A boundary element‐finite element procedure for porous and fractured media flow

A coupled boundary element‐finite element procedure is presented for linear and nonlinear fluid flow simulation in porous and fractured aquifers. Quadratic variation of both element geometry and fundamental singularity is used in the constitutively linear direct boundary element formulation. Compatible 3‐to 9‐noded Lagrangian finite elements are used to represent the plane flow domain for mixed linear and nonlinear flows, alike. Nodes on the external contour of the boundary element domain are only retained if flux boundary conditions are not prescribed, thus resulting in reduced matrix dimension. The geometric conductance of the linear boundary element region is evaluated only once. The resulting system matrices remain sparse, positive definite, and may be arranged for symmetry. Nonlinearity, in this context, is restricted to turbulent flow at high Reynolds numbers, although other nonlinearities may be easily accommodated using a similar procedure. A Missbach relationship is implemented to represent turbulent flow in rock fractures. Turbulent effects are confined to the finite element domain, and the resulting nonlinear equations are solved by direct iteration. Validation studies are completed against analytical solutions to linear and nonlinear flow problems. Excellent agreement is obtained with relatively sparing nodal coverage.