Body-fitted Grid Generation For The Geological Conditions

Grid generation is the link between geometric model and numerical algorithm, geometry model has to be divided into a certain standard grid to its numerical solution. On the geophysical studing under complicated geological conditions, the complexity of the medium makes grid generation higher demand. The rectangular grid used in finite difference presents its limitations, irregular grid has emerged as one of the main techniques to solve the problem with complex geological conditions. The current irregular mesh generation methods are interpolation method, mapping method, unstructured grid and variable grid. In the Interpolation method, the broken line is used to approximate the topography, and the value on the free surface is replaced by the value on the regular grid points. So, the method itself leads to the existence of errors; The basic idea of the mapping method is to transform the rough boundary into the horizontal border, while the physical space of the differential equations into differential equations for the calculation of space,in which the calculation of numerical simulation is implemented, The main problem is that the free boundary must be a smooth surface, In addition, the depth of physical space is reseted by division method, which will cause to bring some stability problems (such as zero-denominator problem); the basic idea of non-structural grid metheod is to use split to accommodate the irregular undulating surface and irregular, but it needs a large number of irregular grid computing, meanwhile, finite difference scheme on irregular grid is complex and cumbersome; Variable grid method means changing the grid spacing according to the needs of different regions, the grid spaceing in the adjustment field may lead to instability in numerical calculating.From the point of numerical grid generation view, this paper is to improve the deficiency of these methods. Grid is the primary problem to be solved, sometimes referred to as pre-treatment in numerical calculation. Quality of the grid is to affect the precision and efficiency of geophysical simulation. Computational domain grid generation is to be divided in accordance with certain principles, so coordinate system on the original problem is transformed to the new coordinate system to solve it. According to the practical problems to design different grid, such as grid should be more intensive in the field where gradient larger, and a new coordinate system should ensure the orthogonality near the boundary. So it's more effective and convenient, Improve accuracy and ensure the stability of solutions to simplify boundary conditions, thereby reducing the required computing time and computer capacity. Therefore, the grid should be decided by the kind of medium.Complexity of the medium in different geophysical fields for the physical structure, physical properties and spatial and temporal distribution is different, sometimes even decisive. The medium underground has two intrinsic properties, one is structural form in three-dimensional space; the other is medium in every directions is complexity of variation. Three-dimensional topography model is the approximation of the first properties– tridimensional. while the model parameters are used to describe the second media property - non-uniformity. Current geophysical problems of the complicated geological conditions are also reflected in these two areas, One is topography, the other is complex medium underground.For the issue of irregular topography, taking into account the similarity with the fluid medium, this paper introduces to generate body-fitted grid to meet the needs of grid computing. Body-fitted grid is developed in CFD, in which grid lines as irregular borders to guarantee the exact description of the surface, also it allow grid spacing and angle adjustment, the body-fitted grid based on Poisson Equation method is generated with a smooth and inherent flexibility. In addition, Hilgenstock method is used to adjust the grid orthogonality of the boundary nodes to facilitate the realization of free boundary conditions.For the issue of inhomogeneous media underground, the paper quotes adaptive grid technology. Adaptive grid generation technology to automatically adjust the distribution of media in the region use the dense low grid, high-speed region using the sparse grid, so that we can use the least amount of computation for maximum accuracy.In summary, the proposed mesh generation algorithm has the following advantages:1) Body-fitted grid can accurately describe the nature of the surface, so to avoid the error in interpolation method;2) Grid in the free boundary has good orthogonality to facilitate the realization of free boundary conditions.3) Adaptive grid generation technology enables to avoid instability in variable step grid;4) Body-fitted grid of rectangular is a kind of structure grid, so to avoid facing complex difference scheme in the non-structural grid.After the advisable grid generation of the geophysical model, the application of coordinate transformation method to achieve curved coordinate system is proposed, Numerical simulation of geophysical concept. Coordinate transformation method through the rectangular coordinate system of geophysical equations transform into curvilinear coordinate system grid to solve the rule, not only break the surface mapping method on the shape of the limit, but also avoid the complicated derivation of difference schemes, achieve the numerical calculation really in the curvilinear coordinate system. The uniform transformation relation between the two system make the method more universal, with a wide range of applications.In this paper, the curvelinear coordinates and numerical simulation of geophysical processes and may experience the issues discussed and the basic potential of a DC field equations and reflection seismic equation gives the song an example coordinate system control equation derived.Finally, the preparation of a automatic grid generation program, by importing the model parameters (including the model shape, size, distribution and other geophysical parameters data), the model automatically generate body-fitted grid, and Geophysics model gridgeneration is visual to ajust the grid distribution behavior manually, eventually export the grid coordinates and the required data of numerical simulation related with the coordinates.