A new approach to computations of forces in magnetic fluids

The hydrostatic equilibrium of a linear magnetic fluid subject to an applied stationary magnetic field, is studied in a 2D geometry. The free boundary mechanical equilibrium equation has been solved by using a new method based on a pseudo-unsteady procedure which dynamically converge toward the equilibrium. The position of the fluid is modeled by defining a phase characteristic function w; with w = 1 in liquid and w = 0 in air. This function is numerically computed by associating at each cell of the mesh a scalar field equal to the portion of the cell area occupied by the fluid