Galilean invariant fluid–solid interfacial dynamics in lattice Boltzmann simulations

Flow force and torque on submerged bodies in lattice-Boltzmann methods via momentum exchange

“…No rigorous proof was presented for these methods. Both [10] and [22] present a similar methods that are based in computing the momentum exchange in a reference frame comoving with the wall.…”

“…In particular, we find that the corrections proposed in [9] and [6] are adequate when evaluating the force in a reference frame fixed to the lattice. In the spirit of our deduction of ME, we also deduce the alternative description presented in [10,22], which is based on a reference frame comoving with the body.…”

“…First, it is computationally more efficient, since it is not necessary to determine the sets A + t and A − t . As a result the method is always explicit and it presents a notorius noise decrease in force evaluation as shown in [10].…”

“…This noise have been observed before. In [10,22] the authors show some alternative methods to avoid this undesirable effect. As the time derivative of the momentum P i,t is independent of the inertial reference frame, we can recover these methods by repeating the derivation we did before by choosing, for each lattice node x A and direction i, a convenient reference frame.…”

Hydrodynamic Force Evaluation by Momentum Exchange Method in Lattice Boltzmann Simulations

“…Over the past two decades, the lattice Boltzmann method (LBM) [1][2][3][4][5] has developed into a promising and alternative numerical approach for the simulations of complex fluid flows [6][7][8][9]. Hydrodynamic force evaluation in LBM mainly includes the momentum exchange method [10][11][12][13], the stress integration method [14][15][16], the immersed boundary method [17][18][19], etc. The methods based on the boundary integration have difficulty to solve the Navier-Stokes equations on complex boundary geometries, as well as a challenge to find a suitable computational mesh to compute fluid flow [10].…”