NUMERICAL SIMULATION OF PROCESS SYSTEMS MODELLED BY CONVECTIVE PARTIAL DIF tRENTIAL EQUATIONS

Abstract

The so)atiort method of the partial differential equation should be chosen based on its classi cat#on. We are considering the system of differential equations with two independent variables, namely one direction and one time, 1.1 Classes of partiat differentia! equations The.parcia differential equations that arise in transport phenomena are usually the first Order conservation equariaas or secg id order PDPs that are classified as elliptic, parabolic, and,hyperbolic. Partial differential equations in two independent variables, with no derivatives greater than second order, can be written, Sn general in the following Form. i 8Zu ZOtt Cu .4a2r wBc~xar+C 2+D fE Ill In this equation, the coefficients A to 0 may be zero, constant, functions of x and y only, or functions of x, y, and U. In nddit' functions of OC~lc~t or au/8x as well as arabo i coefficients: on the following relationship among the If s 4 A C> 0, the equation is hyperboisc. If B2 —4 AC ; 0, the equation is parabolic If B2 —4 A O'< I?, the equation