Improved angular discretization and error analysis of the lattice boltzmann method for solving radiative heat transfer in a participating medium

In this paper, some improvements to the lattice Boltzmann method (LBM) for solving radiative heat transfer in a participating medium are presented and validated. Validation of the model is performed by investigating the effects of spatial and angular discretizations and extinction coefficient on the solution. The error analysis and the order of convergence of the scheme are also reporte

From Rayleigh-B\'enard convection to porous-media convection: how porosity affects heat transfer and flow structure

We perform a numerical study of the heat transfer and flow structure of Rayleigh-B\'enard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $\phi$ in the flow properties during the transition process from the traditional RB convection with $\phi=1$ (so no obstacles included) to Darcy-type porous-media convection with $\phi$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities $\phi$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonously as a function of $\phi$; namely, with decreasing $\phi$, it first increases, before it decreases for $\phi$ approaching 0. The non-monotonous behaviour of $Nu(\phi)$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $\phi$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ vs $Ra$, namely, a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux, and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer

Do nonlinear waves in random media follow nonlinear diffusion equations?

Probably yes, since we find a striking similarity in the spatio-temporal evolution of nonlinear diffusion equations and wave packet spreading in generic nonlinear disordered lattices, including self-similarity and scaling.Comment: 6 pages, 4 figure

Thermomechanical force application

The present work conducted in Summer 1987 continues investigations on Thermal Components for 1.8 K Space Cryogenics (Grant NAG 1-412 of 1986). The topics addressed are plug characterization efforts in a small pore size regime of sintered metal plugs, characterization in the nonlinear regime, temperature profiles in a heat supply unit for a fountain effect pump and modeling efforts

Unstable Mixed Convection Flow in a Horizontal Porous Channel with Uniform Wall Heat Flux

Buoyancy-induced instability of the horizontal flow in a plane-parallel porous channel is analysed. A model of momentum transfer is adopted where a quadratic form-drag contribution is taken into account. The basic fluid flow is parallel and stationary. Due to the uniform wall heating and the effect of the buoyancy, the velocity and the vertical temperature gradient depend on the vertical coordinate. The dynamics of small-amplitude perturbations on the basic mixed convection flow is studied numerically. Transverse, longitudinal and general oblique rolls are investigated. It is proved that the longitudinal rolls are the normal modes triggering the instability at the lowest Darcy\u2013Rayleigh numbers. The condition of neutral stability is studied for different values of the form-drag parameter and of the P\ue9clet number

High Order Asymptotic Preserving DG-IMEX Schemes for Discrete-Velocity Kinetic Equations in a Diffusive Scaling

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the porous media equation, the advection-diffusion equation, and the viscous Burgers equation. Our approach is based on the micro-macro reformulation of the kinetic equation which involves a natural decomposition of the equation to the equilibrium and non-equilibrium parts. To achieve high order accuracy and uniform stability as well as to capture the correct asymptotic limit, two new ingredients are employed in the proposed methods: discontinuous Galerkin spatial discretization of arbitrary order of accuracy with suitable numerical fluxes; high order globally stiffly accurate implicit-explicit Runge-Kutta scheme in time equipped with a properly chosen implicit-explicit strategy. Formal asymptotic analysis shows that the proposed scheme in the limit of epsilon -> 0 is an explicit, consistent and high order discretization for the limiting equation. Numerical results are presented to demonstrate the stability and high order accuracy of the proposed schemes together with their performance in the limit