A joint absorbing boundary for the multiple-relaxation-time lattice Boltzmann method in seismic acoustic wavefield modeling

Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.

THE INTERACTION OF A SHOCK WAVE WITH THE BOUNDARY LAYER IN A REFLECTED SHOCK TUNNEL

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the Increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.

Wind-forced equatorial wave dynamics of the Pacific Ocean during 2014/2015 and 2015/2016 E1 Nino events

The equatorial wave dynamics of interannual sea level variations between 2014/2015 and2015/2016 El Nino events are compared using the Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics Climate Ocean Model(LICOM) forced by the National Centers for Environmental Prediction(NCEP) reanalysis I wind stre s s and heat flux during 2000-2015.In addition,the LICOM can reproduce the interannual variability of sea surface temperature anomalies(SSTA) and sea level anomalies(SLA) along the equator over the Pacific Ocean in comparison with the Hadley center and altimetric data well.We extracted the equatorial wave coefficients of LICOM simulation to get the contribution to SLA by multiplying the meridional wave structure.During 2014/2015 El Nino event,upwelling equatorial Kelvin waves from the western boundary in April2014 reach the eastern Pacific Ocean,which weakened SLA in the eastern Pacific Ocean.However,no upwelling equatorial Kelvin waves from the western boundary of the Pacific Ocean could reach the eastern boundary during the 2015/2016 El Nino event.Linear wave model results also demonstrate that upwelling equatorial Kelvin waves in both 2014/2015 and 2015/2016 from the western boundary can reach the eastern boundary.However,the contribution from stronger westerly anomalies forced downwelling equatorial Kelvin waves overwhelmed that from the upwelling equatorial Kelvin waves from the western boundary in 2015.Therefore,the western boundary reflection and weak westerly wind burst inhibited the growth of the 2014/2015 El Nino event.The disclosed equatorial wave dynamics are important to the simulation and prediction of ENSO events in future studies.

Benchmark solutions for sound propagation in an ideal wedge

Sound propagation in a wedge-shaped waveguide with perfectly reflecting boundaries is one of the few range- dependent problems with an analytical solution, and hence provides an ideal benchmark for a full two-way solution to the wave equation. An analytical solution for the sound propagation in an ideal wedge with a pressure-release bottom was presented by Buckingham and Tolstoy [Buckingham and Tolstoy 1990 J. Acoust. Soc. Am. 87 1511]. The ideal wedge problem with a rigid bottom is also of great importance in underwater acoustics. We present an analytical solution to the ideal wedge problem with a perfectly reflecting bottom, either rigid or pressure-release, which may be used to provide a means for investigating the sound field in depth-varying channels, and to establish the accuracy of numerical propagation models. Closed-form expressions for coupling matrices are also provided for the ideal waveguides characterized by a ho- mogeneous water column bounded by perfectly reflecting boundaries. A comparison between the analytical solution and the numerical solution recently proposed by Luo et al. [Luo W Y, Yang C M and Zhang R H 2012 Chin. Phys. Lett. 29 014302] is also presented, through which the accuracy of this numerical model is illustrated.

Epidemic modeling:Diffusion approximation vs.stochastic differential equations allowing reflection

A birth-death process is considered as an epidemic model with recovery and transmittance from outside.The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differential equation taking values in[0,1].For intermediate size or semilarge populations,the fraction of infected individuals is approximated by a diffusion formulated as a stochastic differential equation.That diffusion approximation however needs to be killed at the boundary{0}U{1}.An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.