A partitioned two-step solution algorithm for concurrent fluid flow and stress–strain numerical simulation in solidification processes

Abstract 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 sub-surface 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 modeling 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 solid-oriented 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 computation time and other numerical aspects are also developed at the end in order to show the potential improvements of this methodology.