Heat flux expressions that satisfy the conservation laws in atomistic system involving multibody potentials

Heat flux expressions are derived for multibody potential systems by extending the original Hardy's methodology and modifying Admal & Tadmor's formulas. The continuum thermomechanical quantities obtained from these two approaches are easy to compute from molecular dynamics (MD) results, and have been tested for a constant heat flux model in two distinctive systems: crystalline iron and polyethylene (PE) polymer. The convergence criteria and affecting parameters, i.e. spatial and temporal window size, and specific forms of localization function are found to be different between the two systems. The conservation of mass, momentum, and energy are discussed and validated within this atomistic–continuum bridging.