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This paper proposes a density-based topology optimization method for natural convection problems using the lattice Boltzmann method (LBM). As the LBM can be developed as a completely explicit scheme, its attractive features over the traditional ones, such as the finite element method, are (1) suitability for solving unsteady flow problems and (2) scalability for large-scale parallel computing. We develop an LBM code for solving unsteady natural convection problems and provide its sensitivity analysis based on the so-called adjoint lattice Boltzmann method. Notably, the adjoint equation is derived from the discrete particle velocity Boltzmann equation and can be solved similarly to the original LBM concerning unsteady natural convection problems. We first show that the proposed method can produce similar results to the previous work in a steady-state natural convection problem. We then demonstrate the efficacy of the proposed method through 2D numerical examples concerning unsteady natural convection. As a large-scale problem, we tackle a 3D unsteady natural convection problem on a parallel supercomputer. All the developed codes written in C++ are available at . [ABSTRACT FROM AUTHOR]

We consider the problem of determining the stress-strain state of an orthotropic multicomponent cylinder affected by unsteady surface elastic diffusive perturbations. The coupled system of elastic diffusion equations in the polar coordinate system is used as a mathematical model. Diffusion relaxation effects, implying finite rates of diffusion flux propagation, are taken into account. The solution to this problem is sought in the integral form and is represented as convolutions of Green's functions with functions defining surface elastodiffusive perturbations. We use the Laplace transform by time and Fourier series expansion in Bessel functions of the first kind to find Green's functions. The Laplace transform inversion is done analytically due to residues and operational calculus tables. An analytical solution to the problem is obtained. A numerical study of the interaction of mechanical and diffusion fields in a continuous orthotropic cylinder is performed. We used three-component material as an example. The cylinder is under pressure, which is uniformly distributed over it surface. We use three-component material as an example. [ABSTRACT FROM AUTHOR]

In this paper, the unsteady vibrations of an ortotropic rectangular Kirchhoff–Love plate are studied. In general formulation, the plate is under the action of longitudinal and transverse forces, bending and torque moments. It also set a diffusion fluxes density and a diffusion fluxes relaxation. The coupled elastic diffusion orthotropic multicomponent continuum model has been used to formulate the problem. The d'Alembert variational principle has been used to obtain the plate transverse elastic diffusion vibrations equations from the model. [ABSTRACT FROM AUTHOR]