Operator-splitting algorithm for three-dimensional convection-diffusion problems

An operator-splitting algorithm for the three-dimensional convection-diffusion equation was presented. The flow region was discretized into tetrahedronal elements which were fixed in time. The transport equation was split into two successive initial value problems: a pure convection problem and a pure diffusion problem. For the pure convection problem, solutions were found by the method of characteristics. The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point. A cubic polynomial was used to interpolate the concentration and its derivatives within each element. For the diffusion problem, an explicit finite element algorithm was employed. Numerical examples were given which agree well with the analytical solutions.