Discrete differential operators on a class of lattices

Abstract

Lattice differential operators are known to preserve key properties of their analytical counterpart, such as isotropy, fundamental vector identities due to the symmetries of the discrete kinetic lattice. Here, we present the idea of discrete lattice operators derived on a body-centered-cubic (BCC) lattice. These operators show quite a high degree of accuracy and isotropy as compared to the earlier simple cubic (SC) representations of the same while maintaining a relatively smaller stencil. To illustrate the usefulness of these schemes, we have considered a couple of examples, such as passive scalar transport and fluctuating hydrodynamics.