  We present faster algorithms for approximate maximum flow in undirected
graphs with good separator structures, such as bounded genus, minor free, and
geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a
recursive $\sqrt{n}$-vertex separator structure, our algorithm finds an
$1-\epsilon$ approximate maximum flow in time $\tilde{O}(m^{6/5}
\poly{\epsilon^{-1}})$, ignoring poly-logarithmic terms. Similar speedups are
also achieved for separable graphs with larger size separators albeit with
larger run times. These bounds also apply to image problems in two and three
dimensions.
  Key to our algorithm is an intermediate problem that we term grouped $L_2$
flow, which exists between maximum flows and electrical flows. Our algorithm
also makes use of spectral vertex sparsifiers in order to remove vertices while
preserving the energy dissipation of electrical flows. We also give faster
spectral vertex sparsification algorithms on well separated graphs, which may
be of independent interest.
