CN106569270B - The adaptive unstructured triangular grid method of regular grid rate pattern - Google Patents
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Abstract
Grid generating process is analogized to the process of skeleton balancing by a kind of adaptive unstructured triangular grid method of regular grid rate pattern, this method, generates the high quality grid that sizing grid is distributed with speed adaptive.In addition this method considers the information of the second order gradient fields of rate pattern, grid node is mapped on the implicit physical property interface that regular digital grid model defines, the side of unstrctured grid unit is set to be bonded with the physical property boundary surface self-adaption in rate pattern, realize accurate conversion of the regular digital grid model to unstrctured grid, achieve the purpose that preserve important physical property interface, reliable unstrctured grid model is provided for the method for numerical simulation of finite element.
Description
Technical field
This disclosure relates to finite element Seismic wave numerical modeling method, more particularly to a kind of regular grid rate pattern it is adaptive
Answer unstructured triangular grid method.
Background technology
Currently, just turning to hills, piedmont tectonic belts etc. with west area, the emphasis of oil-gas seismic exploration in south China and answering
Miscellaneous area.These regional surface conditions complexes, hypsography is violent, and height difference changes very greatly, and lithology velocity variations are led greatly
Cause near surface structure inhomogeneities serious, while subsurface structure is complicated, as fold is strong, mature fault, constructs steep, stratum change
Change big etc..These features lead to the problem of these low Earthquakes data signal-to-noise ratio and various aspects such as static correction is difficult.Fundamentally
It solves the problems, such as these explorations, needs that the propagation law and wave field characteristics of seismic wave under the conditions of relief surface deep recognize
Know, and FInite Element is to carry out complicated earth surface and the most effective technological means of complicated structure Earthquakes wave numerical simulation.
When carrying out Seismic wave numerical modeling, it is necessary first to (including p-and s-wave velocity, close to geophysics-geological model
Degree etc.) to carry out gridding spatially discrete.Finite difference calculus generally uses regular grid, and finite element rule uses non-knot more
Network forming lattice.At present in field of seismic exploration, rate pattern is mostly defined on regular grid, with the shape of dimensional matrix data
Formula provides, the main reason is that finite difference calculus is still current most popular Seismic wave numerical modeling technology, and rule
The data structure of grid is simple, is used convenient for widely propagating.But there is the mistakes of model for the rate pattern that regular grid defines
Sampling and the problems such as lack explicit boundary.Unstrctured grid refers to the grid of no rule topology relationship.It can be right
Model carries out fit mesh generation.Particularly, triangular mesh can simulate arbitrarily complicated hypsography and the ground of complexity
Lower construction, therefore can preferably portray the interface information in model.In addition, can adapt to underground medium using unstrctured grid
Physical parameter variation, adaptive adjustment sizing grid and density, the problem of without causing over-sampling.Therefore, for
Model with labyrinth, unstrctured grid possess stronger adaptability.
Since current rate pattern is substantially defined on regular grid, and FInite Element uses unstrctured grid, because
This requires consideration for how the model triangle gridding that will be defined on regular grid.In addition, being had using high-orders such as the discontinuous Galerkins
When limit member method for numerical simulation, in order to ensure simulation precision and computational efficiency, also have to the unstrctured grid subdivision quality used
Higher demand.
For the geophysicses such as speed-geological model, most interested is the place of underground medium physical parameter mutation.
When carrying out Seismic wave numerical modeling, the presence for respecting fully these interface informations is needed.It is cutd open when carrying out grid using conventional thinking
Timesharing, needs regular grid defining rate pattern and is converted to digital picture, then carries out image preprocessing, sketches the contours of in model
Portion boundary line (segment), i.e. physical model finally carry out mesh generation to the conversion process of geometrical model to geometrical model.
For simple block model, because its interface is clear, region division is easy, and it is a kind of good to can yet be regarded as using the thinking of image procossing
Method.But when subsurface model complexity, when interface information is in disorder, it is cumbersome to carry out region division using image procossing.And
And inventor has found that several steps of conventional thinking are relatively independent, can not form an independent, adaptive grid
Subdivision tool.
The generation of grid is typically considered a complicated task, therefore mesh generator is also always with black box
Form writes link independently of limited metacode.Distmesh be by Per-Olof Persson (2005) propose one kind it is non-
Often simple triangular mesh generation technique.It is different from traditional grid generation method based on geometrical concept, Distmesh is calculated
The whole machine balancing of analogy and steel skeleton construction of the method based on triangular mesh and steel skeleton construction, is capable of providing high quality
Mesh generation as a result, simultaneously can physical property distribution adaptively change mesh-density, but Distmesh algorithms are difficult to ensure and cut open
Adaptive fitization of the unstrctured grid and physical property interface that divide.For these reasons, expect a kind of suitable for mountain front etc.
The adaptive unstructured triangular grid method of the regular grid rate pattern in complicated (earth's surface/underground) area.
Invention content
The purpose of the disclosure is to establish a kind of non-knot that can be effectively matched regular digital grid model suitable for complex area
Structure triangle gridding method.
Solution used by the disclosure is as follows：
A kind of adaptive unstructured triangular grid method of regular grid rate pattern, includes the following steps：
Step 1：Define mesh-density function
Step 2：According to the mesh-density functionIn regular grid rate pattern region at the beginning of random distribution
The grid node of beginning；
Step 3：Delaunay unstructured triangular grid subdivisions are carried out to the grid node, and by unstructured triangular grid
Node coordinate be defined as two-dimensional array variable p=[x z]；
Step 4：The unstructured triangular grid is analogous to skeleton structure, is defined each in the unstructured triangular grid
The power F (p) of skeleton arm suffered by node；
Step 5：Second order derivation is carried out to the regular grid rate pattern, obtains the two of the regular grid rate pattern
Second order gradient field of force imgF is arranged according to the second order gradient fields in rank gradient fields, and second order gradient field of force imgF is proportional to institute
Second order gradient fields are stated, what each grid node for then obtaining the unstructured triangular grid by two-dimentional most neighbor interpolation was subject to
Second order gradient field force imgF (p)；
Step 6：Build the partial differential equation system of the unstructured triangular grid node coordinate and node resultant force about the time
System, wherein node resultant force is made of the power F (p) of the skeleton arm and the second order gradient field force imgF (p)；
Step 7：Partial Differential Equation System described in discretization, the update for obtaining the unstructured triangular grid node coordinate are closed
It is formula, according to the node coordinate of present moment and node resultant force, calculates the node coordinate at next moment, obtain newer grid
Node；
Step 8：Judge whether the Partial Differential Equation System tends to balance, if the Partial Differential Equation System is not yet
It tends to balance, return to step 3 proceeds to step 9 if the Partial Differential Equation System tends to balance；
Step 9：Delaunay unstructured triangular grid subdivisions are carried out for the grid node of final updated, are obtained final
Unstructured triangular grid unit obtains described final non-structural according to the regular grid rate pattern two dimension most neighbor interpolation
The physical parameter of triangle gridding unit exports mesh point coordinate, the grid cell number transitivity parameter of the grid cell.
Preferably, limited according to the VELOCITY DISTRIBUTION of the regular grid rate pattern and seismic wave in the step 1
Spatial sampling demand in first method simulation, defines mesh-density function
Preferably, in the step 1, the mesh-density functionWherein vsFor shear wave velocity,
fmaxFor the maximum frequency of the wavelet used in the seismic wave FInite Element, N indicates required in one most short seismic wave wavelength
Sampling number.
Preferably, it in the step 4, is defined in unstructured triangular grid according to the topological structure of the skeleton and is each saved
The power F (p) of the suffered skeleton arm of point, the power F (p) include in the unstructured triangular grid each node it is horizontal with it is vertical
The upward stress of histogram：
Wherein, FintIndicate function of internal force f (l, l from the skeleton arm0), FextIndicate the external force from boundary, F
(p) first is classified as x-component, and second is classified as z-component.
Preferably, function of internal force f (l, the l0) calculated according to following formula：
Wherein l is the physical length of the skeleton arm, l0For desired unstructured triangular grid length, k is coefficient of elasticity.
Preferably, the unstructured triangular grid node moves under the action of the node resultant force.
Preferably, in the step 6, the Partial Differential Equation System is：
The primary condition of the Partial Differential Equation System is p (0)=p0。
Preferably, in the step 7, the update relational expression of the unstructured triangular grid node coordinate is：pn+1=pn
+ Δ t (F+imgdimgF), wherein pn+1For the node coordinate at n+1 moment, pnFor the node coordinate at n moment, Δ t is update
Time step, imgd is adjustment parameter.
Preferably, in the step 7, pass through partial differential equation system described in Euler's time discrete format discretization forward
System.
The advantages of disclosure is the finite element Seismic wave numerical modeling for complicated earth surface and complicated structure model, is based on
A kind of Distmesh triangular mesh generation algorithms, it is proposed that adaptive unstructured triangular grid side of regular grid rate pattern
Method, to provide the unstrctured grid model of high quality for complex area seismic wave high-precision finite element numerical simulation.
With traditionally need regular grid rate pattern being converted to digital picture, then carry out image preprocessing, sketch the contours
Go out model inner boundary line, the method for finally carrying out mesh generation to geometrical model is compared, and disclosed method is based on
Distmesh trellis algorithms realize the ad aptive mesh octatree of rate pattern, make mesh-density distribution with model medium velocity size
Changes in distribution, the close ideal of grid cell quality.In addition, disclosed method introduces the second order gradient fields information of rate pattern,
It is directed toward physical property interface from both sides in second order gradient fields, the grid node near physical property interface can be mapped to physical property boundary
On face, and then achieve the purpose that grid cell boundary is bonded with physical property interface.Disclosed method realizes regular grid speed
The adaptive unstructured triangular grid for spending model overcomes conventional method and needs artificial extraction physical property interface, takes time and effort
The shortcomings that, can be that a kind of higher order algorithm offer of finite element Seismic wave numerical modeling algorithm, especially the discontinuous Galerkin etc. is good
Good unstructured triangular grid model.
Description of the drawings
Disclosure illustrative embodiments are described in more detail in conjunction with the accompanying drawings, the disclosure above-mentioned and its
Its purpose, feature and advantage will be apparent.
Fig. 1 shows the adaptive unstructured triangular grid method of regular grid rate pattern accoding to exemplary embodiment
Flow chart.
Fig. 2 shows two-dimensional regular grid rate pattern and its mesh-density requirement accoding to exemplary embodiment.
Fig. 3 (a) and Fig. 3 (b) shows the second order gradient fields of regular grid rate pattern accoding to exemplary embodiment respectively
Distribution and its partial enlarged view.
Fig. 4 shows the second order gradient fields distribution function in physical property interface both sides accoding to exemplary embodiment.
Fig. 5 shows the non-structural triangulation network for being not used that algorithm generates when second order gradient fields accoding to exemplary embodiment map
Lattice.
Fig. 6 shows the unstructured triangular grid unit that the mapping of second order gradient fields accoding to exemplary embodiment generates.
Marmousi models in Fig. 7 display example embodiments.
Fig. 8 and Fig. 9 is shown respectively through the adaptive non-structural of regular grid rate pattern accoding to exemplary embodiment
Triangle gridding method carries out the Marmousi models of Fig. 7 the result and its partial enlarged view of mesh generation.
Specific implementation mode
The preferred embodiment of the disclosure is more fully described below with reference to accompanying drawings.Although showing the disclosure in attached drawing
Preferred embodiment, however, it is to be appreciated that can realize the disclosure without should be by embodiments set forth herein in a variety of manners
It is limited.On the contrary, these embodiments are provided so that the disclosure is more thorough and complete, and can be by the model of the disclosure
It encloses and is completely communicated to those skilled in the art.
The disclosure provides a kind of adaptive unstructured triangular grid method of regular grid rate pattern, including following step
Suddenly：
Step 1：According to the sky in the VELOCITY DISTRIBUTION of the regular grid rate pattern and seismic wave Finite Element Method Simulation
Between sample requirement, define mesh-density function
Step 2：According to the mesh-density functionIn regular grid rate pattern region at the beginning of random distribution
The grid node of beginning；
Step 3：Delaunay unstructured triangular grid subdivisions are carried out to the grid node, and by the non-structural triangle
The node coordinate of grid is defined as two-dimensional array variable p=[x z]；
Step 4：The unstructured triangular grid of subdivision is analogous to skeleton structure, skeleton structure is the non-structural triangulation network
Lattice define the power F of the skeleton arm in the unstructured triangular grid suffered by each node according to the topological structure of the skeleton
(p), F represents arm strength field；
Step 5：Second order derivation is carried out to the regular grid rate pattern, obtains the two of the regular grid rate pattern
Second order gradient field of force imgF is arranged according to second order gradient fields in rank gradient fields, and second order gradient field of force imgF is proportional to second order gradient fields,
Wherein second order gradient field of force imgF is defined on the regular grid, and unstructured triangular grid is obtained by two-dimentional most neighbor interpolation
The second order gradient field force imgF (p) that is subject to of each grid node；
Step 6：Time variable is introduced, builds the unstructured triangular grid node coordinate and node resultant force about the time
Partial Differential Equation System, wherein the arm strength field F and second order gradient field of force imgF together constitute all non-structural triangles
The composite force field of grid node, the power F (p) of the skeleton arm and the second order gradient field force imgF (p) constitute described non-structural three
The node resultant force that angle grid node is subject to, unstructured triangular grid node move under the action of the resultant force；
Step 7：Partial Differential Equation System described in discretization, the update for obtaining the unstructured triangular grid node coordinate are closed
It is formula pn+1=pn+ Δ t (F+imgF), wherein pn+1For the node coordinate at n+1 moment, pnFor the node coordinate at n moment, Δ t is
Newer time step, imgd are adjustment parameter, according to the node coordinate of present moment and node resultant force, to calculate next
The node coordinate at moment obtains newer grid node；
Step 8：Judge whether the Partial Differential Equation System tends to balance, if the Partial Differential Equation System is not yet
It tends to balance, return to step 3 re-starts Delaunay unstructured triangular grid subdivisions for newer grid node, calculates
The node resultant force of unstructured triangular grid node, calculates next newer node coordinate；If the Partial Differential Equation System
It tends to balance, proceeds to step 9；
Step 9：Delaunay unstructured triangular grid subdivisions are carried out for the grid node of final updated, are obtained final
Unstructured triangular grid unit obtains described final non-structural according to the regular grid rate pattern two dimension most neighbor interpolation
The physical parameter (such as speed, density etc.) of triangle gridding unit, exports mesh point coordinate, the grid list of the grid cell
First number transitivity parameter.
Preferably, the mesh-density functionWherein vsFor shear wave velocity, fmaxFor described
The maximum frequency of wavelet used in seismic wave FInite Element, N indicate sampling number required in one most short seismic wave wavelength.
Preferably, the power F (p) include the node of the unstructured triangular grid in the horizontal and vertical directions by
Power：
Wherein, FintIndicate function of internal force f (l, l from the skeleton arm0), FextIndicate the external force from boundary, F
(p) first is classified as x-component, and second is classified as in z-component.
Preferably, function of internal force f (l, the l0) calculated according to following formula：
Wherein l is the physical length of the skeleton arm, l0For desired unstructured triangular grid length, k is coefficient of elasticity.
Preferably, the Partial Differential Equation System is：
The primary condition of the Partial Differential Equation System is p (0)=p0。
Preferably, pass through Partial Differential Equation System described in Euler's time discrete format discretization forward.
Below with reference to exemplary embodiment description according to the adaptive non-structural of the regular grid rate pattern of the disclosure
Triangle gridding method the described method comprises the following steps (see Fig. 1)：
Step 1：It is adopted according to the space in the VELOCITY DISTRIBUTION of regular grid rate pattern and seismic wave Finite Element Method Simulation
Sample demand defines mesh-density functionWherein, vsFor shear wave velocity, fmaxFor seismic wave FInite Element mould
The maximum frequency of wavelet used in quasi-, N indicate sampling number required in one most short seismic wave wavelength.Fig. 2 shows basis
Regular grid rate pattern and its mesh-density requirement of exemplary embodiment.
Step 2：According to the mesh-density function of definitionIn regular grid rate pattern region at the beginning of random distribution
The grid node of beginning.
Step 3：Delaunay unstructured triangular grid subdivisions are carried out to initial grid node, and by the non-structural triangulation network
The node coordinate of lattice is defined as two-dimensional array variable p=[x z], and (wherein x, z indicate horizontally and vertically to sit respectively
Mark).
Step 4：The unstructured triangular grid of subdivision is analogous to skeleton structure.According to (i.e. non-structural the three of skeleton structure
Angle grid) topological structure defines the power F (p) of the skeleton arm suffered by each skeleton node (i.e. grid node) in skeleton, and F is represented
Arm strength field.Power F (p) includes the stress of skeleton node (i.e. grid node) in the horizontal and vertical directions：
Wherein, FintIndicate function of internal force f (l, l from skeleton arm0), FextIndicate the external force from boundary, the of F
One is classified as x-component, and second is classified as z-component.Function of internal force f (l, l0) active force of Hookean spring can be simulated, and only consider
Repulsive force, without attraction.Function of internal force f (l, l0) calculated according to following formula：
Wherein l is the physical length of skeleton arm, l0For desired unstructured triangular grid length, k is coefficient of elasticity.
Step 5：Second order derivation is carried out to regular grid rate pattern, is obtained secondly rank gradient fields, and according to rate pattern
Second order gradient fields be arranged corresponding second order gradient field of force imgF, in embodiment, second order gradient field of force imgF is proportional to second order
Gradient fields.
In speed, uniformly local second order gradient is zero to second order gradient fields, can be formed closely in the interface both sides of velocity variations
It is seemingly perpendicularly oriented to the vector at interface, as shown in Fig. 3 (a) and Fig. 3 (b).Second order gradient fields have good characteristic, somewhere interface two
The second order gradient fields distribution function of side, second order gradient is close to zero on interface, and second order gradient reaches maximum near interface, far
It is become zero from interface gradients, as shown in Figure 4.The second order gradient field of force is defined on regular grid, is obtained by two dimension most neighbor interpolation
Obtain the second order gradient field force imgF (p) that each grid node of unstructured triangular grid is subject to.
Step 6：Introducing time variable t, structure unstructured triangular grid node coordinate and node resultant force are inclined about the time
Differential Systems：
Wherein the primary condition of equation system is p (0)=p0.Arm strength field F and second order gradient field of force imgF are together constituted
The composite force field of all skeleton (grid) nodes, the power F (p) and second order gradient field force imgF (p) of skeleton arm constitute non-structural triangle
The node resultant force that grid node is subject to, node move under the action of resultant force.
Step 7：Partial Differential Equation System in discretization step 6, above equation system may be used simply forward
Euler's time discrete format.In tn=n time Δts, Approximating Solutions pn≈p(tn).By following formula, according to present moment grid node
Coordinate and node resultant force seek the mesh point coordinate at next moment：
pn+1=pn+Δt·(F+imgd·imgF)
Wherein pn+1For the node coordinate at n+1 moment, pnFor the node coordinate at n moment, Δ t is newer time step,
Imgd is adjustment parameter, it makes algorithm make compromise between mesh quality and physical property interface laminating degree.
As shown in figure 5, when not using second order gradient fields to map grid node, there is no to boundary in model for grid
Face carries out fit subdivision, and interface grid is uneven.Grid has been substantially carried out along boundary after second order gradient fields information is added
The fit subdivision in face, the perfect fitting especially for SIN function interface and sphenoid interface have absolutely proved that basis is shown
The validity of the method for example property embodiment, is shown in Fig. 6.
Step 8：Judge whether the Partial Differential Equation System tends to balance, if the Partial Differential Equation System is not yet
It tends to balance, return to step 3 re-starts Delaunay unstructured triangular grid subdivisions for newer grid node, calculates
The resultant force of the power and second order gradient field force of the skeleton arm that unstructured triangular grid node is subject to calculates next newer node and sits
Mark；If the Partial Differential Equation System tends to balance, step 9 is proceeded to.Meet F when Partial Differential Equation System tends to balance
(p)=0, grid node no longer moves.Grid tends to be best at this time, at the same corresponding grid unit boundary substantially with rate pattern
In physical property interface fitting.
Step 9：Delaunay unstructured triangular grid subdivisions are carried out for the grid node of final updated, are obtained final
Unstructured triangular grid unit obtains described final non-structural according to the regular grid rate pattern two dimension most neighbor interpolation
The physical parameter of triangle gridding unit exports mesh point coordinate, the grid cell number transitivity parameter of the grid cell.
The Marmousi models used in Fig. 7 display example embodiments, Fig. 8 and Fig. 9 are shown respectively by according to example
The adaptive unstructured triangular grid method of the regular grid rate pattern of property embodiment, to the Marmousi models of Fig. 7 into
The result and its partial enlarged view of row mesh generation.From Fig. 8 and Fig. 9 as it can be seen that on the whole, mesh quality is good, grid is for weight
It wants interface to sketch the contours pure and fresh, realizes the requirement for carrying out fit subdivision along important physical property interface, this point is from partial enlarged view
It must be more clear.The mesh-density in the upper right corner is obviously bigger than other parts in Fig. 9, this also fully shows unstrctured grid energy
Enough according to the distribution adaptive determining mesh-density of underground medium the characteristics of.
Disclosed method is applied to the mesh modeling process of seismic wave finite element numerical simulation pre-treatment.The side of the disclosure
Method is based on Distmesh unstructured triangular grid subdivision algorithms, and grid generating process is analogized to the process of skeleton balancing, generates
The high quality grid that sizing grid is distributed with speed adaptive.In addition, this method considers the letter of the second order gradient fields of rate pattern
Breath, grid node is mapped on the implicit physical property interface that regular digital grid model defines, make the side of unstrctured grid unit with
Physical property boundary surface self-adaption fitting in rate pattern, realizes accurate conversion of the regular digital grid model to unstrctured grid, reaches
To the purpose for preserving important physical property interface, reliable unstrctured grid model is provided for the method for numerical simulation of finite element.
Embodiment of the disclosure is described above, above description is exemplary, and non-exclusive, and also not
Example is respectively applied disclosed by being limited to.Without departing from the scope and spirit of embodiment described, for the art
Those of ordinary skill for many modifications and changes will be apparent from.The selection of term used herein, it is intended to best
The principle and practical application of embodiment is explained on ground, or so that other those of ordinary skill of the art is understood and disclosed herein
Embodiment.
Claims (9)
1. a kind of adaptive unstructured triangular grid method of regular grid rate pattern, includes the following steps：
Step 1：Define mesh-density function
Step 2：According to the mesh-density functionRandom distribution is initial in regular grid rate pattern region
Grid node；
Step 3：Delaunay unstructured triangular grid subdivisions are carried out to the grid node, and by the section of unstructured triangular grid
Point coordinates is defined as two-dimensional array variable p=[x z]；
Step 4：The unstructured triangular grid is analogous to skeleton structure, defines each node in the unstructured triangular grid
The power F (p) of suffered skeleton arm；
Step 5：Second order derivation is carried out to the regular grid rate pattern, obtains two ladders of the regular grid rate pattern
Field is spent, second order gradient field of force imgF is set according to the second order gradient fields, second order gradient field of force imgF is proportional to described two
Then rank gradient fields obtain the second order that each grid node of the unstructured triangular grid is subject to by two dimension most neighbor interpolation
Gradient field force imgF (p)；
Step 6：The Partial Differential Equation System of the unstructured triangular grid node coordinate and node resultant force about the time is built,
Described in node resultant force be made of the power F (p) of the skeleton arm and the second order gradient field force imgF (p)；
Step 7：Partial Differential Equation System described in discretization obtains the more new relation of the unstructured triangular grid node coordinate
Formula calculates the node coordinate at next moment, obtains newer grid section according to the node coordinate of present moment and node resultant force
Point；
Step 8：Judge whether the Partial Differential Equation System tends to balance, if the Partial Differential Equation System tends to not yet
Balance, return to step 3 proceed to step 9 if the Partial Differential Equation System tends to balance；
Step 9：Delaunay unstructured triangular grid subdivisions are carried out for the grid node of final updated, obtain final non-knot
Structure triangle gridding unit obtains the final non-structural triangle according to the regular grid rate pattern two dimension most neighbor interpolation
The physical parameter of grid cell exports mesh point coordinate, the grid cell number transitivity parameter of the grid cell.
2. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 1, wherein
In the step 1, according to the space in the VELOCITY DISTRIBUTION of the regular grid rate pattern and seismic wave Finite Element Method Simulation
Sample requirement defines mesh-density function
3. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 1, wherein
In the step 1, the mesh-density functionWherein vsFor shear wave velocity, fmaxIt is limited in seismic wave
The maximum frequency of wavelet used in first method, N indicate sampling number required in one most short seismic wave wavelength.
4. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 1, wherein
In the step 4, the skeleton arm in unstructured triangular grid suffered by each node is defined according to the topological structure of the skeleton
Power F (p), the power F (p) includes each stress of node in the horizontal and vertical directions in the unstructured triangular grid：
Wherein, FintIndicate function of internal force f (l, l from the skeleton arm0), FextIndicate the external force from boundary, F's (p)
First is classified as x-component, and second is classified as z-component.
5. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 4, wherein institute
State function of internal force f (l, l0) calculated according to following formula：
Wherein l is the physical length of the skeleton arm, l0For desired unstructured triangular grid length, k is coefficient of elasticity.
6. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 1, wherein institute
Unstructured triangular grid node is stated to move under the action of the node resultant force.
7. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 1, wherein
In the step 6, the Partial Differential Equation System is：
The primary condition of the Partial Differential Equation System is p (0)=p0。
8. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 1, wherein
In the step 7, the update relational expression of the unstructured triangular grid node coordinate is：pn+1=pn+Δt·(F+imgd·
ImgF), wherein pn+1For the node coordinate at n+1 moment, pnFor the node coordinate at n moment, Δ t is newer time step, imgd
For adjustment parameter.
9. the adaptive unstructured triangular grid method of regular grid rate pattern according to claim 1, wherein
In the step 7, pass through Partial Differential Equation System described in Euler's time discrete format discretization forward.
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