LAUSR

Numerical methods for modeling the behavior of an industrial aluminum electrolyzer are investigated and developed. Solving a prototype problem that brings out the specific features of aluminum electrolysis, we compare two approaches to investigating the relaxation of oscillations in an electrolyzer with a free boundary between the phases. The first approach is the classical finite-difference method while the second approach uses smoothed particle hydrodynamics (SPH). The SPH method had not been applied previously to model aluminum electrolysis and it required development in this context. In particular, a new algorithm was proposed for one of the SPH subproblems that allowed for the dependence of acceleration on the velocity. The computational characteristics and the accuracy of the two methods are compared for the relaxation of free interface oscillations. The strengths and weaknesses of the two methods are discussed, as well as their potential for applications. It is shown that SPH is applicable to more realistic three-dimensional problems, such as real-time feedback control of aluminum electrolysis that can ensure online prevention of the onset of MHD instability.