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Meshless Methods and Its Applications in Porous Media Problems

Submission Deadline: 31 December 2025 View: 1096 Submit to Special Issue

Guest Editors

Prof. Dr. Eldho T.I.

Email: eldho@civil.iitb.ac.in

Affiliation: Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

Homepage:

Research Interests: Groundwater Flow and Pollution Investigation; Computational Fluid Dynamics; Application of Numerical Methods in Water and Environment

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Dr. Tinesh Pathania

Email: tineshpathania@iitism.ac.in

Affiliation: Department of Environmental Science and Engineering Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad, 826004, Jharkhand, India

Homepage:

Research Interests: Groundwater Flow and Contaminant Transport Modelling, Groundwater Remediation, Meshless Models, Surface-Groundwater Interactions  

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Dr. Aatish Anshuman

Email: aanshuman@iitbbs.ac.in

Affiliation: Depart of Civil Engineering, School of Infrastructure, Indian Institute of Technology Bhubaneswar, Odisha, 751001, India

Homepage:

Research Interests: Groundwater Flow and Transport Simulation, Reactive transport, Machine learning application 

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Dr. Sanjukta Das

Email: sanjukta.das1221@gmail.com

Affiliation: Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

Research Interests: Groundwater remediation, Bioremediation, Meshless methods, Hybrid weak strong form methods, Simulation-Optimization

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Summary

The conventional numerical methods such as Finite Difference Method and Finite Element Method are based on the construction of mesh/grid. However, the processes of meshing and re-meshing can be cumbersome and, at times, computationally inefficient; these challenges are effectively addressed by meshless methods. In the meshless method, each node does not need to have a connection with its adjacent nodes. Various meshless methods have been developed in the past. Based on the formulation of the technique, the meshless methods can be broadly classified into strong form, weak form, and a combination of strong and weak form. The study of flow and transport in porous media is a critical issue with widespread applications across numerous fields, including hydrogeology, groundwater management, chemical engineering, and various branches of mechanical and metallurgical engineering. In recent years, meshless methods have gained widespread adoption in various fields, particularly for addressing complex challenges such as the simulation of groundwater flow and contaminant transport. These methods offer significant advantages in modeling problems where traditional mesh-based approaches may be less effective or efficient.


The primary aim and scope of the proposed special issue, "Meshless Methods and Their Applications in Porous Media Problems," is to curate a comprehensive collection of the latest research advancements in meshless methods, with a particular focus on their applications to porous media challenges. The proposed collection of recent research articles will illuminate current trends and offer insights into future perspectives in the field. 


Suggested Themes

· Meshless methods and their advancements.

· Application of meshless methods to various porous media problems.

· Meshless methods for groundwater flow simulation and management

· Meshless methods for contaminant transport simulation in porous media

· Meshless methods and their application for groundwater remediation

· Simulation – optimization modeling using meshless methods and AI/ ML tools


Keywords

Meshless method; Porous media problem; Groundwater flow; Contaminant transport; Radial point collocation method; Meshless Local Petrov Galerkin method; Element-free Galerkin method

Published Papers


  • Open Access

    ARTICLE

    Solving the BBMB Equation in Shallow Water Waves via Space-Time MQ-RBF Collocation

    Hongwei Ma, Yingqian Tian, Fuzhang Wang, Quanfu Lou, Lijuan Yu
    CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 3419-3432, 2025, DOI:10.32604/cmes.2025.070791
    (This article belongs to the Special Issue: Meshless Methods and Its Applications in Porous Media Problems)
    Abstract This study introduces a novel single-layer meshless method, the space-time collocation method based on multiquadric-radial basis functions (MQ-RBF), for solving the Benjamin-Bona-Mahony-Burgers (BBMB) equation. By reconstructing the time variable as a space variable, this method establishes a combined space-time structure that can eliminate the two-step computational process required in traditional grid methods. By introducing shape parameter-optimized MQ-RBF, high-precision discretization of the nonlinear, dispersive, and dissipative terms in the BBMB equation is achieved. The numerical experiment section validates the effectiveness of the proposed method through three benchmark examples. This method shows significant advantages in computational efficiency, More >

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