indian Institute of Technology Ropar