scholarly journals Modelling Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds Using the Lattice Boltzmann Method

2021 ◽  
Vol 9 ◽  
Author(s):  
Jonathan Lemus ◽  
Allan Fries ◽  
Paul A. Jarvis ◽  
Costanza Bonadonna ◽  
Bastien Chopard ◽  
...  

Field observations and laboratory experiments have shown that ash sedimentation can be significantly affected by collective settling mechanisms that promote premature ash deposition, with important implications for dispersal and associated impacts. Among these mechanisms, settling-driven gravitational instabilities result from the formation of a gravitationally-unstable particle boundary layer (PBL) that grows between volcanic ash clouds and the underlying atmosphere. The PBL destabilises once it reaches a critical thickness characterised by a dimensionless Grashof number, triggering the formation of rapid, downward-moving ash fingers that remain poorly characterised. We simulate this process by coupling a Lattice Boltzmann model, which solves the Navier-Stokes equations for the fluid phase, with a Weighted Essentially Non Oscillatory (WENO) finite difference scheme which solves the advection-diffusion-settling equation describing particle transport. Since the physical problem is advection dominated, the use of the WENO scheme reduces numerical diffusivity and ensures accurate tracking of the temporal evolution of the interface between the layers. We have validated the new model by showing that the simulated early-time growth rate of the instability is in very good agreement with that predicted by linear stability analysis, whilst the modelled late-stage behaviour also successfully reproduces quantitative results from published laboratory experiments. The results show that the model is capable of reproducing both the growth of the unstable PBL and the non-linear dependence of the fingers’ vertical velocity on both the initial particle concentration and the particle diameter. Our validated model is used to expand the parameter space explored experimentally and provides key insights into field studies. Our simulations reveal that the critical Grashof number for the instability is about ten times larger than expected by analogy with thermal convection. Moreover, as in the experiments, we found that instabilities do not develop above a given particle threshold. Finally, we quantify the evolution of the mass of particles deposited at the base of the numerical domain and demonstrate that the accumulation rate increases with time, while it is expected to be constant if particles settle individually. This suggests that real-time measurements of sedimentation rate from volcanic clouds may be able to distinguish finger sedimentation from individual particle settling.

2015 ◽  
Vol 17 (5) ◽  
pp. 1169-1184 ◽  
Author(s):  
Pierre Lallemand ◽  
François Dubois

AbstractWe show that a single particle distribution for the “energy-conserving” D2Q13 lattice Boltzmann scheme can simulate coupled effects involving advection and diffusion of velocity and temperature. We consider various test cases: non-linear waves with periodic boundary conditions, a test case with buoyancy, propagation of transverse waves, Couette and Poiseuille flows. We test various boundary conditions and propose to mix bounce-back and anti-bounce-back numerical boundary conditions to take into account velocity and temperature Dirichlet conditions. We present also first results for the de Vahl Davis heated cavity. Our results are compared with the coupled D2Q9-D2Q5 lattice Boltzmann approach for the Boussinesq system and with an elementary finite differences solver for the compressible Navier-Stokes equations. Our main experimental result is the loss of symmetry in the de Vahl Davis cavity computed with the single D2Q13 lattice Boltzmann model without the Boussinesq hypothesis. This result is confirmed by a direct Navier Stokes simulation with finite differences.


Author(s):  
Insaf Mehrez ◽  
Ramla Gheith ◽  
Fethi Aloui ◽  
Samia Ben Nasrallah

This paper presents a Lattice Boltzmann (LB) model for incompressible axisymmetric thermal flows. The forces and source terms are added into the Lattice Boltzmann Equation (LBE) and the incompressible Navier-Stokes equations are recovered by the Chapman-Enskog expansion. The model of Zhou [1] is applied for axial, radial and azimuthal velocities and the model of Q.Li et al [2] is computed for temperature variation. The source term of the scheme is simple and without velocity gradient terms. This approach can solve problems including several physical phenomena and complicated force forms as the flow between two coaxial cylinders. Good agreement is obtained between the present work, the analytic solutions and results of previous studies in cylindrical pipe. It proves the efficiency and simplicity of the proposed model compared to other ones. The Taylor-Couette (TC) system is treated with water flow characterized by a radius ratio η = 0.5 and an aspect ratio Γ = 3.8. Three Reynolds numbers of 85, 100 and 150 are tested. The influence of the end-wall boundary conditions and the influence of thermal conditions on the flow structure and on the temperature distribution along the inner and outer cylinders are analyzed.


2016 ◽  
Vol 8 (6) ◽  
pp. 887-910 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu

AbstractIn this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.


2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Sheng Chen

To simulate turbulent buoyant flow in geophysical science, where usually the vorticity-streamfunction equations instead of the primitive-variables Navier-Stokes equations serve as the governing equations, a novel and simple thermal lattice Boltzmann model is proposed based on large eddy simulation (LES). Thanks to its intrinsic features, the present model is efficient and simple for thermal turbulence simulation. Two-dimensional numerical simulations of natural convection in a square cavity were performed at high Rayleigh number varying from 104 to 1010 with Prandtl number at 0.7. The advantages of the present model are validated by numerical experiments.


Sign in / Sign up

Export Citation Format

Share Document