Decomposition solution of multidimensional groundwater equations

SummaryThe method of decomposition of Adomian is an approximate analytical series to solve linear or nonlinear differential equations. An important limitation is that a decomposition expansion in a given coordinate explicitly uses the boundary conditions in such axis only, but not necessarily those on the others. This paper presents improvements of the method that permit the practical consideration of all of the conditions imposed on multidimensional initial-value and boundary-value problems governed by (nonlinear) groundwater equations, and the analytical modeling of irregularly-shaped heterogeneous aquifers subject to sources and sinks. The method yields simple solutions of dependent variables that are continuous in space and time, which easily permit the derivation of heads, gradients, seepage velocities and fluxes, thus minimizing instability. It could be valuable in preliminary analysis prior to more elaborate numerical analysis.

Research highlights
► We develop improvements of Adomian’s decomposition to problems in higher-dimensional domains.
► Combining partial decomposition yields a simple solution that uses all boundary conditions.
► Irregularly geometries, heterogeneity, nonlinearity, and multiple wells, are easily considered.