Eulerian-Lagrangian formulation of the equations for groundwater denitrification using bacterial activity

A mathematical model for groundwater denitrification using bacterial activity is presented. The model includes the momentum and mass balance equations for water and nitrogen, substrate and bacteria, and chemical reactions between them. The resulting multiphase, multicomponent, flow and transport governing equations, are coupled and nonlinear. A Eulerian-Lagrangian formulation of the equations is developed. The water and gas flow and transport equations are split into forward advection along characteristics, and a residual at a fixed frame of reference. Discontinuities, sharp fronts and steep gradients of the dependent variables are imposed on the advection mode and solved exactly. It is believed that this novel method will avoid numerical artifacts for the solution of the multiphase flow equations (e.g., upstream permeability) and numerical dispersion for the transport equation.