  Operator split forcing schemes exploiting a symmetrization principle, i.e.
Strang splitting, for cascaded lattice Boltzmann (LB) methods in two- and
three-dimensions for fluid flows with impressed local forces are presented.
Analogous scheme for the passive scalar transport represented by a
convection-diffusion equation with a source term in a novel cascaded LB
formulation is also derived. They are based on symmetric applications of the
split solutions of the changes on the scalar field/fluid momentum due to the
sources/forces over half time steps before and after the collision step. The
latter step is effectively represented in terms of the post-collision change of
moments at zeroth and first orders, respectively, to represent the effect of
the sources on the scalar transport and forces on the fluid flow. Such
symmetrized operator split cascaded LB schemes are consistent with the
second-order Strang splitting and naturally avoid any discrete effects due to
forces/sources by appropriately projecting their effects for higher order
moments. All the force/source implementation steps are performed only in the
moment space and they do not require formulations as extra terms and their
additional transformations to the velocity space. These result in particularly
simpler and efficient schemes to incorporate forces/sources in the cascaded LB
methods unlike those considered previously. Numerical study for various
benchmark problems in 2D and 3D for fluid flow problems with body forces and
scalar transport with sources demonstrate the validity and accuracy, as well as
the second-order convergence rate of the symmetrized operator split
forcing/source schemes for the cascaded LB methods.
