Fluid-solid Boundary Conditions Research Articles

Modeling seismic waves in ocean with the presence of irregular seabed and rough sea surface

Abstract For the simulation of seismic wavefields in the ocean, it is very important to consider the influences of the irregular seabed and the rough sea surface. To numerically model seismic waves in the ocean, the fluid seawater and the solid seabed must be treated separately, and the air–fluid and fluid–solid boundary conditions must be considered simultaneously. A fluid–solid configuration is created with the influences of a rough sea surface and an irregular seabed to carry out wavefield simulation. Based on the boundary conformal grids, the 2D acoustic wave equations (in the fluid media), the 2D elastic wave equations (in the solid media) and two boundary conditions (at the interface between air and fluid and the interface between fluid and solid) are converted from the Cartesian coordinate system into a curvilinear coordinate system. In curvilinear coordinates, the seismic wave equations and boundary conditions are discretized with finite-difference operators. At the left, right and bottom boundaries of the model, the convolutional perfectly matched layer boundary condition is used to absorb artificial reflections. The numerical simulation results show that the snapshots and shot gathers of the rough sea surface model are more complex and contain stronger reflections than those of the flat model. The rough sea surface and the pattern of the irregular seabed have a great influence on the propagation of seismic waves in the ocean.

Modelling and analysis of slip conditions in hydrodynamic lubrication of a piston skirt-cylinder contact

Purpose After more than a century of agreement with the postulate of non-slip condition (adhesion to the wall), the study of fluid-solid boundary conditions has shown renewed interest over the past two decades. Although numerous studies have not yet been arrived to a complete description of slip phenomena, however, it appears that the influence of wetting and/or surface roughness results in a weak interaction between fluid and solid; thus, the presence of the slip phenomenon is observed at the fluid-solid interface. The purpose of this paper is to highlight the presence of the slip phenomenon at the lubricated piston skirt-cylinder contact. Design/methodology/approach For this proposal, a modified Reynolds equation and operating characteristics are determined by taking into account the slip conditions at the interface between oil-film and entire cylinder surface. Findings The findings indicate that the operating characteristics are strongly influenced when the slip conditions are taken into account at the interface between oil-film and cylinder surface. The friction force and dissipated power might be reduced to improve diesel engine performances. Originality/value Various research studies have been conducted to model the slip phenomenon in different lubricated contacts over the past two decades. However, there are no studies available concerning the piston-cylinder system. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0483/

Using a half-implicit integration scheme for the SPH-based solution of fluid–solid interaction problems

A Smoothed Particles Hydrodynamics (SPH) method for fluid dynamics is coupled with a rigid and deformable body dynamics solution to yield a framework for solving fluid–solid interaction (FSI) problems. The two-way, force–displacement, coupling of the fluid and solid phases is captured via boundary condition enforcing (BCE) markers. The partial differential equations governing each phase are discretized in space separately and the resulting ordinary and/or algebraic differential equations are integrated in time independently with coupling enforced via fluid–solid boundary conditions. Particular attention is paid to enforcing fluid incompressibility via a projection step that computes the pressure field as the solution of a linear system. The numerical solution leverages hybrid parallel computing: the rigid and flexible body dynamics is handled on the CPU using multiple cores; at the same time, the fluid phase is handled on the graphics processing unit (GPU). The methodology is validated against experimental data and numerical results obtained using two open-source solvers. Several case studies are reported to gauge the accuracy, efficiency, and scalability of the solver. The highlights of the proposed solution are: tight enforcement of fluid incompressibility; ability to handle coupled physics that combines fluid, rigid, and deformable bodies; ability to handle friction and contact; and, scalable implementation that simultaneously employs CPU and GPU computing.

Fluid Velocity Slip and Temperature Jump at a Solid Surface

A comprehensive review of current analytical models, experimental techniques, and influencing factors is carried out to highlight the current challenges in this area. The study of fluid–solid boundary conditions has been ongoing for more than a century, starting from gas–solid interfaces and progressing to that of the more complex liquid–solid case. Breakthroughs have been made on the theoretical and experimental fronts but the mechanism behind the phenomena remains a puzzle. This paper provides a review of the theoretical models, and numerical and experimental investigations that have been carried out till date. Probable mechanisms and factors that affect the interfacial discontinuity are also documented.

A comparative study of lattice Boltzmann methods using bounce‐back schemes and immersed boundary ones for flow acoustic problems

SUMMARYIn order to find applicable treatments of moving boundary conditions based on the lattice Boltzmann method in flow acoustic problems, three bounce‐back (BB) methods and four kinds of immersed boundary (IB) methods are compared. We focused on fluid–solid boundary conditions for flow acoustic problems especially the simulations of sound waves from moving boundaries. BB methods include link bounce‐back, interpolation bounce‐back and unified interpolation bounce‐back methods. Five IB methods are explicit and implicit direct‐forcing (Explicit‐IB and Implicit‐IB), two kinds of partially saturated computational methods and ghost fluid method. In order to reduce the spurious pressure generated by the fresh grid node changing from solid domain to fluid domain for BB methods and sharp IB methods, we proposed two new kinds of treatments and compared them with two existing ones. Simulations of the benchmark problems prove that the local evolutionary iteration (LI) is the best one in treatments of the fresh nodes. In addition, for standing boundary problems, although BB methods have a little higher accuracy, all the methods have similar accuracy. However, for moving boundary problems, IB methods are more appropriate than BB methods, because IB methods' smooth interpolation of pressure eld produces less disturbing spurious pressure waves. With improved treatments of fresh nodes, BB methods are also acceptable for moving boundary acoustic problems. In comparative tests in respective type, unified interpolation bounce‐back with LI, Implicit‐IB, and ghost fluid with LI are the best choices. Copyright © 2013 John Wiley & Sons, Ltd.

Elastic imaging with exact wavefield extrapolation for application to ocean-bottom 4C seismic data

A central component of imaging methods is receiver-side wavefield backpropagation or extrapolation in which the wavefield from a physical source scattered at any point in the subsurface is estimated from data recorded by receivers located near or at the Earth’s surface. Elastic reverse-time migration usually accomplishes wavefield extrapolation by simultaneous reversed-time ‘injection’ of the particle displacements (or velocities) recorded at each receiver location into a wavefield modeling code. Here, we formulate an exact integral expression based on reciprocity theory that uses a combination of velocity-stress recordings and quadrupole-dipole backpropagating sources, rather than the commonly used approximate formula involving only particle velocity data and dipole backpropagating sources. The latter approximation results in two types of nonphysical waves in the scattered wavefield estimate: First, each arrival contained in the data is injected upward and downward rather than unidirectionally as in the true time-reversed experiment; second, all injected energy emits compressional and shear propagating modes in the model simulation (e.g., if a recorded P-wave is injected, both P and S propagating waves result). These artifacts vanish if the exact wavefield extrapolation integral is used. Finally, we show that such a formula is suitable for extrapolation of ocean-bottom 4C data: Due to the fluid-solid boundary conditions at the seabed, the data recorded in standard surveys are sufficient to perform backpropagation using the exact equations. Synthetic examples provide numerical evidence of the importance of correcting such errors.

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Multiphase flow in the vascular system of wood: From microscopic exploration to 3-D Lattice Boltzmann experiments

This paper provides insights into liquid free water dynamics in wood vessels based on Lattice Boltzmann experiments. The anatomy of real wood samples was reconstructed from systematic 3-D analyses of the vessel contours derived from successive microscopic images. This virtual vascular system was then used to supply fluid–solid boundary conditions to a two-phase Lattice Boltzmann scheme and investigate capillary invasion of this hydrophilic porous medium. Behavior of the liquid phase was strongly dependent on anatomical features, especially vessel bifurcations and reconnections. Various parameters were examined in numerical experiments with ideal vessel bifurcations, to clarify our interpretation of these features.

A finite difference method for a coupled model of wave propagation in poroelastic materials

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.

Synthetic logs of multipole sources in boreholes based on the Kelvin-Voigt stress-strain relation

SUMMARY We design a numerical algorithm for wave simulation in a borehole due to multipole sources. The stress–strain relation of the formation is based on the Kelvin–Voigt mechanical model to describe the attenuation. The modelling, which requires two anelastic parameters and twice the spatial derivatives of the lossless case, simulates 3-D waves in an axisymmetric medium by using the Fourier and Chebyshev methods to compute the spatial derivatives along the vertical and horizontal directions, respectively. Instabilities of the Chebyshev differential operator due to the implementation of the fluid–solid boundary conditions are solved with a characteristic approach, where the characteristic variables are evaluated at the source central frequency. The algorithm uses two meshes to model the fluid and the solid. The presence of the logging tool is modelled by imposing rigid boundary conditions at the inner surface of the fluid mesh. Examples illustrating the propagation of waves are presented, namely, by using monopoles, dipoles and a quadrupoles as sources in hard and soft formations. Moreover, the presence of casing and layers is considered. The modelling correctly simulates the features—traveltime and attenuation—of the wave modes observed in sonic logs, namely, the P and S body waves, the Stoneley wave, and the dispersive S waves in the case of multipole sources.

A comparative study of immersed-boundary and interpolated bounce-back methods in LBE

The Interpolated Bounce-Back (IBB) method and Immersed Boundary (IB) method are compared for fluid-solid boundary conditions in the Lattice Boltzmann Equation (LBE) in terms of their numerical accuracy and computational efficiency. We carry out simulations for the flow past a circular cylinder asymmetrically placed in the channel in two dimensions with the Reynolds number Re = 20 and 100, corresponding to steady and unsteady flows, respectively. The results obtained by the LBE method are compared with the existing data. We observe that the LBE with either the IBB or IB methods for the no-slip boundary conditions exhibits a second-order rate of convergence. While the computational cost for both methods are comparable, the interpolated bounce-back method is more accurate than the immersed-boundary method with the same mesh size. Consequently the IBB method is more efficient computationally, while the IB method is easier to implement.

On a non-isothermal, non-Newtonian lubrication problem with Tresca law: Existence and the behavior of weak solutions

We consider a problem describing the motion of an incompressible, non-isothermal, and non-Newtonian fluid in a three-dimensional thin domain. We first establish an existence result for weak solutions of this problem. Then we study the asymptotic analysis when one dimension of the fluid domain tends to zero. A specific weak Reynolds equation, the limit of Tresca fluid–solid boundary conditions, and the limit boundary conditions for the temperature are obtained. The uniqueness result for the limit problem is also proved.

An evaluation of lattice Boltzmann schemes for porous medium flow simulation

We quantitatively evaluate the capability and accuracy of the lattice Boltzmann equation (LBE) for modeling flow through porous media. In particular, we conduct a comparative study of the LBE models with the multiple-relaxation-time (MRT) and the Bhatnagar–Gross–Krook (BGK) single-relaxation-time (SRT) collision operators. We also investigate several fluid–solid boundary conditions including: (1) the standard bounce-back (SBB) scheme, (2) the linearly interpolated bounce-back (LIBB) scheme, (3) the quadratically interpolated bounce-back (QIBB) scheme, and (4) the multi-reflection (MR) scheme. Three-dimensional flow through two porous media—a body-centered cubic (BCC) array of spheres and a random-sized sphere-pack—are examined in this study. For flow past a BCC array of spheres, we validate the linear LBE model by comparing its results with the nonlinear LBE model. We investigate systematically the viscosity-dependence of the computed permeability, the discretization error, and effects due to the choice of relaxation parameters with the MRT and BGK schemes. Our results show unequivocally that the MRT–LBE model is superior to the BGK–LBE model, and interpolation significantly improves the accuracy of the fluid–solid boundary conditions.

Simulations of rough interface scattering

This paper describes numerical simulations of rough interface scattering. Both Dirichlet and fluid–solid boundary conditions are treated. The Rayleigh–Fourier method is used to compute exact plane-wave scattering amplitudes and results are compared to various approximations. The small-slope approximation of Voronovich performs remarkably well, while the tangent-plane approximation is shown to miss some essential physics of scattering. It is observed that at the Rayleigh angle there is a peak in the backscattering amplitude, even for plane-wave incidence. It is argued that the statistics of plane-wave scattering amplitudes are Gaussian.