A solution-scheme for the convective-diffusion equation
This paper presents a versatile solution-scheme for the convective- diffusion equation. A small-time, asymptotic, solution for an instantaneous point source of scalar contaminant is expressed as a three- dimensional, Hermite polynomial expansion and manipulated, using superposition, to generate the contaminant concentration field that results at larger times and for arbitrary, continuous or instantaneous, source contaminant distribution. This equation is commonly used to model contaminant dispersion in complex environmental flows so that the considerable degree of generality, flexibility and efficiency of this solution-scheme highly commends it to this application. The off-diagonal terms in the diffusivity tensor and the non-zero gradient of this term and the mean-velocity field are shown to make a significant contribution to the evolution of the contaminant concentration field resulting from the instantaneous release of contaminant from a point source.
three-dimensional, Hermite polynomial expansion
off-diagonal terms in the diffusivity tensor
scientific article; zbMATH DE number 3915919