Structure and Isotropy of Lattice Pressure Tensors for Multi-range Potentials

TL;DR

This paper analyzes the tensorial structure of lattice pressure tensors in multi-range lattice Boltzmann models, revealing how to better achieve isotropy and reduce spurious currents in simulations of non-ideal interfaces.

Contribution

It introduces a novel approach to constructing forcing schemes that ensure isotropy in lattice pressure tensors, improving simulation accuracy for non-ideal interfaces.

Findings

Lattice pressure tensors' isotropy can be controlled via multi-range potentials.

New forcing schemes reduce spurious currents in simulations.

The approach enhances implementation of forcing symmetries in LBM.

Abstract

We systematically analyze the tensorial structure of the lattice pressure tensors for a class of multi-phase lattice Boltzmann models (LBM) with multi-range interactions. Due to lattice discrete effects, we show that the built-in isotropy properties of the lattice interaction forces are not necessarily mirrored in the corresponding lattice pressure tensor. This finding opens a different perspective for constructing forcing schemes, achieving the desired isotropy in the lattice pressure tensors via a suitable choice of multi-range potentials. As an immediate application, the obtained LBM forcing schemes are tested via numerical simulations of non-ideal equilibrium interfaces and are shown to yield weaker and less spatially extended spurious currents with respect to forcing schemes obtained by forcing isotropy requirements only. From a general perspective, the proposed analysis yields an approach for implementing forcing symmetries, never explored so far in the framework of the Shan-Chen method for LBM. We argue this will be beneficial for future studies of non-ideal interfaces.