Numerical Grid Generation: Foundations and Applications

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Numerical Grid Generation Foundations and Applications. By: Joe E. Thompson, Z.U.A. Warsi and C. Wayne Mastin. Copyright, , Joe F. Thompson. Buy Numerical grid generation: Foundations and applications on ykoketomel.ml ✓ FREE SHIPPING on qualified orders.

Seismic waveform simulation with pseudo-orthogonal grids for irregular topographic models Ying Rao. Oxford Academic. Google Scholar. Yanghua Wang. Cite Citation. Permissions Icon Permissions. Abstract In seismic waveform simulation, an irregular topography such as mountainous areas cannot be simplified to a flat surface. Numerical solutions , Tomography , Seismic tomography , Computational seismology , Wave propagation.

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Solving Poisson's eq. While orthogonality in boundary grids is necessary for properly setting any absorbing boundary condition for waveform simulation, smoothness is critical to the accuracy of waveform simulation. Open in new tab Download slide. Then a proper absorbing boundary condition is critical in cases with an irregular topography, as a small incidence angle in a flat boundary could be a big angle in an irregular boundary.

Then, the acoustic wave eq. In this example, the PML consists of 20 cells. Search ADS. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. Efficient waveform tomography for lithospheric imaging: implications for realistic, two-dimensional acquisition geometries and low-frequency data.

Numerical simulation of 2D wave propagation on unstructured grids using explicit differential operators. Tensorial formulation of the wave equation for modelling curved interfaces. Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves. Crustal seismic imaging from multifold ocean bottom seismometer data by frequency domain full waveform tomography: application to the eastern Nankai trough.

References

A numerical procedure for the generation of orthogonal body-fitted coordinate systems with direct determination of grid points on the boundary. Seismic waveform inversion in the frequency domain, part 2: fault delineation in sediments using crosshole data. Inverse theory applied to multi-source crosshole tomography I: acoustic wave-equation method. Two-dimensional velocity models from wide-angle seismic data by wavefield inversion.

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Consider a region between two boundaries, both of which are formed of cylinders with hemi-spherical caps, these being coaxial with one inside the other. Consequently, each segment of the physical boundary corresponds to a plane segment of the boundary of the transformed region that is parallel to a coordinate plane there. Warsi [15] has given an extensive collection of concepts from tensor analysis and differential geometry applicable to the generation of curvilinear coordinate systems. The writing of this text has been a cooperative effort over the last two years, spurred on by the institution of a graduate course in numerical grid generation, as well as an annual short course, at Mississippi State. Interface correspondence then can be established by input by setting the image-point correspondence on the appropriate block sides, i. Some slightly more complicated examples of the alternatives introduced above now follow: Still another alternative in this case would be to collapse the intrusion to a slit in the transformed region: Here the physical cartesian coordinates are specified and are double-valued on the vertical slit, , in the transformed region. The implementation of algebraic turbulence models is more reliable with near-orthogonality at the boundary, since information on local boundary normals is usually required in such models.

Multiscale imaging of complex structures from multifold wideaperture seismic data by frequency-domain full-waveform tomography: application to a thrust belt. Google Preview. New curvilinear scheme for elastic wave propagating in presence of curved topography. Direct control of the grid point distribution in meshes generated by elliptic equations. A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging.

Crosshole seismic waveform tomography, I: strategy for real data application. Traction image method for irregular free surface boundaries in finite difference seismic wave simulation. Considering the second equation in Poisson's eq. The body-fitted grid method can also generate 3-D meshes for irregular topography, by adding another dimension in the eq. Issue Section:. Download all figures. View Metrics. Email alerts New issue alert.

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Elliptic grid generation based on Laplace equations and algebraic transformations S. A general three-dimensional elliptic grid generation system on a composite block structure Joe F. Three-dimensional elliptic grid generation about fighter aircraft for zonal finite-difference computations Reese L. A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation Reese L. Wayne Mastin.

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Elliptic grid generation system: control functions revisited—I Bharat K. Numerical grid generation in arbitrary surfaces through a second-order differential-geometric model Z. Numerical grid generation: foundations and applications Joe F. Thompson , Z. One might, therefore, infer that structured grids might not meet some of those requirements — otherwise, why bother with hybrid — and that would be correct. Structured grids have a reputation for taking a long time to generate. On the other hand, structured grids give you two things that unstructured meshes may lack: quality and control.

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Because unstructured and hybrid meshing algorithms are highly automated you necessarily give up some control. The control afforded to you by structured grids ensure that you generate precisely the grid you need. Also, structured grids or more specifically, hexahedral cells are widely acknowledged to be superior to unstructured meshes tet cells. Another example of the use of structured grids for aeroacoustic applications is the airfoil grid we generated for a test case from the 2nd workshop benchmark problems for airframe noise computations BANC-II , shown in Figure 3.

These last two bullet points are why boundary layers are best modeled in an unstructured mesh with prism layers: they provide structure in the direction away from the wall. The good news is that Pointwise has an extensive suite of structured grid technology dating back to and the birth of its predecessor, Gridgen. In fact, structured grids should be viewed in equal light with Pointwise's other meshing tools in terms of breadth of applicability and depth of capability.

Rather than delving into the issue of quantifying why and how structured grids may be better than unstructured a topic for another article , this article will review and highlight Pointwise's capabilities in structured grid generation. This structure contrasts with an unstructured mesh in which a connectivity table has to be maintained and queried to find any point's neighbors. In fact, structure is the source of one of the benefits of structured grids in terms of computational performance. Finding neighbors directly via the structure is much faster and uses less memory than having to look them up in a table i.

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The best - and freely available - online reference for structured grid generation is the classic text by Joe Thompson et al, Numerical Grid Generation: Foundations and Applications [Reference 3]. There are many mathematical methods with which structured grids can be generated. Pointwise's suite, though not comprehensive, provides a broad range of capability that can be applied to virtually any type of geometry.

Note that the use of structured grids implies that the distribution of boundary points has been performed in a manner such that dimensions number of grid points of opposite boundaries are identical. Domains surface grids will have four boundaries edges and blocks volume grids will have six boundaries faces. These topological considerations won't be discussed in what follows, only the grid methods themselves.

Handbook of Grid Generation

Algebraic methods in Pointwise serve two purposes. First, they initialize the grid in every domain and block. That grid will be sufficient in terms of cell quality for many geometries. In other cases, this algebraic grid serves as the starting point for elliptic PDE methods described below. Transfinite interpolation TFI is a very simple set of algebraic equations i. In other words, the location of each interior grid point is computed based on the locations of the grid's boundary points. TFI is applied automatically in Pointwise to initialize structured surface and volume grids, domains and blocks respectively.

Because TFI is a relatively fast computation an 88x88x88 block takes only a second to TFI on a laptop , it isn't actually applied to a block until that block's grid points are needed e. Cell quality in a TFI'd grid is influenced by the choice of interpolants. You have three interpolant choices in Pointwise.