Analysis of Particle Tracking Errors Associated with Spatial Discretization

Abstract This paper addresses two particular problems which arise in particle tracking calculations because of the spatial discretization used in the block‐centered finite‐difference flow model. These two problems are: (1) the presence of a “weak” sink or source (i.e., a sink or source that does not result in complete inward or outward gradients on all interfaces of the cell containing the sink or source); and (2) the use of a model grid with varying vertical cell dimensions within an individual layer. While these problems can be mitigated by using a sufficiently fine spatial discretization, there are always computational and practical limitations on the number of model nodes. Two procedures are presented in this paper which minimize particle tracking errors associated with weak sinks/sources or vertically distorted grids. The first procedure uses an approximate analytical solution to define the velocity distribution inside a model cell containing a weak sink/source so that the capture of the particles entering the cell can be determined accurately. The second procedure establishes an automatic adjustment of the particle vertical coordinate according to the degree of vertical grid distortion. These procedures are shown to be effective, and improve the accuracy of particle tracking results under nonideal spatial discretizations.