Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics

Lattice Boltmzmann Methods (LBM) have been proved to be very effective methods for computational aeroacoustics (CAA), which have been used to capture the dynamics of weak acoustic fluctuations. In this paper, we propose a strategy to reduce the dispersive and disspative errors of the two-dimensional (2D) multi-relaxation-time lattice Boltzmann method (MRT-LBM). By presenting an effective algorithm, we obtain a uniform form of the linearized Navier-Stokes equations corresponding to the MRT-LBM in wave-number space. Using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods, we propose a class of minimization problems to optimize the free-parameters in the MRT-LBM. We obtain this way a dispersion-relation-preserving LBM (DRP-LBM) to circumvent the minimized dispersion error of the MRT-LBM. The dissipation relation precision is also improved.And the stability of the MRT-LBM with the small bulk viscosity is guaranteed. Von Neuman analysis of the linearized MRT-LBM is performed to validate the optimized dispersion/dissipation relations considering monochromatic wave solutions. Meanwhile, dispersion and dissipation errors of the optimized MRT-LBM are quantitatively compared with the original MRT-LBM . Finally, some numerical simulations are carried out to assess the new optimized MRT-LBM schemes.Comment: 33 page

Sensitivity analysis and determination of free relaxation parameters for the weakly-compressible MRT-LBM schemes

It is well-known that there exist several free relaxation parameters in the MRT-LBM. Although these parameters have been tuned via linear analysis, the sensitivity analysis of these parameters and other related parameters are still not sufficient for detecting the behaviors of the dispersion and dissipation relations of the MRT-LBM. Previous researches have shown that the bulk dissipation in the MRT-LBM induces a significant over-damping of acoustic disturbances. This indicates that MRT-LBM cannot be used to obtain the correct behavior of pressure fluctuations because of the fixed bulk relaxation parameter. In order to cure this problem, an effective algorithm has been proposed for recovering the linearized Navier-Stokes equations from the linearized MRT-LBM. The recovered L-NSE appear as in matrix form with arbitrary order of the truncation errors with respect to ${\delta}t$. Then, in wave-number space, the first/second-order sensitivity analyses of matrix eigenvalues are used to address the sensitivity of the wavenumber magnitudes to the dispersion-dissipation relations. By the first-order sensitivity analysis, the numerical behaviors of the group velocity of the MRT-LBM are first obtained. Afterwards, the distribution sensitivities of the matrix eigenvalues corresponding to the linearized form of the MRT-LBM are investigated in the complex plane. Based on the sensitivity analysis and the recovered L-NSE, we propose some simplified optimization strategies to determine the free relaxation parameters in the MRT-LBM. Meanwhile, the dispersion and dissipation relations of the optimal MRT-LBM are quantitatively compared with the exact dispersion and dissipation relations. At last, some numerical validations on classical acoustic benchmark problems are shown to assess the new optimal MRT-LBM

Mean radiant temperature from global-scale numerical weather prediction models

In human biometeorology, the estimation of mean radiant temperature (MRT) is generally considered challenging. This work presents a general framework to compute the MRT at the global scale for a human subject placed in an outdoor environment and irradiated by solar and thermal radiation both directly and diffusely. The proposed framework requires as input radiation fluxes computed by numerical weather prediction (NWP) models and generates as output gridded globe-wide maps of MRT. It also considers changes in the Sun’s position affecting radiation components when these are stored by NWP models as an accumulated-over-time quantity. The applicability of the framework was demonstrated using NWP reanalysis radiation data from the European Centre for Medium-Range Weather Forecasts. Mapped distributions of MRT were correspondingly computed at the global scale. Comparison against measurements from radiation monitoring stations showed a good agreement with NWP-based MRT (coefficient of determination greater than 0.88; average bias equal to 0.42 °C) suggesting its potential as a proxy for observations in application studies

Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.Comment: Accepted for publication in the Journal of Computational Physic