Post-stack reverse-time migration using a finite difference method based on triangular grids

Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular grids maintains the simplicity of the difference method and the precision of the finite element method. It can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. We apply a finite difference method based on triangular grids for post-stack reverse-time migration for the first time. Tests on model data verify that the combination of the two methods can achieve near-perfect results in application.

A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES

We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.

A NEW DISPLACEMENT-TYPE STABILITY EQUATION AND GENERAL STABILITY ANALYSIS OF LAMINATED COMPOSITE CIRCULAR CONICAL SHELLS WITH TRIANGULAR GRID STIFFENERS

In this paper, based on the theory of Donnell-type shallow shell, a new displacement-type stability equations is first developed for laminated composite circular conical shells with triangular grid stiffeners by using the variational calculus and generalized smeared-stiffener theory. The most general bending stretching couplings, the effect of eccentricity of stiffeners are considered. Then, for general stability of composite triangular grid stiffened conical shells without twist coupling terms, the approximate formulas are obtained for critical external pressure by using Galerkin's procedure. Numerical examples for a certain C/E composite conical shells with inside triangular grid stiffeners are calculated and the results are in good agreement with the experimental data. Finally, the influence of some parameters on critical external pressure is studied. The stability equations developed and the formulas for critical external pressure obtained in this paper should be very useful in the astronautical engineering design.

Image interpolation algorithm on a triangular grid

A new method for constructing a fitting surface on a triangular grid is presented. Assuming images are obtained by sampling from the original scene. Conventional polynomial interpolation methods generally construct the fitting surface on a square grid. Different from existing methods, the new method constructs the fitting surface on a triangular grid which can divide the original surface more detailed and improve approximation accuracy. As the quality of the image edges plays a key role in visual effects of image, the new method uses image edges as constraints to get a triangle grid. The new method constructs a cubic polynomial patch locally using image data to approximate the original surface. Experimental comparison results of the new method with other methods show that the new method can produce high-quality images and remove the zigzagging artifact.

Robust Falk-Neilan Finite Elements for the Reissner-Mindlin Plate

The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conforming or consistent in the sense that no projection/reduction is introduced.Theoretical proof and numerical confirmation are presented.

Triangular Curved Surface Construction of A Series ofArbitrary Disordered Points in Space

Constructing Bernstein-Bezier triangular interpolating curve surface interpolating a series of arbitrary disordered data points is of considerable importance for the design and modeling of surfaces with a variety of continuity information. In this article. a kind of simple and reliable algorithm that can process complex field triangular grid generating is presented, and a group of formulae for determining triangular curved surface with wholly C1 continuity are given. It can process arbitrary non-convex boundary and can be used to construct surfaces inner holes.

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameteri- zation in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in trans- versely homogeneous elliptically anisotropic media. Seis- mic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in ellipti- cally anisotropic media with an irregular surface.

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

An Application of Finite Volume WENO Schemeto Numerical Modeling of Tidal Current

A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established by use of the finite volume WENO scheme which maintains both uniform high order accuracy and an essentially non-oscillatory shock transition on unstructured triangular grid. The third order TVD Range-Kutta method is used for time discretization. The model has been firstly tested against four cases： 1） tidal forcing, 2） seiche oscillation, 3） wind setup in a closed bay, and 4） onedimensional dam-break water flow. The results obtained in the present study compare well with those obtained from the corresponding analytic solutions idealized for the above four cases. The model is then applied to the simulation of tidal circulation in the Yangpu Bay, and detailed model calibration and verification have been conducted with measured tidal current in the spring tide, middle tide, and neap tide. The overall performance of the model is in qualitative agreement with the data observed in 2005, and it can be used to calculate the flow in estuaries and coastal waters.

Modelling and simulating Chikungunya spread with an unstructured triangular cellular automata

In this work we propose a mathematical model to simulate Chikungunya spread;the spread model is implemented in a C++ cellular automata code defined on unstructured triangular grids and space visualizations are performed with Python.In order to simulate the time space spread of the Chikungunya diseases we include assumptions such as:heterogeneous human and vector densities,population mobility,geographically localized points of infection using geographical information systems,changes in the probabilities of infection,extrinsic incubation and mosquito death rate due to environmental variables.Numerical experiments reproduce the qualitative behavior of diseases spread and provide an insight to develop strategies to prevent the diseases spread.

An automatic isotropic/anisotropic hybrid grid generation technique for viscous flow simulations based on an artificial neural network

Based on the author’s previous research, a novel hybrid grid generation technique is developed by introducing an Artificial Neural Network(ANN) approach for realistic viscous flow simulations. An initial hybrid grid over a typical geometry with anisotropic quadrilaterals in the boundary layer and isotropic triangles in the off-body region is generated by the classical mesh generation method to train two ANNs on how to predict the advancing direction of the new point and to control the grid size. After inputting the initial discretized fronts, the ANN-based Advancing Layer Method(ALM) is adopted to generate the anisotropic quadrilaterals in boundary layers. When the high aspect ratio of the anisotropic grid reaches a specified value, the ANN-based Advancing Front Method(AFM) is adopted to generate isotropic triangles in the off-body computational domain.The initial isotropic triangles are smoothed to further improve the grid quality. Three typical cases are tested and compared with experimental data to validate the effectiveness of grids generated by the ANN-based hybrid grid generation method. The experimental results show that the two ANNs can predict the advancing direction and the grid size very well, and improve the adaptability of the isotropic/anisotropic hybrid grid generation for viscous flow simulations.