Lattice-Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers

The thermal lattice Boltzmann equation (TLBE) with multiple-relaxation-times (MRT) collision model is used to simulate the steady thermal con- vective ows in the two-dimensional square cavity with differentially heated vertical walls at high Rayleigh numbers. The MRT-TLBE consists of two sets of distribution functions, i.e., a D2Q9 model for the mass-momentum equations and a D2Q5 model for the temperature equation. The dimension- less ow parameters are the following: the Prandtl number Pr = 0:71 and the Rayleigh number Ra = 106, 107, and 108. The D2Q9+D2Q5 MRT-TLBE is shown to be second-order accurate and to be capable of yielding results of benchmark quality, including various Nusselt numbers and local hydrody- namic intensities. The results obtained by using the MRT-TLBE agree well with existing benchmark data obtained by other methods

Lattice-Boltzmann Simulations of the Thermally Driven 2D Square Cavity at High Rayleigh Numbers

The thermal lattice Boltzmann equation (TLBE) with multiple-relaxation-times (MRT) collision model is used to simulate the steady thermal convective flows in the two-dimensional square cavity with differentially heated vertical walls at high Rayleigh numbers. The MRT-TLBE consists of two sets of distribution functions, i.e., a D2Q9 model for the mass-momentum equations and a D2Q5 model for the temperature equation. The dimensionless flow parameters are the following: the Prandtl number Pr = 0.71 and the Rayleigh number Ra = 106, 107, and 108. The D2Q9 + D2Q5 MRT-TLBE is shown to be second-order accurate and to be capable of yielding results of benchmark quality, including various Nusselt numbers and local hydrodynamic intensities. Our results also agree well with existing benchmark data obtained by other method

Double population cascaded lattice boltzmann method

Lattice Boltzmann Methods (LBM) are powerful numerical tools to simulate heat and mass transfer problems. Instead of directly integrating the N-S equations, LBM solves the discretized form of the Boltzmann Transport Equation (BTE), keeping track of the microscopic description of the systems. Therefore, LBM can solve fluid flows with great stability and computational efficiency, especially complex geometry fluid flows. For thermal flows, double distribution function (DDF) LBM scheme is the most popular and successful approach. But it is evident from the literature that existing double distribution function (DDF) LBM approaches, which use two collision operators, involve collision schemes which violate Galilean invariance, therefore producing instabilities for flows with high Re and Ra numbers. In this thesis, a double population cascaded lattice Boltzmann method is developed to improve the DDF LBM scheme from this drawback. The proposed method reduces the degree of violation of Galilean invariance, increasing the stability and accuracy of the LBM scheme. The scheme was implemented to simulate advection-diffusion, forced convection and natural convection heat transfer problems. The proposed scheme was also successfully tested for turbulent flow regimes and 3-D fluid flow in porous media. The results obtained from this work are in strong agreement with those available in the literature obtained through other numerical methods and experiments.Os métodos de ”Lattice”Boltzmann (LBM) são potentes ferramentas numéricas para simular problemas de transferência de massa e calor. Ao invés de integrar diretamente as equações de Navier-Stokes, o método LBM resolve, de forma discretizada, a equação de transporte de Boltzmann, acompanhando a descrição microscópica dos sistemas. O método LBM pode solucionar fluxo de fluidos com grande estabilidade e eficiência computacional, especialmente fluxos em geometrias complexas. Para fluxos térmicos, o esquema LBM de dupla função de distribuição (DDF) é a abordagem mais popular e bem sucedida. Mas é evidente, a partir da literatura, que as abordagens LBM de dupla função de distribuição (DDF), as quais utilizam dois operadores de colisão, envolvem esquemas de colisão que violam a invariância de Galileu, produzindo instabilidades para fluxos com números Re e Ra altos. Nesta tese, o método de ”Lattice”Boltzmann em cascata de dupla população em cascata é desenvolvido para corrigir o esquema DDF LBM. O método proposto reduz o grau de violação da invariância de Galileu, aumentando a estabilidade e acurácia do método LBM. O método foi implementado para simular problemas de advecção, difusão, convecções natural e forçada típicos de transferências de calor. O esquema proposto foi também bem sucedido em regimes de fluxo turbulento e em escoamentos 3-D em meios porosos. Os resultados obtidos neste trabalho estão fortemente de acordo com experimentos e métodos numéricos disponíveis na literatura

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time