One of the critical challenges encountered when modeling solidification processes is to achieve a concurrent and efficient computation of fluid flow and solid mechanics. Several detrimental casting defects justify this development: cracks, either as a result of stresses built at surface or subsurface in solidified regions during the filling stage of ingot casting, or due to hot tears deep in the mushy zone during solidification; macrosegregation, as a result of thermo-solutal convection flows and possible deformation of solid. It is therefore of crucial importance to provide for a global and synthetic analysis of casting processes considering a single numerical modelling that includes coupling between fluid flow and solid mechanics. A two-step solution strategy combining fluid flow and solid mechanics has been developed. A partitioned formulation is used, performing at each time increment, separately a solidoriented resolution and a fluid-oriented resolution. Liquid flow (natural convection or forced flow during ingot filling stage), solidification shrinkage as well as thermally induced deformation of the solid regions are taken into account. The paper presents the numerical formulation in a level set finite element context, and associated validation tests. Application in a practical case corresponding to an ingot filling is proposed in order to investigate the solidification process and associated fluid flow and stress evolutions. Some discussions on computations time and others numerical aspects are also developed at the end in order to show the potential improvements of this methodology.

Control of macrosegregation phenomena and deformation related defects is a main issue in steel continuous casting. Numerical simulation could help industrial engineers to master these defects.However, as a first step, it is essential to achieve a concurrent computation of fluid flow in the bulk liquid and stress-strain evolution in the already solidified regions. With this aim in view, a new specific partitioned solver has been developed to model the liquid flow, essentially induced by the inlet jet distributed by the submerged nozzle, as well as the thermal deformation of the solid shell. The solver procedure allows simulating the transient regime, up to convergence to the steady-state regime. For this purpose, the computational finite element mesh moves and grows continuously. Within this evolving mesh, three different zones are defined: the solid shell as a pure Lagrangian zone, the liquid nozzle region as a pure Eulerian zone, and an intermediate Eulerian-Lagrangian zone. Conservation equations (energy, mass, and momentum) are solved in a general arbitrary Lagrangian-Eulerian framework, with a level-set formulation to track the free surface evolution at the meniscus. The article is composed of two parts. In the first part, the model is detailed with the resolution steps involved in the coupled resolution approach. In the second part, a simple verification test case is firstly proposed, followed by a more relevant and practical application to model an industrial pilot continuous casting process.