Numerical Solutions of Advection-Diffusion Equation under Local Ill-Posed Conditions

Abstract

Two-phase flow dynamics plays an important role in the understanding of the kinetics of unclear reactors and boilers. Difficulties has been reported in obtaining the numerical solution of two-phase flow by the two-fluid model which was described as basically ill-posed. Our previous paper described the behavior of the numerical solution of the heat-conduction equation under the ill-posed condition. In the present paper we show the effect of the convection term of the advection-diffusion equation under the ill-posed condition. The present study serves as an alternative to understanding the ill-posedness of the two-fluid model.