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Large scale multiphysics and multiscale simulations based on meshless methods
Šarler, Božidar
Structure of a novel meshless solution procedure for calculation of solid and fluid mechanics problems, coupled with the electromagnetic fields, is presented. The discretisation of the governing ...coupled set of partial differential equations is defined on a set of nodes which can be non-uniformly distributed. The domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields are represented with radial basis functions collocation on a subset of nodes, present in the influence area. The micro-scale problems are tackled through transition rules between the nodes. All governing equations are solved in their strong form. The polygonisation is not present. The large deformation and growth problems are handled by node redistribution and activation of additional nodes. The solution procedure can be adapted in node redistribution and/or refinement sense, which is of utmost importance when coping with the fields exhibiting sharp gradients. The method is extremely simple to code and accurate, allowing straightforward parallelisation. Besides this, the inclusion of complicated physics is transparent, reducing the development time. The coding in 2D or 3D is almost identical. Applications to several large-scale industrial problems are shown, particularly in the field of thermomechanical processing of steel and aluminium alloys.
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