  In this paper, we consider a nonlinear and nonlocal parabolic model for
multi-species ionic fluids and introduce a semi-implicit finite volume scheme,
which is second order accurate in space, first order in time and satisfies the
following properties: positivity preserving, mass conservation and energy
dissipation. Besides, our scheme involves a fast algorithm on the convolution
terms with singular but integrable kernels, which otherwise impedes the
accuracy and efficiency of the whole scheme. Error estimates on the fast
convolution algorithm are shown next. Numerous numerical tests are provided to
demonstrate the properties, such as unconditional stability, order of
convergence, energy dissipation and the complexity of the fast convolution
algorithm. Furthermore, extensive numerical experiments are carried out to
explore the modeling effects in specific examples, such as, the steric
repulsion, the concentration of ions at the boundary and the blowup phenomenon
of the Keller-Segel equations.
