  We devised a first order time stepping ensemble hybridizable discontinuous
Galerkin (HDG) method for a group of parameterized convection diffusion PDEs
with different initial conditions, body forces, boundary conditions and
coefficients in our earlier work [3]. We obtained an optimal convergence rate
for the ensemble solutions in $L^\infty(0,T;L^2(\Omega))$ on a simplex mesh;
and obtained a superconvergent rate for the ensemble solutions in
$L^2(0,T;L^2(\Omega))$ after an element-by-element postprocessing if
polynomials degree $k\ge 1$ and the coefficients of the PDEs are independent of
time. In this work, we propose a new second order time stepping ensemble HDG
method to revisit the problem. We obtain a superconvergent rate for the
ensemble solutions in $L^\infty(0,T;L^2(\Omega))$ without an element-by-element
postprocessing for all polynomials degree $k\ge 0$. Furthermore, our mesh can
be any polyhedron, no need to be simplex; and the coefficients of the PDEs can
dependent on time. Finally, we present numerical experiments to confirm our
theoretical results.
