Compact adaptive-grid scheme for high numerical resolution simulations of isotachophoresis

In a previous publication we demonstrated a fast simulation tool for solution of electrophoretic focusing and separation. We here describe the novel mathematical model and numerical algorithms used to create this code. These include the representation of advection-diffusion equations on an adaptive grid, high-resolution discretization of the equations (sixth order compact), a new variational-based approach for controlling the motion of grid points, and new boundary conditions which enable solution in a moving frame of reference. We discuss the advantages of combining a high-resolution discretization with an adaptive grid in accurately resolving sharp interfaces in isotachophoresis, and provide verification against known analytical solutions and comparison with prevailing exiting numerical algorithms.