Abstract

A method of numerical calculation of the magnetic field in the current-carrying liquid based on the calculation of the integral Bio-Savart-Laplace applied to the study of the characteristics of the eleсtrovortex flows taking place in the the electroarc and electroslag melting furnaces was developed. The developed methodology is focused on the use of unstructured grids and does not require a priori information about the shape of the calculational area . Programming technology for GPU NVIDIA CUDA using GTX660 graphics card was used to accelerate calculations. The method "fast Fast Inverse Square Root has been used to optimize operations, square root and division. The technique has been tested on the problem having an analytical solution – finding the magnetic field distribution in a circular cylinder in a two and three-dimensional cases.

A good agreement between analytical and numerical solutions and an increase of the calculational rate up to 110 times for the three-dimensional problem and up to 44 times for the two-dimensional axisymmetric problem compared with the calculation on the CPU Intel Core i7 2600k processor with a clock frequency of 3.4 GHz has been got.

Keywords

Magnetic field, electrovortex flow, NVIDIA CUDA, fast inverse square root, Biot–Savart law, electric current.