Numerical investigation on applications simulated via using lattice Boltzmann method
Authors:   , An Bo 
Published: October 2023

The present doctoral thesis is about the numerical investigation simulated via using lattice Boltzmann method (LBM), the applications cover a large scale of subjects, including
1. Mathematical-physical equations
A new lattice Boltzmann method (LBM) 9-bit model is presented to solve mathematical-physical equations, such as, Laplace equation, Poisson equation, Wave equation and Burgers equation. The main benefits of the new model proposed is that is faster than the previous existing models and has a better accuracy.
2. Lid-driven isosceles right-angled triangular cavity
We employ lattice Boltzmann simulation to numerically investigate the two-dimensional incompressible flow inside a right-angled isosceles triangular enclosure driven by the tangential motion of its hypotenuse. We analyze the bifurcation sequence that takes the flow from steady to periodic and then quasi-periodic and show that the invariant torus is finally destroyed in a period-doubling cascade of a phase-locked limit cycle. As a result, a strange attractor arises that induces chaotic dynamics.
3. Improvements for the numerical stability of original LBM
In order to study the flow behavior at high Reynolds numbers, two modified models, known as the multiple relaxation-time lattice Boltzmann method (MRT-LBM) and large-eddy-simulation lattice Boltzmann method (LESLBM), have been employed. The MRT-LBM was designed to improve numerical stability at high Reynolds numbers, by introducing multiple relaxation time terms, which consider the variations of density, energy, momentum, energy flux and viscous stress tensor. The LES-LBM model implements the large eddy simulation turbulent model into the conventional LBM, allowing to study the flow at turbulent Reynolds numbers. LES-LBM combined with Quadruple-tree Cartesian cutting grid (tree grid) was employed for the first time to characterize the flow dynamics over a cylinder and a hump, at relatively high Reynolds numbers.

La tesi doctoral està centrada en simulacions numèriques utilitzant la metodologia de lattice Boltzmann method (LBM), les aplicacions desenvolupades inclouen. 1. Equacions Físic-Matemàtiques Un nou mètode de lattice Boltzmann (LBM) anomenat 9-bit model, es utilitzat per resoldre equacions físic- matemàtiques, tal com l'equació de Laplace, l'equació de Poisson, l'equació de Ones i la de Burguers. Els majors beneficis de aquest nou model proposat son que necessita menys temps computacional i es mes precís que els models precedents. 2. Cavitat triangular isòsceles amb tapa superior lliscant. El mètode de Lattice Boltzmann ha sigut utilitzat per investigar el flux incompressible bidimensional en el interior de una cavitat triangular isòsceles on la tapa superior es desplaça. S'ha trobat tot el col·lectiu de bifurcacions que apareixen desde el flux estacionari, passant per el periòdic i per quasi-periòdic, s'ha demostrat que la estructura toroïdal es destrueix al augmentar el número de Reynolds en forma de cascada period-doubling de un cicle limit tipus phase-locked. Com a resultat, flux caòtic es induït. 3. Millores de la estabilitat numèrica del mètode original LBM Per tal de estudiar el comportament del flux a alts números de Reynolds, dos models modificats coneguts com el model de multiple-relaxation-time lattice Boltzmann method (MRT-LBM), i el model large-eddy-simulation lattice Boltzmann method (LES-LBM), han sigut utilitzats. El model MRT-LBM fou dissenyat per millorar la estabilitat numèrica a alts números de Reynolds introduint múltiples termes de relaxació, els quals consideren les variacions de densitat, energia, quantitat de moviment, flux de energia i del tensor de tensions viscoses. El model LES-LBM implementa el model de turbulència de large-eddy-simulation al model convencional de LBM, permetent així estudiar fluxos turbulents a alts números de Reynolds. El model LES-LBM combinat amb un mallat tipus tree grid, Quadripole-tree Cartesian cutting grid, ha sigut emprat per primera vegada per tal de caracteritzar el flux al voltant de un cilindre i de mig cilindre a alts números de Reynolds.