A novel way of computing the Basset term in unsteady multiphase flow computations

The inclusion of the Basset (history) term in the equation of motion of a sphere in creeping flow increases substantially the computational time and memory requirements for a numerical solution of the trajectory of the sphere. A transformation of the equation of motion of a sphere in a fluid is obtained, in which the velocity of the sphere does not appear in the history integral. Although the transformed equation is a second-order ordinary differential equation (ODE), it is explicit in the dependent variable and presents considerable advantages in reduced computational time and memory requirements.