The project “Innovative Numerical Methods for Non-Newtonian Flows and Porous Media” (InNoPor) seeks to position itself at the forefront of applied research, proposing an ambitious program to overcome the limitations of current numerical methods in the simulation of complex fluids through porous media.

The initiative, funded by the European Union's Horizon Europe program, brings together an interdisciplinary consortium of eight institutions from Europe and Latin America and promises to generate more accurate and scalable tools with a potential impact ranging from carbon capture to medicine.

Six European universities are participating: Universidade da Coruña - UDC (Spain), Rheinisch-Westfälische Technische Hochschule Aachen - RWTH (Germany), Christian-Albrechts-Universität zu Kiel - CAU (Germany), Forschungsverbund Berlin - WIAS (Germany) and Agencia Estatal Consejo Superior de Investigaciones Científicas - CSIC-IGME (Spain), University of Strathclyde - UoS (United Kingdom); and two Latin American universities: Universidad de Concepción (UdeC) and Universidad del Bío-Bío (UBB).

From the UdeC, the director of the Center for Research in Mathematical Engineering, CI²MA, Dr. Rodolfo Araya Durán, is part of the consortium. "Collaborative work is at the heart of our work as a research center. Contact with colleagues from different scientific and/or disciplinary contexts can only enrich scientific dialogue, which normally translates into significant advances in the discipline," said the academic from the Department of Mathematical Engineering of the Faculty of Physical and Mathematical Sciences.

“This is what this European project aims to do: generate synergies for the advancement of mathematics and its applications,” emphasized the researcher from the Mathematical Modeling Center at the University of Chile.

The complexity of flow and the numerical challenge

The fundamental challenge addressed by InNoPor lies in the difficulty of accurately modeling non-Newtonian flows—those whose viscosity changes with the force applied, such as polymers or magma—through porous media.

Phenomena such as the injection of fluids into underground reservoirs to improve oil extraction, the dispersion of volcanic ash in the atmosphere, or the transport of drugs in biological tissues depend on this complex interaction, but existing models lack the robustness and efficiency necessary for reliable predictions.

InNoPor responds to this gap with an innovative proposal based on the development and rigorous analysis of advanced methodologies, including IMEX (Implicit-Explicit) temporal discretization schemes, adaptive mesh methods (AFEM), and stabilized formulations. The overall objective is to advance applied mathematics by designing, analyzing, and implementing numerical methods that combine precision, stability, and computational scalability.

Scientific excellence with global impact

This collaboration between researchers from European and Chilean institutions not only fosters scientific synergy in the fields of applied mathematics, Fluid Mechanics, Computer Science, and Earth System Science, but also establishes a framework for knowledge transfer through structured training programs and a total of 49 months of planned exchanges, ensuring that researchers gain experience in cutting-edge techniques and real geological applications.

The potential application of InNoPor transcends academia, with direct implications for the five mission areas of the Horizon Europe program and the UN Sustainable Development Goals (SDGs).

In terms of climate and environmental challenges, InNoPor's advanced modeling is crucial for CO₂ capture and storage (CCS) in the subsurface and for the remediation of contaminated soils and aquifers through the injection of reactive or biocompatible fluids. This contributes directly to ‘Adaptation to climate change’ (Horizon Europe) and SDG 13 (Climate Action). In addition, accurate simulations will support the design of porous barriers to mitigate pollution in marine and coastal environments and improve water filtration technologies, aligning with SDG 6 (Clean Water and Sanitation).

In other areas, the project results will inform the development of underground thermal energy storage systems using non-Newtonian fluids, which are essential for sustainable district heating and cooling and contribute to SDG 7 (Affordable and Clean Energy) and the mission of ‘Climate-neutral and smart cities’.

In addition, in geophysics, the methods will be applied to simulate realistic scenarios, such as ash dispersion and lava flows from volcanic eruptions, improving risk assessment. The project also has biomedical applications by simulating the flow of non-Newtonian fluids in porous tissues, which is relevant to drug delivery and tumor growth, connecting with the EU's ‘Cancer: technical innovation for efficiency’ mission.

Technically, the project focuses on resolving simulation bottlenecks. InNoPor will work on the proposal and mathematical analysis of IMEX schemes for nonlinear flows, spatial stabilization to ensure the positivity of densities, and the complete numerical analysis of finite element methods (FEM) for power-law fluids through porous media.

A crucial point is the development of stable and convergent solutions for inverse problems in filtration and chromatography, which are fundamental for inferring unknown properties of porous media from measurable data.

The project covers a period of 48 months and evolves from a Technology Readiness Level (TRL) 3 to TRL 5, seeking, in addition to theoretical advances, a firm commitment to open science through the creation of an open access platform that integrates new solvers and datasets, which will ensure that the computational tools developed are accessible to the academic and industrial community, maximizing the impact and long-term sustainability of this international collaboration.