Higher-order schemes for 3D first-arrival traveltimes and amplitudes

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. T47-T56 ◽  
Author(s):  
Songting Luo ◽  
Jianliang Qian ◽  
Hongkai Zhao
Keyword(s):  
Point Source ◽  
Helmholtz Equation ◽  
Higher Order ◽  
Two Dimensional ◽  
Order Convergence ◽  
Third Order ◽  
First Order ◽  
First Arrival ◽  
Function Smooth ◽  
Good Agreement

In the geometrical-optics approximation for the Helmholtz equation with a point source, traveltimes and amplitudes have upwind singularities at the point source. Hence, both first-order and higher-order finite-difference solvers exhibit formally at most first-order convergence and relatively large errors. Such singularities can be factored out by factorizing traveltimes and amplitudes, where one factor is specified to capture the corresponding source singularity and the other factor is an unknown function smooth near the source. The resulting underlying unknown functions satisfy factored eikonal and transport equations, respectively. A third-order Lax-Friedrichs scheme is designed to compute the underlying functions. Thus, highly accurate first-arrival traveltimes and reliable amplitudes can be computed. Furthermore, asymptotic wavefields are constructed using computed traveltimes and amplitudes in the WKBJ form. Two-dimensional and 3D examples demonstrate the performance of the proposed algorithms, and the constructed WKBJ Green’s functions are in good agreement with direct solutions of the Helmholtz equation before caustics occur.

Comparison of Numerical and Perturbation Solutions of Two-Dimensional Nonlinear Water-Wave Problems

1976 ◽  
Vol 20 (03) ◽  
pp. 160-170
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Perturbation Theory ◽  
Numerical Solutions ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Wave System ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Past ◽  
Wave Problems ◽  
Good Agreement

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite-difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstream waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Vibroacoustic Comparisons and Acoustic Power Insulation Mechanisms of Multidirectional Stiffened Laminated Plates

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
Fourier Transform ◽  
High Efficiency ◽  
Three Dimensional ◽  
Acoustic Power ◽  
Higher Order ◽  
Laminated Plates ◽  
Transverse Displacement ◽  
Third Order ◽  
First Order ◽  
Implicit Equations

Vibroacoustic characteristics of multidirectional stiffened laminated plates with or without compliant layers are explored in the wavenumber and spatial domains with the help of the two-dimensional continuous Fourier transform and discrete inverse fast Fourier transform. Implicit equations of motion for the arbitrary angle ply laminated plates are derived from the three-dimensional higher order and Reddy third order shear deformation plate theories. The expressions of acoustic power of the stiffened laminated plates with or without complaint layers are formulated in the wavenumber domain, which is a significant method to calculate acoustic power of the stiffened plates with multiple sets of cross stiffeners. Vibroacoustic comparisons of the stiffened laminated plates are made in terms of the transverse displacement spectra, forced responses, acoustic power, and input power according to the first order, Reddy third order, and three-dimensional higher order plate theories. Sound reduction profiles of compliant layers are further examined by the theoretical deductions. This study shows the feasibility and high efficiency of the first order and Reddy third order plate theories in the broad frequency range and allows a better understanding the principal mechanisms of acoustic power radiated from multidirectional stiffened laminated composite plates with compliant layers, which has not been adequately addressed in its companion paper. (Cao and Hua, 2012, “Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers,” ASME J. Vib. Acoust., 134(5), p. 051001.)

Solving 2-D Slamming Problems by the Higher-Order MPS Method With an Improved Pressure Gradient Model

2019 ◽  
Author(s):  
Ruosi Zha ◽  
Heather Peng ◽  
Wei Qiu
Keyword(s):  
Pressure Gradient ◽  
Kernel Function ◽  
Particle Interaction ◽  
Interaction Model ◽  
Water Entry ◽  
Higher Order ◽  
Mps Method ◽  
First Order ◽  
Moving Particle ◽  
Good Agreement

Abstract A higher-order moving particle semi-implicit (MPS) method was developed to solve water entry problems. The Wendland kernel function was applied in the particle interaction model. Various models for pressure gradient were investigated. To overcome the inconsistency in the original MPS methods, a pressure gradient correction was implemented to guarantee the first-order consistency of gradient. The corrective matrix was modified by using the derivative of the kernel function. A particle shifting technique was also applied to improve the numerical stability. Validation studies were carried out for water entry of a rigid wedge with the tilting angles of 0°, 10° and 20°, and a rigid ship section. The solutions by the present method are generally in good agreement with experimental data and other published numerical results.

On Some Physical Properties of a Unified Lepton-Hadron Field Model with Composte Bosons

1982 ◽  
Vol 37 (11) ◽  
pp. 1295-1300 ◽  
Author(s):  
H. Stumpf
Keyword(s):  
Physical Properties ◽  
Permutation Group ◽  
Field Model ◽  
Higher Order ◽  
Lepton Number ◽  
Third Order ◽  
First Order ◽  
Unified Field ◽  
Intrinsic Parity ◽  
Pseudo Color

In preceding papers a lepton-hadron unified field model was introduced by means of a third order nonlinear spinorfield equation. In this paper an improved interpretation to this model is given which tries to incorporate the advantages of various current matter models and to avoid their drawbacks. In particular charge and lepton number are introduced, while the extended unstable baryon states are distinguished from lepton states by an intrinsic parity. A theorem is derived which allows a biunique decomposition of the nonlinear higher order spinorfield equation into nonlinear first order spinorfield equations and the simultaneous introduction of a permutation group of the subfields. These subfields are identified as pseudo-color fields.

A Class of Hybrid DG/FV Methods for Conservation Laws III: Two-Dimensional Euler Equations

2012 ◽  
Vol 12 (1) ◽  
pp. 284-314 ◽  
Author(s):  
Laiping Zhang ◽  
Wei Liu ◽  
Lixin He ◽  
Xiaogang Deng
Keyword(s):  
Euler Equations ◽  
Lower Order ◽  
Wave Interaction ◽  
Weak Shock ◽  
Higher Order ◽  
Two Dimensional ◽  
Dynamic Reconstruction ◽  
Third Order ◽  
Dg Method ◽  
Hybrid Grids

AbstractA concept of “static reconstruction” and “dynamic reconstruction” was introduced for higher-order (third-order or more) numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods had been developed for one-dimensional conservation law using a “hybrid reconstruction” approach, and extended to two-dimensional scalar equations on triangular and Cartesian/triangular hybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piece-wise polynomial are computed locally in a cell by the traditional DG method (called as “dynamic reconstruction”), while the higher-order derivatives are re-constructed by the “static reconstruction” of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FV schemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstrate the performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction, subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonic flow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FV method achieves the desired third-order accuracy, and the applications demonstrate that they can capture the flow structure accurately, and can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy.

scholarly journals Tunable layered-magnetism–assisted magneto-Raman effect in a two-dimensional magnet CrI3

2020 ◽  
Vol 117 (40) ◽  
pp. 24664-24669
Author(s):  
Wencan Jin ◽  
Zhipeng Ye ◽  
Xiangpeng Luo ◽  
Bowen Yang ◽  
Gaihua Ye ◽  
...  
Keyword(s):  
Phonon Scattering ◽  
Raman Effect ◽  
Higher Order ◽  
Magnetic Phase Transitions ◽  
Two Dimensional ◽  
Phonon Coupling ◽  
Scattering Mechanism ◽  
First Order ◽  
Critical Magnetic Fields ◽  
The Rich

We used a combination of polarized Raman spectroscopy experiment and model magnetism–phonon coupling calculations to study the rich magneto-Raman effect in the two-dimensional (2D) magnet CrI3. We reveal a layered-magnetism–assisted phonon scattering mechanism below the magnetic onset temperature, whose Raman excitation breaks time-reversal symmetry, has an antisymmetric Raman tensor, and follows the magnetic phase transitions across critical magnetic fields, on top of the presence of the conventional phonon scattering with symmetric Raman tensors in N-layer CrI3. We resolve in data and by calculations that the first-order Ag phonon of the monolayer splits into an N-fold multiplet in N-layer CrI3 due to the interlayer coupling (N≥2) and that the phonons within the multiplet show distinct magnetic field dependence because of their different layered-magnetism–phonon coupling. We further find that such a layered-magnetism–phonon coupled Raman scattering mechanism extends beyond first-order to higher-order multiphonon scattering processes. Our results on the magneto-Raman effect of the first-order phonons in the multiplet and the higher-order multiphonons in N-layer CrI3 demonstrate the rich and strong behavior of emergent magneto-optical effects in 2D magnets and underline the unique opportunities of spin–phonon physics in van der Waals layered magnets.

Closed-form representations of iterated Darboux transformations for the massless Dirac equation

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150064
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Closed Form ◽  
Scalar Potential ◽  
Higher Order ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
First Order ◽  
Dirac Systems ◽  
Form Representation ◽  
Exactly Solvable

It is shown that first-order Darboux transformations for the two-dimensional massless Dirac equation with scalar potential and for the Schrödinger equation are the same up to a change of coordinates. As a consequence, we obtain a closed-form representation of iterated, higher-order Darboux transformations for our Dirac equation. We use the formalism to generate several new exactly-solvable Dirac systems through higher-order Darboux transformations.

scholarly journals GENERATION OF HIGHER ORDER NONCLASSICAL STATES VIA AN INTENSE ELECTROMAGNETIC FIELD

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1421-1427 ◽  
Author(s):  
ANIRBAN PATHAK
Keyword(s):  
Anharmonic Oscillator ◽  
Higher Order ◽  
Intense Laser ◽  
Squeezed State ◽  
Order Operator ◽  
Nonclassical States ◽  
Third Order ◽  
Operator Solution ◽  
First Order ◽  
Model Hamiltonian

Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of generation of higher order nonclassical states. It is found that the higher order squeezed and higher order antibunched states can be produced by this interaction. It is also shown that the higher order nonclassical states may appear separately, i.e. a higher order antibunched state is not essentially higher order squeezed state and vice versa.

On higher-order wave theory for submerged two-dimensional bodies

1969 ◽  
Vol 38 (2) ◽  
pp. 415-432 ◽  
Author(s):  
Nils Salvesen
Keyword(s):  
Free Surface ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Drag ◽  
Higher Order ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
Free Surface Waves ◽  
Body Shapes

The importance of non-linear free-surface effects on potential flow past two-dimensional submerged bodies is investigated by the use of higher-order perturbation theory. A consistent second-order solution for general body shapes is derived. A comparison between experimental data and theory is presented for the free-surface waves and for the wave resistance of a foil-shaped body. The agreement is good in general for the second-order theory, while the linear theory is shown to be inadequate for predicting the wave drag at the relatively small submergence treated here. It is also shown, by including the third-order freesurface effects, how the solution to the general wave theory breaks down at low speeds.

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