Development of innovative meshless methods for multiphysics and multiscale simulation of cutting-edge technologies

The research project’s scientific goals focused on enhancing the physical modelling capabilities and further developing meshless methods for solid and fluid mechanics of multiphase systems in the presence of electromagnetic (EM) fields. The project is based on: a) Further development of our following results: pioneering demonstration of coupled temporal and spatial adaptivity based on quadtree manipulation of scattered data, novel multilevel techniques for fast solution of systems of equations arising from meshless discretisations, novel techniques for stabilisation of convection dominated problems, novel meshless solvers for solution of non-Newtonian fluids, compressible flow, turbulence based on the large eddy simulation (LES), phase-field (PF) simulation of microstructure evolution, 3D simulation of magnetohydrodynamics, modelling of Stokes flow problems with free boundaries. b) Experience in implementing the listed scientific achievements in simulation systems used in industry and large international research centres. Based on spatial and temporal averaging, the improved physical models have included movement of the dispersed solid particles in gas-liquid systems, more detailed LES turbulence and more involved constitutive relations of solid mechanics models. The PF formulation has been used for compressible two-phase flow, microstructure evolution and crack propagation modelling. The EM field has been used on the macroscopic level to control the macrosegregation in solidification and on the microscopic level to control the particles’ distribution and accelerate the micro-jets. Our meshless simulation system has been developed further due to accuracy, efficiency, simple numerical implementation, modularity, a similar formulation in 2D and 3D and different possibilities of automatically controlling the quality of the results. The boundary meshless method for Stokes flow has been upgraded to solve moving-boundary problems by combining the Euler-Lagrange formulation with the transient fundamental solution. The meshless method has been formulated for enhanced stability and convergence using radial basis functions, polynomials and least-squares. The adaptivity has been extended to scattered node distribution and block-structured octree setting, combined with the implicit time-stepping formulation. The simulation system has been further modified for high-performance computing. These upgrades have enabled the development of technologies based on our own simulation tools. The driving force behind the upgrades is the need to develop a simulation of vertical continuous casting of steel and sample delivery systems for femtosecond crystallography. The study has gained experimentally verified basic knowledge on the simulation of cutting-edge meshless technologies of multiscale and multiphysics systems. The upgraded basic knowledge will be used to simulate various processes in nature and technology.

The completed research project has formed a part of the fundamental research spectra conducted at the Laboratory for Fluid Dynamics and Thermodynamics, University of Ljubljana and the Laboratory for Simulation of Materials and Processes, IMT. The research project belonged to the modern research area of modelling, simulation and optimisation of processes and materials, which plays an increasingly important role in international research because of the need for digitalisation, inexpensive products with a large know-how input, new materials and environmentally friendly technologies. Our research contents are actively integrated into this research area by their leading basic and applied components. In the framework of our fundamental research, we seek new approaches in complex multiphysics modelling of multiphase systems at multiple scales, with advanced meshfree methods for moving boundary problems, and with the development of international test cases and reference solutions for validation and verification of Stefan problems. We demonstrate leading research results in all three mentioned areas. We have among others, demonstrated the first development and application of meshless methods to industrially relevant turbulent fluid flow problems, compressible flow, two-phase flow, first application of meshless methods in point automata, and phase-field microstructure modelling. We have, among others, for the first time demonstrated discretisation independent results of macrosegregation, suggested the first international test case for continuous casting of steel, etc. Our meshless algorithms for fast online simulation of solidification in continuous casting of steel found application in more than 200 steel plants all over the World.

International education, which stems from the current research topics, found its place in cooperation with several renowned international summer schools. Further, the research project has acted as a base for graduate education in Slovenia. Two post-graduate students have completed their PhD studies (Dr. Grega Belšak, Dr. Rana Khush Bakhat) within the project.

With the gained knowledge, we have further extended our industrial impact in the metallurgical and pharmaceutical industries and large international research centres. Slovenia has approx. 100 export-oriented companies only for alloy manufacturing with 10,000 jobs. The project team has a big end-user pull from these companies. The completed research has a direct link and influence on international research areas (Europe, USA, Asia) through several international projects, mainly based on the development of new sample delivery systems in femtosecond crystallography, which are important in the development of new drugs. This demonstrates the international scientific and educational excellence and relevance of the completed research for Slovenia and beyond. The project’s contents have aligned with all three Horizon Europe research priorities: Excellent Science, Global Challenges and European Industrial Competitiveness, and Innovative Europe.

Based on the knowledge gained in this project, we have at the end of 2025, signed a contract on long-term collaboration with one of the largest producers of steel processing equipment Danieli, Butrio, Italy.

Due to the international reputation of our research, we organised the prestigious Eurotherm conference in Bled from June 10 to 13, 2024, which is held every 4 years with 350 participants from 35 countries. We were also entrusted with the organisation of the Advances in Solidification Processing conference from June 4 to 8, 2028 at Bled.