Numerical optimization studies of axi-symmetric unsteady sprays

Numerical experiments were made on a system of nonlinear, axisymmetric, unsteady equations for the modeling of realistic two-spray combustion. An alternating direction implicit (ADI) method is an efficient finite difference approach involving a solution of a set of tridiagonal matrices; the hyperbolic equations can be handled by the method of characteristics since the finite difference technique is inadequate in cases such as multivalued functions of the droplet radius and velocities. A computer code for solving model equations includes the numerical parameters of spatial mesh-size, time steps for the discretization of the differential equations and of the spray injection description, and the number of characteristics utilized.