DEVELOPMENT OF INNOVATIVE MESHLESS METHODS FOR MULTIPHYSICS AND MULTISCALE SIMULATION OF CUTTING-EDGE TECHNOLOGIES

The research project's scientific goals focus on significantly enhancing the physical modelling capabilities and further developing meshless numerical methods for complex solid and fluid mechanics of multiphase systems in the presence of electromagnetic and ultrasound fields. The project is based on: a) Further development of our internationally recognised and awarded breakthrough results achieved in the preceding basic project: 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, phase-field simulation of microstructure evolution, three-dimensional simulation of magnetohydrodynamics, modelling of Stokes flow problems with free boundaries, etc. b) Experience in implementing of listed scientific and precompetitive achievements in simulation systems used globally in industry and large international research centres. Based on spatial and temporal averaging, will the improved physical models include movement of the dispersed solid particles in gas-liquid systems, more detailed large-eddy simulation of turbulence and more involved constitutive relations of solid mechanics models. The phase-field formulation will be employed for compressible two-phase flow, microstructure evolution and crack propagation modelling. The ultrasound and electromagnetic field combination will be on the macroscopic level used to control the macrosegregation in solidification and on the microscopic level to control the particles' distribution and accelerate the micro-jets. Our original meshless simulation system is being developed further due to accuracy, efficiency, simple numerical implementation, modularity, a similar formulation in two and three dimensions and different possibilities of automatically controlling the quality of the results. The boundary meshless method for Stokes flow will be upgraded to solve moving boundary problems based on a combination of Euler-Lagrange formulation and transient fundamental solution. The strong form meshless method will be formulated for enhanced stability and convergence using radial basis functions, polynomials and several least-squares variants. The adaptivity will be extended to scattered node distribution and block-structured octree setting, combined with the implicit time-stepping formulation. The simulation system will be further modified for high-performance computing. The listed upgrades will enable the competitive development of cutting-edge technologies based on our own flexible and expandable simulation tools. The driving force of the upgrades are the needs required in developing a comprehensive simulation of vertical continuous casting of steel and sample delivery systems in femtosecond crystallography. Three brand new large investments in high-end laboratory equipment: a laser system for characterising velocity conditions in mini fluidic systems, an experimental laboratory device for continuous casting, and a high-performance supercomputing platform will be used for model validation. International test cases for Stefan's problems will be supplemented with new complex tasks. The proposed study is expected to gain new, experimentally verified basic knowledge regarding the simulation of cutting-edge technologies based on the innovative meshless solution of multiscale and multiphysics systems. It will influence further experimental and theoretical developments, design and education. Specific upgrades of the deduced basic knowledge will be used to cope with various complex processes in nature and technology. The prominent international Eurotherm 2024 conference, and summer school dealing with Stefan problems, are scheduled in the project.