Nonphysical Wave Research Articles

Space–time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation

The space–time adaptive ADER–DG finite element method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical method does not use any ideas of splitting or fractional time steps methods. The modification of the LST–DG predictor has been developed, based on a local partition of the time step in cells in which strong reactivity of the medium is observed. This approach made it possible to obtain solutions to classical problems of flows with detonation waves and strong stiffness, without significantly decreasing the time step. The results obtained show the very high applicability and efficiency of using the ADER–DG–PN method with a posteriori sub–cell limiting for simulating reactive flows with detonation waves. The numerical solution shows the correct formation and propagation of ZND detonation waves. The structure of detonation waves is resolved by this numerical method with subcell resolution even on coarse spatial meshes. The smooth components of the numerical solution are correctly and very accurately reproduced by the numerical method. Non–physical artifacts of the numerical solution, typical for problems with detonation waves, such as the propagation of non–physical shock waves and weak detonation fronts ahead of the main detonation front, did not arise in the results obtained. The results of simulating rather complex problems associated with the propagation of detonation waves in significantly inhomogeneous domains are presented, which show that all the main features of detonation flows are correctly reproduced by this numerical method. It can be concluded that the space–time adaptive ADER–DG–PN method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting is perfectly applicable to simulating fairly complex reacting flows with detonation waves.

Can towed-streamer seismic data be used for elastic wave imaging? Synthetic and field data examples

In marine seismic exploration, towed-streamer seismic data acquisition stands out as a prevalent and economical approach. These data record scalar pressure and capture P waves, including those that are converted from subseabed S waves. Theoretically, towed-streamer seismic data can be used to reconstruct S wavefields for elastic wave imaging via backward extrapolation. Our research applies an acoustic-elastic coupled equation that includes a pressure term to perform elastic reverse time migration (ERTM), using the pressure seismic data as the boundary condition for backward extrapolation. The feasibility of using towed-streamer seismic data for elastic wave imaging of complex subsurface structures is confirmed through synthetic and field data examples. The investigation demonstrates how the smoothness of velocity and density models impacts the quality of ERTM using towed-streamer seismic data. We find that using smooth velocity and density models for elastic wave imaging can enhance imaging quality by using transmitted S waves. Furthermore, certain nonphysical S waves generated during backward extrapolation can contribute to PS images, as evidenced by a synthetic data example. Overall, the results indicate that the towed-streamer seismic data for elastic wave imaging have potential in marine seismic exploration. Moving forward, it is crucial to focus on refining the quality of PS images and reducing artifacts caused by the backward-extrapolated nonphysical waves.

Developing an immersed boundary method for compressible flow

AbstractDevelopment of a 3D sharp interface ghost node immersed boundary method (IBM) within a fluid solver based on the compressible Navier–Stokes equations is underway. The objective of the IBM is to accurately apply boundary conditions at fluid–solid interfaces. The Navier–Stokes solver is currently being verified using various test cases, including the classic cylinder in cross flow. As part of this verification process, particular attention was given to investigating the effects of different lateral boundary conditions. The results demonstrate that extrapolation boundary conditions exhibit better agreement with the literature compared to symmetry conditions, in cases with relatively narrow domains. These findings highlight the potential benefits of extrapolation boundary conditions in reducing confinement effects and removing nonphysical waves in external flow problems.

Nonlinear internal wave reflection and transmission at an interface

The reflection and transmission of internal waves at a horizontal interface between layers of constant buoyancy frequency are treated. This interface is a simple model of the atmospheric tropopause. The waves are weakly nonlinear and obey the nonlinear Schrödinger equation away from the interface. The waves are horizontally periodic and vertically confined to a long packet. The interfacial conditions are formally taken to third order, and include higher-order linear as well as nonlinear effects. The higher-order linear affects show an instability at the interface for steep waves. Numerical results for shorter wave packets show that the higher-order linear terms result in non-physical wave generation, and are ultimately neglected for such cases. Nonlinear effects result in a decrease in the reflected wave amplitudes and an increase in the transmitted wave amplitudes when compared to linear theory. Overall, the nonlinear effects make the interface more transparent to upwardly propagating internal waves.

Artifact Suppression for the Joint Imaging of Primaries and Internal Multiples

Internal multiples bring great challenges for conventional seismic data imaging and interpretation, in which primaries only are regarded as signals. It is of great importance to suppress the internal multiples before conventional imaging, which is computationally expensive. Considering that internal multiples are also real reflections from the underground interfaces and reverse time migration (RTM) can realize the imaging of multiples. Instead of suppression before imaging, we propose to do the joint imaging of primaries and internal multiples based on RTM. However, the artifacts caused by the internal multiples should be suppressed to guarantee the precision. First, the imaging condition based on up-going and down-going extrapolated wavefield separation is introduced to improve the imaging accuracy. Then, the generation mechanism of image artifacts is analyzed, it concludes that nonphysical wave paths caused by the missing boundary wavefields under the surface result in the infidelity reversed-time backward-extrapolation, which is the main reason for the artifacts. Next, we propose to apply the modeling boundary wavefields with a match based on pseudomultichannel matching filter to compensate the missing boundary wavefields, which can avoid the image artifacts and realize high-precision joint imaging. Finally, the feasibility and effectiveness of the proposed method are verified by numerical examples and field data.

Time filters and spurious acoustics in artificial compression methods

Artificial compression methods are used in computational fluid dynamics as a cost-effective way of solving for the velocity and pressure in a flow. However, relaxation of compressibility in these algorithms yields nonphysical oscillations in the pressure. This report presents analysis and computational tests of time filters to reduce nonphysical acoustic waves in artificial compression methods.

Slab-geometry surface waves on steep gradients and the origin of related numerical issues in a variety of ICRF codes

In the ion cyclotron range of frequencies, electromagnetic surface waves are physically relevant for wave–filament interactions, parasitic edge losses and sheath–plasma waves. They are also important numerically, where non-physical surface waves may occur as side effects of slab-geometry approximations. We give new, completely general, mathematical techniques to construct dispersion relations for electromagnetic surface waves between any two media, isotropic or anisotropic, and first-order corrections for when the material interface is steep but continuous. We discuss numerical issues (localized non-convergence, undesired power generation) that arise in numerical calculations due to the presence of surface waves.

Anisotropic elastic finite-difference modeling of sources and receivers on Lebedev grids

The Lebedev grid finite-difference (FD) method allows modeling of anisotropic elastic-wave propagation. On Lebedev grids, erroneous point-source excitations can create spurious (nonphysical) waves. The only known remedy for such artifacts in the literature is the Lisitsa-Vishnevsky method. This method uses a distributed array to create point sources and point receivers on the FD grid. However, the Lisitsa-Vishnevsky method does not fully eliminate spurious artifacts. A novel approach is found in the FD-consistent point source, which suppresses spurious artifacts entirely. The method requires no array recording to create point receivers. The advantage of this method over the Lisitsa-Vishnevsky method is determined with two anisotropic modeling examples.

2D and 3D amplitude‐preserving elastic reverse time migration based on the vector‐decomposed P‐ and S‐wave records

ABSTRACTThe elastic reverse time migration approach based on the vector‐wavefield decomposition generally uses the scalar product imaging condition to image the multicomponent seismic data. However, the resulting images contain the crosstalk artefacts and the polarity reversal problems, which are caused by the nonphysical wave modes and the angle‐dependent reduction of image amplitudes, respectively. To overcome these two problems, we develop an amplitude‐preserving elastic reverse time migration approach based on the vector‐decomposed P‐ and S‐wave seismic records. This approach includes two key points. The first is that we employ the vector‐decomposed P‐ and S‐wave multicomponent records to independently reconstruct the PP and PS reflection images to mitigate the crosstalk artefacts. The second is that we propose two schemes in addressing the issue of polarity reversal problem in the conventional PP image. One solution is to adopt the angle‐dependent equation. Another one is to reconstruct an amplitude‐preserving PP image with a separated scalar P‐wave particle velocity, which has a clear physical meaning. Numerical examples using two‐dimensional and three‐dimensional models demonstrate that the proposed elastic reverse time migration approach can provide the images with better amplitude‐preserving performance and fewer crosstalk artefacts, compared with the conventional elastic reverse time migration approach based on the scalar product imaging condition.

Excitation of the Zenneck Wave by a Tapered Line Source Above the Earth or Ocean

A tapered vertical line source over the surface of the earth or ocean is explored as a means of communication. Two types of tapers for the line source are explored. One is a “Zenneck-wave” taper and the other is an “optimum” taper. The Zenneck-wave taper is chosen to excite the Zenneck wave to the extent possible. The Zenneck wave is a “nonphysical wave” that propagates on a semiinfinite lossy earth. The wave is nonphysical in the sense that a simple source such as a dipole will not excite a field that resembles the Zenneck wave at large distances from the source. However, by using a tapered line source, a field that resembles the Zenneck wave can be produced along the surface of the earth or ocean out to some distance. The optimum taper is chosen to optimize the field at a given horizontal distance from the line source on the surface of the earth or ocean. The optimum line source can be used to produce a field along the surface of the earth or ocean that is nearly constant over a large range of distances, something that does not seem easily attainable with other types of sources.

Effects and correction of angular momentum non-conservation in RNEMD for calculating thermal conductivity

The effects of angular momentum non-conservation in reverse non-equilibrium molecular dynamics (RNEMD) for thermal conductivity calculation are investigated. The velocity swapping operation in RNEMD results in an abnormal angular momentum flux when the center-of-mass velocity of heat source is considerable. The angular momentum is found to motivate a nonphysical wave motion at high heat flux, which was regarded as a novel heat conduction mechanism in earlier researches. This additional heat transport channel may lead to a nonphysical increase in the computed thermal conductivity. Therefore, we propose an improved RNEMD, in which the hottest/coldest atoms are selected in center-of-mass frames. The results show that the improved RNEMD can greatly reduce the nonphysical correlation at any heat flux, eliminate the wave motion mode, and give constant thermal conductivity. Our research reveals a nonphysical effect from angular momentum non-conservation in RNEMD, and provides an improved RNEMD for heat transport in solid materials.

Analysis of direction-decomposed and vector-based elastic reverse time migration using the Hilbert transform

Straightforward implementations of elastic reverse time migration (ERTM) often produce imaging artifacts associated with incorrectly imaged mode conversions, crosstalk, and back-scattered energies. To address these issues, we introduced three approaches: (1) vector-based normalized crosscorrelation imaging conditions (VBNICs), (2) directional separation of wavefields to remove low-wavenumber noise, and (3) postimaging filtering of the dip-angle gathers to eliminate the artifacts caused by nonphysical wave modes. These approaches are combined to create an effective ERTM workflow that can produce high-quality images. Numerical examples demonstrate that, first, VBNICs can produce correct polarities for PP/PS images and can compute migrated dip-angle gathers efficiently by using P/S decomposed Poynting vectors. Second, they achieve improved signal-to-noise and higher resolution when performing up/down decomposition before applying VBNICs, and left/right decomposition enhances steep dips imaging at the computational cost of adding the Hilbert transform to a spatial direction. Third, dip filtering using slope-consistency analysis attenuates the remaining artifacts effectively. An application of the SEG advanced modeling program (SEAM) model demonstrates that our ERTM workflow reduces noise and improves imaging ability for complex geologic areas.

Transport diffuse interface model for simulation of solid-fluid interaction

For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a “0=0” equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phase-density equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves, such as shear waves in fluids, are introduced by the artificial treatment. In this paper, a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.

An analysis of the Robert–Asselin time filter for the correction of nonphysical acoustics in an artificial compression method

Artificial compression methods create nonphysical acoustic waves. Time filters, often used in geophysical fluid dynamics, are shown in this paper to selectively damp these acoustics. We analyze the stability of a two‐step artificial compression method with the Robert–Asselin (RA) time filter, and provide tests delineating the filter's positive effects on both stability and accuracy.

Numerical Analysis of an Artificial Compression Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers

Magnetohydrodynamics (MHD) is the study of the interaction of electrically conducting fluids in the presence of magnetic fields. MHD applications require substantially more efficient numerical methods than currently exist. In this paper, we construct two decoupled methods based on the artificial compression method (uncoupling the pressure and velocity) and partitioned method (uncoupling the velocity and electric potential) for magnetohydrodynamics flows at low magnetic Reynolds numbers. The methods we study allow us at each time step to solve linear problems, uncoupled by physical processes, per time step, which can greatly improve the computational efficiency. This paper gives the stability and error analysis, presents a brief analysis of the non-physical acoustic waves generated, and provides computational tests to support the theory.

A conservative, second order, unconditionally stable artificial compression method

This report presents a new artificial compression method for incompressible, viscous flows. The method has second order consistency error and is unconditionally, long time, energy stable for the velocity and, weighted by the timestep, for the pressure. It uncouples the pressure and velocity and requires no artificial pressure boundary conditions. When the viscosity ν=0 the method also exactly conserves a system energy. The method is based on a Crank–Nicolson Leapfrog time discretization of the slightly compressible model (1−ε1graddiv)ut+u⋅∇u+12(divu)u−νΔu+∇p=fand ε2pt+divu=0.This report presents the method, gives a stability analysis, presents numerical tests and gives a preliminary analysis with tests of the non-physical acoustic waves generated. Consideration of the physical fidelity of the artificial compression method leads to a related method.

A numerical wave-maker for internal solitary waves with timely updated mass source/sink terms

On the basis of the two-dimensional Navier–Stokes equations, a new numerical method is proposed to generate internal solitary waves (ISWs) of expected parameters by adding a source term above the interface and a sink term below the interface into the continuity equation. Fluxes between the source and the sink are balanced to assure mass conservation, and the source/sink regions (the spatial windows over which the sink/source terms are placed) are adjusted as functions of time with the interface motion. Thus, the nonphysical trailing waves can be eliminated, which makes it easy to assure the prescribed ISW parameters. Moreover, a new layout is presented to avoid the difficulty of sizing and positioning the source/sink region, which has been proved to be an intrinsic drawback of the traditional mass source method. Numerical experiments are performed to validate the proposed method by analyzing the wave displacements and vertical profiles of velocity fields. It is shown that the numerical waveform remains stable with much less trailing waves than previous methods, and the numerical results are in good agreement with theoretical and experimental results. In addition, through sensitivity analysis, a reasonable method to determine the width of source/sink region is recommended.

Separating quasi-P-wave in transversely isotropic media with a vertical symmetry axis by synthesized pressure applied to ocean-bottom seismic data elastic reverse time migration

Quasi-P (qP)-wavefield separation is a crucial step for elastic P-wave imaging in anisotropic media. It is, however, notoriously challenging to quickly and accurately obtain separated qP-wavefields. Based on the concepts of the trace of the stress tensor and the pressure fields defined in isotropic media, we have developed a new method to rapidly separate the qP-wave in a transversely isotropic medium with a vertical symmetry axis (VTI) by synthesized pressure from ocean-bottom seismic (OBS) data as a preprocessing step for elastic reverse time migration (ERTM). Another key aspect of OBS data elastic wave imaging is receiver-side 4C records back extrapolation. Recent studies have revealed that receiver-side tensorial extrapolation in isotropic media with ocean-bottom 4C records can sufficiently suppress nonphysical waves produced during receiver-side reverse time wavefield extrapolation. Similarly, the receiver-side 4C records tensorial extrapolation was extended to ERTM in VTI media in our studies. Combining a separated qP-wave by synthesizing pressure and receiver-side wavefield reverse time tensorial extrapolation with the crosscorrelation imaging condition, we have developed a robust, fast, flexible, and elastic imaging quality improved method in VTI media for OBS data.

Stability property of numerical Cherenkov radiation and its application to relativistic shock simulations

Abstract We studied the stability property of numerical Cherenkov radiation in relativistic plasma flows employing particle-in-cell simulations. Using the implicit finite-difference time-domain method to solve the Maxwell equations, we found that nonphysical instability was greatly inhibited with a Courant–Friedrichs–Lewy (CFL) number of 1.0. The present result contrasts with recently reported results (Vay et al. 2011, J. Comp. Phys., 230, 5908; Godfrey & Vay 2013, J. Comp. Phys., 248, 33; Xu et al. 2013, Comput. Phys. Commun., 184, 2503) in which magical CFL numbers in the range 0.5–0.7 were obtained with explicit field solvers. In addition, we found employing higher-order shape functions and an optimal implicitness factor further suppressed long-wavelength modes of the instability. The findings allowed the examination of the long-term evolution of a relativistic collisionless shock without the generation of nonphysical wave excitations in the upstream. This achievement will allow us to investigate particle accelerations in relativistic shocks associated with, for example, gamma-ray bursts.

A spectral multiscale method for wave propagation analysis: Atomistic–continuum coupled simulation

In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in system description across the interface between two scales, can be satisfactorily overcome by the proposed method. We propose an efficient spectral domain decomposition of the total fine scale displacement along with a potent macroscale equation in the Laplace domain to eliminate the spurious interfacial reflection. We use Laplace transform based spectral finite element method to model the macroscale, which provides the optimum approximations for required dynamic responses of the outer atoms of the simulated microscale region very accurately. This new method shows excellent agreement between the proposed multiscale model and the full molecular dynamics (MD) results. Numerical experiments of wave propagation in a 1D harmonic lattice, a 1D lattice with Lennard-Jones potential, a 2D square Bravais lattice, and a 2D triangular lattice with microcrack demonstrate the accuracy and the robustness of the method. In addition, under certain conditions, this method can simulate complex dynamics of crystalline solids involving different spatial and/or temporal scales with sufficient accuracy and efficiency.