Computer-assisted modelling method for the behavior of a steel volume having a volumetric surface

A steel volume influencing system, comprising:

• a digital mass storage device for storing a computer program;
• a computer connected to the mass storage device for execution of the computer program where the program:
• resolves a thermal conduction equation and a phase change equation to determine a subsequent state of the steel volume based on an instantaneous initial state of the steel volume and an instantaneous influence quantity via a volumetric surface on the steel volume, wherein at least one influence quantity includes a local influence for a plurality of surface elements of the volumetric surface and the local influences operate via the plurality of surface elements of the steel volume,
• identifies a local energy content of the steel volume where the initial state and the determined subsequent state for a plurality of volume elements of the steel volume comprise local proportions of modeled phases of the steel and a quantity, wherein
• the modeled phases of the steel comprise austenite and a first further phase which can transform between austenite and the first further phase, and
• the initial state and the determined subsequent state for at least one of the volume elements further comprise a local distribution in concentration of a mobile alloy element in the steel,
• determines which concentrations of the mobile alloy element are present on both sides of a first phase boundary between austenite and the first further phase for the at least one of the volume elements based upon the phase change equation,
• resolves a first Stefan problem,
• determines, based on the resolution of the Stefan problem, if the distribution in concentration of the mobile alloy element changes in an austenitic zone of the at least one of the volume elements and if the first phase boundary is displaced,
• determines the local proportions of the phases based on the position of the first phase boundary defined by the extent of the displacement of the first phase boundary, and
• determines an influence quantity based on an initial quantity determined from the initial state and a desired subsequent quantity, and
• generates an influencing signal according to the determined influence quantity;
• and
• an influencing device that receives the influencing signal from the computer and influences the temperature of the steel volume.