Numerical solutions for isoelectric focusing and isotachophoresis problems

This study combines an adaptive mesh redistribution (AMR) method and the space–time conservation element and solution element (CESE) method to construct a high-resolution scheme for the solution of electrophoresis pre-concentration and separation problems. In the proposed AMR–CESE scheme, the fine mesh points are moved toward the regions of discontinuity within the solution domain in accordance with the equidistribution principle. To reduce the numerical dissipation within the regions of the solution domain with a large spatial mesh, the spatial component of the CESE scheme is treated using a Courant–Friedrichs–Lewy (CFL) number insensitive scheme. The validity of the proposed approach is confirmed by comparing the results obtained for typical isoelectric focusing (IEF) and isotachophoresis (ITP) problems with those obtained from the conventional CESE scheme and the finite volume method (FVM), respectively. It is shown that the AMR–CESE scheme yields a better accuracy than uniform fixed-mesh solvers with no more than a minor increase in the computational cost.