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

Symmetrized Operator Split Schemes for Force and Source Modeling in Cascaded Lattice Boltzmann Methods for Flow and Scalar Transport