PROTEUS: A coupled iterative force-correction immersed-boundary multi-domain cascaded lattice Boltzmann solver

Abstract

Most realistic fluid flow problems are characterized by high Reynolds numbers and complex boundaries. Over the last ten years, immersed boundary methods that are able to cope with realistic geometries have been applied to Lattice-Boltzmann (LB) methods. These methods, however, have normally been applied to low Reynolds number problems. Here we present a novel coupling between an iterative force-correction immersed boundary (Zhang et al., 2016) and a multi-domain cascaded LB method. The iterative force-correction immersed boundary method has been selected due to the improved accuracy of the computation, while the cascaded LB formulation is used due to its superior stability at high Reynolds numbers. The coupling is shown to improve both the stability and numerical accuracy of the solution. The resulting solver has been applied to viscous flow (up to a Reynolds number of 100000) passed a NACA-0012 airfoil at a 10 degree angle of attack. Good agreement with results obtained using a body-fitted Navier-Stokes solver has been obtained. The formulation provides a straight forward and efficient method for modeling realistic geometries and could easily be extended to problems with moving boundaries.

PROTEUS: A coupled iterative force-correction immersed-boundary cascaded lattice Boltzmann solver for moving and deformable boundary applications

“…(9) is explicitly modified in order to account for the presence of external forces. Therefore, as shown in our previous study [40], the overall accuracy of the surrounding flow field rather deteriorates as the number of iterations in the IBM increases. A similar result has been reported by Kang [34].…”

“…In the present study, the multi-domain algorithm of Lagrava et al [45] is used under some minor modifications as presented in our previous study [40]. The computational multi-domain algorithm is summarized in Appendix C. It is worth noting that the fine grid scales that can not be resolved by the coarse grid are removed using a filtering operator.…”

“…Wu and Shu [38] developed an implicit velocity correction-based IB-LBM based on Guo's external forcing term [39]. In the present study, the iterative force correction IB scheme proposed by Zhang et al [36] is used as described in our previous study [40]. This paper focuses on the effect of the internal mass in the computation of the aerodynamic forces for viscous fluid flows around moving and deformable boundaries at a wide range of Reynolds numbers.…”

“…This paper focuses on the effect of the internal mass in the computation of the aerodynamic forces for viscous fluid flows around moving and deformable boundaries at a wide range of Reynolds numbers. The coupled iterative direct forcing immersed boundary cascaded lattice Boltzmann method (IDF-CLBM), presented in our previous study [40], is used for the viscous fluid flow simulations. The effect of the internal mass is investigated using the Lagrangian point approximation method.…”

Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

“…Moreover, a thermal cascaded LBM (TCLBM) has been proposed by the present authors to simulate low-Mach compressible thermal flows [31], and several different CLBMs have been developed later for incompressible thermal flows [32][33][34][35][36]. Finally, CLBM has also been extended to simulate shallow water equations [37], moving boundary problems [38], as well as stationary flows with a preconditioning method [39].…”