A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method

A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales

Arrhenius Rate Chemistry Informed Inter-phase Source Terms (ARCIIST) for Macro-Scale Explosive Hydrocodes

A critical factor in hydrocodes designed to simulate explosive material is defining the chemical reaction rate under various conditions. This rate determines how quickly the granular solid explosive is converted to its gaseous products. Currently, the state of the art for macro-scale hydrocodes is to use one of numerous burn models. These burn models are designed to estimate the bulk chemical reaction rate. Unfortunately, these burn rate models are largely based on empirical data and must be recalibrated for every new material being simulated. This research proposes that the use of Arrhenius Rate Chemistry Informed Interphase Source Terms (ARCIIST) in place of these burn models will not only reduce the reliance of simulations on empirically derived data but will also improve the accuracy for these computational codes. ARCIIST was tested by incorporating an Arrhenius reacting chemistry model developed for the cyclic-nitramine RDX by the Naval Research Laboratory (NRL) into the Air Force Research Laboratory\u27s (AFRL) Multi-Phase Explosive Simulation (MPEXS) continuum hydrocode. ARCIIST demonstrated a unique ability to capture critical features in the deflagration to detonation transition process which were washed out by the common pressure-dependent burn models sunder the same conditions. Furthermore, ARCIIST has successfully linked micro-scale chemical kinetics to macro-scale hydrodynamics. It is, therefore, a critical piece to connecting predictive theoretical chemical kinetics to system scale simulations with less reliance on empirical data

The error of the splitting scheme for solving evolutionary equations

AbstractThe accuracy of splitting method is investigated in an abstract Cauchy problem and is shown to be first order in time for general evolutionary equations except for a special case. A general formula for the leading term is obtained. It is also shown as an immediate consequence of the formula that the accuracy is improved from first order to second order by a simple modification. Such a modification was first proposed by Strang [1] for PDEs. Thus, the Strang result is generalized in the present paper to the case of arbitrary evolutionary equations. In particular, it is valid for practically important cases of integro-differential nonlinear kinetic equations, and therefore, there is no need to make additional error estimations in each particular case