Simulation of incompressible fluid over porous media by SPH

Document Type : Complete scientific research article

Authors

1 Ph.D. Student of Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

2 Corresponding Author, Professor, Dept. of Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

3 Associate Prof., Dept. of Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

4 Assistant Prof., Dept. of Civil Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

5 Assistant Prof., Dept. of Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran.

Abstract

Background and objectives: Simultaneous simulation of surface and subsurface flow on the bed is a prerequisite for modeling the movement of pollution in water resources and it is also considered as one of the most challenging and important modeling for protecting soil and water resources. Typically, the Navier-Stokes equations, along with a coupling method, are utilized to simulate this process. Given the inherent complexity of defining the boundary between water and porous media, a common strategy involves separately modeling fluid flow within the fluid zone. The outcomes of this fluid zone simulation are subsequently employed as essential boundary conditions for simulating the flow within the porous medium. This research, in particular, utilizes the smoothed particle hydrodynamic method (SPH) a mesh-less approach to tackle these challenges.
Materials and methods: This article aims to improve the modeling of flow in both environments by proposing a new Navier-Stokes equation with additional terms customized for each specific setting: fluid and porous media. The equations were discretized by SPH method and two steps semi-implicit method. The volume fraction of each particle is calculated in the initial and prediction steps, and the difference between the volume fraction amounts is used to calculate all variables in the current time step. To validate the model, simulation of 2D flow in a cylinder and through the porous media were considered and the results were validated base on the theoretical results.
Results: Upon comparing the estimated free surface fluid level in the cylinder using SPH with the theoretical results, the standard deviations of the ratio of calculated values to observations were found to be 0.015 for the free surface level and 0.18 for pressure. Additionally, the averages ratio of calculated values to observations for free surface level and pressure were 1.04 and 1.2, respectively. To model surface and subsurface flow in a tube containing fluid and a porous medium, the Navier-Stokes equations were solved using the SPH method.
Conclusion: This simultaneous modeling of flow in both environments mitigates errors introduced by multi-step modeling, particularly in cases of complex geometries where accurate interface setup may be challenging. In this study, an additional comparison was conducted between two placement modes of virtual particles: fixed and moving positions. Evaluation of flow velocity values revealed that the accuracy in calculating the vertical component of velocity at the interface was nearly identical for both cases. However, when comparing the horizontal component of velocity, the second case (virtual particles in motion) exhibited a standard deviation of the ratio of calculated values to observations closer to zero by 0.2 compared to the first case which is used fixed virtual particles.

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References

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Journal of Water and Soil Conservation
Volume 32, Issue 3
January 2026
Pages 137-160

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