Domestic research projects


Research projects (co)funded by the Slovenian Research Agency.


  • Member of University of Ljubljana: UL Faculty of Mechanical Engineering
  • Project code: J2-1718
  • Project title: Advanced meshless modelling and simulation of multiphase systems
  • Period: 01.07.2019 - 30.06.2022
  • Range on year: 0,83 FTE
  • Head: prof. dr. Božidar Šarler
  • Research activity: Engineering sciences and technologies 
  • Research Organisation: Link
  • Researchers: Link
  • Citations for bibliographic records: Link

The scientific goals of this research project focus on enhancement of the physical modelling capabilities and further development of meshless numerical methods for multiphase systems in the presence of electromagnetic and ultrasound fields. The physical modelling of liquid-solid systems will be on the macroscopic scale based on volume-averaged multiphase formulation. The turbulent flow will be treated by large-eddy formulation. The description of free and moving boundaries on the micro and macro-scale will be based on the phase-field concept. This framework will be used to study multiscale solidification and compressible laminar two-phase flow of gas and liquid.

The meshless methods are being developed further due to accuracy, efficiency, simple numerical implementation, similar formulation in two and three dimensions and different possibilities of automatically controlling the quality of the results. The local radial basis function meshless method will be extensively upgraded with new algorithms for pressure-velocity coupling, multi-level iteration solvers, meshless block-structured adaptive node refinement, and meshless specific stabilisation of convection. The non-singular method of fundamental solutions will be further developed for accurate evaluation of Neumann boundary conditions, non-linear material response and moving and free boundary problems.

The mass, momentum, energy and species conservation equations will be simultaneously solved on microscopic and macroscopic levels. The emphasis of the project will be on modularity of the meshless simulation system and on numerical implementation on distributed memory computers. The coupling with artificial intelligence for optimisation and model reduction is foreseen. This will allow many contemporary meshless simulations in global metallurgical and pharmaceutical industry, as well as in large international research centers such as in European XFEL for femtosecond crystallography.

The model assumptions will be experimentally validated based on the predictions of new domestic and foreign laboratory and industrial experiments in the fields of liquid-gas microfluidics and liquid-solid microstructure evolution. The existing comparison exercises for Stefan problems will be complemented with new benchmarks for solidification of multicomponent systems in axisymmetry and three dimensions.

The project is based on further development of our internationally recognised and awarded breakthrough results, achieved in the last few years with meshless methods: the first demonstration of h-adaptive simulations, first solution of engineering turbulence modelling, simulation of magnetohydrodnamics and thermomechanics, large deformations, phase-field modelling of moving and free boundary problems, two-phase flow, solution of a spectrum of most complicated international solidification test cases, and a completely new meshless concept for simulations of mesoscopic microstructure evolution that is based on the point automata instead of the cellular automata. Development of numerous industrial simulation systems, based on this new precompetitive knowledge (continuous casting of aluminium alloys and steel in the presence of electromagnetic fields, thin strip casting, hot rolling, micro-jets, etc.)

The proposed study is expected to gain new, experimentally verified basic knowledge regarding the physical modelling of multiphase systems and a meshless solution of multiscale and multiphysics problems. They will influence further experimental and theoretical developments, design and education. Specific upgrades of the deduced basic knowledge will be used for simulation of various processes in nature and technology. Organisation of an international conference and summer school, dealing with Stefan problems, are scheduled in the framework of the proposed project.

The phases of the project and their realization:


Work Package 1: Refinements of the physical models

WP1 - Task 1.1: Compressible flow

WP1 - Task 1.2: Advanced nonlinear solid mechanics formulation

WP1 - Task 1.3: External fields (electromagnetic and ultrasound fields)

WP1 - Task 1.4: Multiscale coupling


Work Package 2: Advances in meshfree methods

WP2 - Task 2.1: Novel algorithms for pressure-velocity couplings

WP2 - Task 2.2: Multi-level iterative solvers for linear problems

WP2 - Task 2.3: Meshless block-structured adaptive node refinement

WP2 - Task 2.4: Meshless-specific stabilisation of convection

WP2 - Task 2.5: Non-singular method of fundamental solutions

WP2 - Task 2.6: Parallel implementation


Work Package 3: Artificial intelligence

WP3 - Task 3.1: Optimisation

WP3 - Task 3.2: Reduced models


Work Package 4: Experimental methods, verification and validation

WP4 - Task 4.1: New verification benchmark tests

WP4 - Task 4.2: Laboratory measurements in Slovenia and Germany

WP4 - Task 4.3: Industrial measurements in Slovenia and China