CN106445882A - Improved CLSVOF method for quickly building signed distance function by VOF function - Google Patents

Improved CLSVOF method for quickly building signed distance function by VOF function Download PDF

Info

Publication number
CN106445882A
CN106445882A CN201610545217.XA CN201610545217A CN106445882A CN 106445882 A CN106445882 A CN 106445882A CN 201610545217 A CN201610545217 A CN 201610545217A CN 106445882 A CN106445882 A CN 106445882A
Authority
CN
China
Prior art keywords
grid
interface
function
distance function
vof
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201610545217.XA
Other languages
Chinese (zh)
Inventor
魏艳红
钱龙根
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN201610545217.XA priority Critical patent/CN106445882A/en
Publication of CN106445882A publication Critical patent/CN106445882A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computing Systems (AREA)
  • Measuring Volume Flow (AREA)

Abstract

For the problems of a complex signed distance function building process, difficult expansion to three dimensions, low building efficiency and the like in an existing CLSVOF method, the invention provides an improved CLSVOF method for quickly building a signed distance function by a VOF function. The method comprises the steps of firstly finding out an interface grid by utilizing a sub-grid technology; secondly converting a VOF function in the interface grid into a signed distance function through a Newton iteration method, and based on this, building a signed distance function of a whole calculation region by adopting a fast scanning method; thirdly performing calculation through a WENO format and an upwind scheme to obtain an accurate interface normal vector value; and finally solving a VOF equation by adopting a corrected THINC algorithm pair.

Description

Improved CLSVOF method for quickly constructing symbol distance function by VOF function
The technical field is as follows:
the invention relates to an improved CLSVOF method for quickly constructing a symbol distance function by a VOF function, belonging to the field of motion interface tracking numerical simulation.
Background art:
the motion interface tracking numerical simulation is a popular research subject at home and abroad at present, relates to a plurality of research fields of materials, physics, chemistry, biology and the like, and has important theoretical value and practical significance for the research on the motion interface tracking numerical simulation.
In the early 80 s of the last century, Volume of fluid (VOF) was first proposed by Hirt and Nichols, national laboratories of los alamos, usa. According to the method, a fluid Volume (VOF) function (the value of which is 0-1) is introduced into a flow field, and the tracking of a motion interface is realized by solving a transport equation of the VOF function. The VOF method is small in calculated amount, high in interface sharpness and good in quality conservation, so that the VOF method is adopted by a large amount of commercial software and domestic and foreign scholars and used for solving the problem of complex motion interfaces. Unfortunately, due to the fact that the VOF function is discontinuous on two sides of the interface, the normal vector of the interface cannot be accurately calculated, and the accuracy of the method is reduced.
In 1988, the concept of Osher and setian of bykeley division university of california based on Hamilton-Jacobi equation provides a famous Level Set Method (Level Set Method), which defines a continuous and smooth Level Set function (such as symbolic Distance function, signaled Distance Functions, SDF), and realizes the tracking of a motion interface by solving a transport equation of the Level Set function. The Level Set method can be used for conveniently calculating the complex interface changes such as crushing, merging and the like; and due to the continuous characteristic of the symbol distance function, the normal vector of the interface can be accurately calculated by combining high-resolution methods such as WENO, TVD and other formats. However, the Level Set method is prone to cause mass non-conservation during the calculation process due to numerical diffusion, re-initialization, and the like.
The VOF method has the defects that the VOF function is discontinuous on two sides of an interface, and normal vectors of the interface cannot be accurately calculated; the Level Set method has the advantages that the Level Set function is continuous, and the interface normal vector can be accurately calculated; if a symbol distance function is introduced into the VOF method and is used for constructing an interface normal vector, the defects of the VOF method can be effectively compensated.
In 2000, Sussamn and Puckett et al, Davis university of California, first combined the VOF Method with a Level Set Method to provide a Coupled VOF and Level Set Method (CLSVOF). The method adopts a PLIC algorithm to solve a VOF equation, and then a symbol distance function is constructed by a linear interface (two dimensions are straight lines and three dimensions are planes) in a grid established by the PLIC algorithm. Due to the complex establishment process of the three-dimensional linear interface, the method is difficult to implement in three-dimensional situations and is difficult to expand to other VOF solving methods.
In 2010, a VOSET method was proposed by grandson eastern university of western ann. The method adopts a geometric method to calculate the distance from the center of each grid to the PLIC linear interface, and then converts the distance into a symbol distance function according to the size of the VOF function. Like the CLSVOF method, this method is also not easily scalable to three dimensions.
In 2013, Yoki et al, Kadifu university, UK, proposed a new CLSVOF method, which uses THINC algorithm proposed by Xiao et al to solve VOF transmission equations. Since there is no geometric interface building process in the THINC algorithm, the symbol distance function needs to be constructed by other methods. Therefore, Yoki et al constructs a 0.5 isosurface of the VOF function by adopting a linear interpolation mode, and then constructs a symbol distance function by a Fast Marching Method (FMM) proposed by Sethian et al and a steady-state solution reinitialization (Re-initialization) proposed by Sussman et al, thereby simplifying the reconstruction process of the symbol distance function. However, the FMM algorithm is too complex in logic, and there is a certain error in constructing the symbol distance function at the interface grid, and the steady-state solution has a large number of iteration steps and low computational efficiency.
The invention content is as follows:
the invention provides an improved CLSVOF method for quickly constructing a symbol distance function by a VOF (Voltage induced distortion) function, aiming at the problem that the symbol distance function constructing process is too complex in the CLSVOF method.
The invention adopts the following technical scheme: an improved CLSVOF method for quickly constructing a symbol distance function by a VOF function comprises the following steps:
the first step is as follows: defining initial VOF function
Defining a VOF function in a grid according to an actual physical interface, wherein the VOF function value of the interface grid is 0-1, the VOF function value of the grid in the interface is 1, and the VOF function value of the grid outside the interface is 0;
the second step is that: obtaining interface grid
Firstly, initializing a symbol distance function through a VOF function value of a grid, wherein the symbol distance function of the grid with the VOF value larger than 0.5 is positive, and the symbol distance function of the grid with the VOF value smaller than 0.5 is negative; secondly, judging whether the current grid is an interface grid or not by adopting a sub-grid technology, wherein the sub-grid technology determines whether the current grid is the interface grid or not by judging whether the symbol distance function values of the current grid and surrounding grids are different, if so, the motion interface is between the two grids, the grids are interface grids, otherwise, the grids are non-interface grids;
the third step: converting VOF function to symbol distance function
Because the VOF function and the symbol distance function represent the same interface, the heavisiside value of the symbol distance function at the interface grid is equal to the VOF function value, and the Newton iteration method is adopted to solve the equivalent relation, so that the symbol distance function of the interface grid, namely the symbol distance function value, can be obtained;
the fourth step: reconstructing a symbol distance function
Reconstructing the symbol distance function by adopting a fast scanning method, wherein the fast scanning method is a fast solution method for solving an Eikonal equation, and the reconstruction of the symbol distance function is equal to the solution of the Eikonal equation |. phi | ═ 1;
the fifth step: obtaining a symbol distance function gradient using a WENO format
After the symbol distance function is reconstructed, acquiring a gradient by adopting a high-precision WENO format;
and a sixth step: defining interface normal vectors by gradients of symbolic distance functions
When defining an interface normal vector, considering windward characteristics, if the flow field speed is negative, taking the right derivative of the sign distance function as the interface normal vector, and if the flow field speed is positive, taking the left derivative of the sign distance function as the interface normal vector;
the seventh step: and solving the VOF transmission equation.
Further, the fourth step comprises the following steps
1. Initializing; setting the grid state at the interface to be 0 and the non-interface grid state to be 1 according to the result given in the third step, initializing the non-interface grid to be a maximum value if the sign distance function value of the non-interface grid is positive, and initializing the non-interface grid to be a minimum value if the sign distance function value of the non-interface grid is negative;
2. gauss Seidel iteration; scanning iteration is carried out on the whole calculation area along different directions according to a format given by a quick scanning method;
3. updating the symbol distance function; and judging whether the symbol distance function needs to be updated or not according to the grid state given by initialization, if the grid state is '1', comparing the symbol distance function value after scanning iteration with the original symbol distance function value, and taking the minimum value, and if the grid state is '0', taking the original value.
Further, the fifth step comprises the following steps
1. Selecting an interpolation template, wherein the left derivative template is { I-2, I-1, I, I +1 and I +2}, and the right derivative template is { I +2, I +1, I, I-1 and I-2 };
2. constructing three third-order approximations s1、s2、s3Taking the left derivative as an example, the interpolation templates are { I-2, I-1, I }, { I-1, I, I +1}, { I, I +1, I +2 };
3. three non-linear weights ω are defined1、ω2、ω3；
4. Defining three smoothing factors β1、β2、β3；
5. A non-linear convex combination of three third-order approximations is constructed.
Further, the seventh step includes the following steps
1. According to the interface speed direction, defining lambda and an upwind grid iup;
2. calculating a hop center of a hyperbolic tangent function
3. Calculating the volume outflow f of the fluid on the grid surfacei+1/2、fi-1/2；
4. The one-dimensional results are split into multiple dimensions.
The invention has the following beneficial effects:
(1) the sub-grid technology, the Newton iteration method, the fast scanning method, the WENO format and the THINC algorithm adopted by the method are simple in logic and easy to program;
(2) the sub-grid technology and the Newton iteration method are suitable for two-dimensional and three-dimensional, and the rapid scanning method is also easy to expand to three-dimensional, so that the method can be easily applied to three-dimensional conditions;
(3) the sub-grid technology can be completed by only one step of calculation, and the general Newton iteration method and the rapid scanning method can be converged by only a few steps, so the method has extremely high calculation efficiency;
(4) the symbol distance function of the interface grid is obtained by a Newton iteration method, the machine precision is achieved, the symbol distance function of the grid outside the interface is obtained by a fast scanning method, the first-order precision is achieved, and the algorithm is equivalent to the existing algorithm;
(5) the symbol distance function construction method designed by the invention does not depend on a VOF solving method, is not only suitable for THINC algorithm, but also suitable for traditional VOF methods such as SLIC and PLIC, and has strong applicability;
(6) the THINC algorithm is an algorithm which does not depend on time steps and has strong numerical stability, and the method perfectly inherits the advantages and has strong algorithm robustness.
Description of the drawings:
fig. 1 is a schematic diagram of the distribution of the initial VOF functions.
FIG. 2 is a schematic diagram of interface grid judgment.
FIG. 3 is a schematic diagram of a distribution of symbol distance functions of an interface grid.
FIG. 4 is a diagram illustrating a fast scan method for updating grid symbol distance function.
FIG. 5 is a diagram of an interpolation template of left and right derivatives of a signed distance function.
Fig. 6(a) and 6(b) are schematic diagrams of the one-dimensional THINC algorithm principle.
The specific implementation mode is as follows:
the invention relates to an improved CLSVOF method for quickly constructing a symbol distance function by a VOF function, which comprises the following steps:
the first step is as follows: defining initial VOF function
The VOF function is defined within the grid according to the actual physical interface. The VOF function value of the interface grid is 0-1, the VOF function value of the grid inside the interface is 1, and the VOF function value of the grid outside the interface is 0.
The second step is that: obtaining interface grid
Firstly, a symbol distance function is initialized through VOF function values of grids. The sign distance function for a grid with a VOF value greater than 0.5 is positive and the sign distance function for a grid with a VOF value less than 0.5 is negative. Secondly, judging whether the current grid is an interface grid or not by adopting a sub-grid technology. The sub-grid technology is to determine whether the current grid is an interface grid by judging whether the sign distance function value of the current grid and the surrounding grid is different. If the number is different, the motion interface is between the two grids, and the grids are interface grids; otherwise, the grid is a non-interface grid.
The third step: converting VOF function to symbol distance function
Since the VOF function and the sign distance function represent the same interface, the sign distance function Heaviside value at the interface grid should be identical to the VOF function value. And solving the equivalent relation by adopting a Newton iterative method to obtain a symbol distance function of the interface grid, namely a symbol distance function value.
The fourth step: reconstructing a symbol distance function
In order to reconstruct the symbol distance function efficiently and quickly, the symbol distance function is reconstructed by adopting a quick scanning method, wherein the quick scanning method is a quick solution for solving an Eikonal equation, and the reconstruction of the symbol distance function is equal to the solution of the Eikonal equation phi 1.
The method comprises the following implementation steps:
1. initializing; according to the result given in the third step, the grid state at the interface is set to "0", and the non-interface grid state is set to "1". If the function value of the symbol distance of the non-interface grid is positive, initializing the non-interface grid to be a maximum value; otherwise, the value is initialized to a minimum value.
2. Gauss Seidel iteration; the entire calculation region is scanned (iterated) in different directions according to the format given by the fast scan method. Generally, only 4 times of scanning are needed in the two-dimensional case, 8 times of scanning are needed in the three-dimensional case, and the algorithm efficiency is extremely high.
3. Updating the symbol distance function; and judging whether the symbol distance function needs to be updated or not according to the grid state given by initialization. And if the grid state is 1, comparing the symbol distance function value after scanning iteration with the original symbol distance function value, and taking the minimum value. If the trellis state is "0", the original value is taken.
The fifth step: obtaining a symbol distance function gradient using a WENO format
After the symbol distance function is reconstructed, the gradient can be obtained by adopting a high-precision WENO format, and the implementation process is illustrated by taking a fifth-order WENO as an example.
The method comprises the following concrete steps:
1. selecting an interpolation template, wherein the left derivative template is { I-2, I-1, I, I +1 and I +2}, and the right derivative template is { I +2, I +1, I, I-1 and I-2 };
2. constructing three third-order approximations s1、s2、s3Taking the left derivative as an example, the interpolation templates are { I-2, I-1, I }, { I-1, I, I +1}, { I, I +1, I +2 };
3. defining three non-linear weightsω1、ω2、ω3；
4. Defining three smoothing factors β1、β2、β3；
5. Constructing a nonlinear convex combination of three third-order approximations;
and a sixth step: defining interface normal vectors by gradients of symbolic distance functions
When defining the normal vector of the interface, the windward characteristic must be considered. If the flow field velocity is negative, taking the right derivative of the sign distance function as an interface normal vector; and if the flow field velocity is positive, taking the left derivative of the symbolic distance function as an interface normal vector.
The seventh step: solving VOF transport equations
In the invention, a THINC algorithm is adopted to solve the VOF transmission equation.
The method comprises the following concrete steps:
1. according to the interface speed direction, defining lambda and an upwind grid iup;
2. calculating a hop center of a hyperbolic tangent function
3. Calculating the volume outflow f of the fluid on the grid surfacei+1/2、fi-1/2；
4. The one-dimensional results are split into multiple dimensions.
In the original THINC method, a Young method is adopted for calculating the normal vector of the interface, and the method only has first-order precision and is not easy to expand to three dimensions. The method adopts the symbol distance function gradient with higher precision to calculate the interface normal vector, and can greatly improve the precision of the THINC algorithm.
The following describes the implementation of the present invention by taking the Zaleska disk interface motion in a two-dimensional rotating flow field as an example.
In this example, the number of grids is 100 × 100, and the unit length is 0.01 mm; the radius of the Zaleska disc is 0.3mm, the center of the circle is located at (0.5 ), the height of the opening is 0.7mm, and the specific distribution is shown in figure 1. The VOF value in the disc is set to be 1, the outer part is 0, and the interface is 0-1.
The second step is that: obtaining interface grid
Firstly, a symbol distance function is initialized through VOF function values of grids. The sign distance function of the grid with the VOF function value larger than 0.5 is positive, the sign distance function of the grid with the VOF function value smaller than 0.5 is negative, and the mathematical expression is as follows.
Wherein M is the side length of the calculation region, Fi,jThe value of the VOF function for the current grid.
Secondly, adopting a sub-grid technology to judge whether the current grid is an interface grid. As shown in fig. 2, for an arbitrary grid Φi,jAssuming its center of mesh is inside the motion interface (phi)<0) If the function value of the symbol distance of the adjacent grid is positive (phi)>0) Then the motion interface must be contained between two grids, which are interface grids. Based on the above judgment conditions, all interface grids in the entire calculation area can be obtained.
The second step is that: converting VOF function to symbol distance function
Since the VOF interface coincides with the Level Set interface, the Heaviside value of the signed distance function at the interface grid should be equal to the VOF function value, and its mathematical expression is as follows:
H(φ)＝F
unfolding the method:
where F is the VOF function, Φ is the symbol distance function, and the interface width, and in this embodiment, the grid length is 1 time.
The above equation can be solved by using a newton iteration method, and the iteration format is:
wherein, H (phi) and phi are respectively the Heaviside and Dirac function values of the symbol distance function. In the above solving process, the minimum value for controlling the iteration stop is eps ═ 1e-8。
The fourth step: reconstructing a symbol distance function
First, the grid is labeled according to the result of the second step. If the interface grid is adopted, the grid state is '0'; otherwise, the trellis state is "1".
Secondly, for the grid of '1', if phi is greater than 0, assigning a maximum value; phi is less than 0, and a maximum value is assigned; the "0" grid holds the original values.
Then, a gaussian seidel iteration is performed in 4 directions, with the iteration format as follows:
wherein h is the size of the grid, a and b are the extreme values of the adjacent grids, and the expression is as follows:
fig. 3 shows the updated grid area scanned in different directions, and the dotted lines represent the physical interface.
Finally, the symbol distance function is updated. If the grid state is '0', updating is not carried out; otherwise, update as follows:
fig. 4 shows the updated interface grid symbol distance function values.
The fifth step: obtaining a sign distance function gradient
First, for an arbitrary grid Φi,jAn interpolation template for the left and right derivatives of the sign distance function is defined, as shown in fig. 5. Taking the left derivative as an example, the expression is as follows:
v1＝D-φi-2
v2＝D-φi-1
v3＝D-φi
v4＝D-φi+1
v5＝D-φi+2
wherein, v1、ν2、ν3、ν4、ν5For five interpolation templates, D-Is the left derivative.
Next, three third order approximations are defined, the expressions of which are as follows:
again, three nonlinear weights are defined, whose expression is as follows:
wherein, to prevent the parameter with zero denominator, 1e is taken in this example-10And S1, S2 and S3 are smoothing factors, and the expression is as follows:
finally, a nonlinear convex combination of three third-order approximations is constructed.
And a sixth step: interface normal vector definition by sign distance function gradient
According to the windward characteristic, if the flow field speed is negative, taking the right derivative of the sign distance function as an interface normal vector; if the flow field velocity is positive, the left derivative of the symbolic distance function is taken as the interface normal vector.
The seventh step: solving VOF transport equations
First, the discrete VOF equation:
wherein,as a function of the fluid volume in the i-grid at the current time,as a function of the volume of fluid at the next instant, fi+1/2And fi-1/2The volumetric outflow of fluid, u, at the right and left grid interfaces, respectivelyi+1/2And ui-1/2Grid right interface and grid left interface speeds, respectively, and Δ t and Δ x are time and space step lengths, respectively.
From the above equation, the key of the VOF method is to solve the fluid volume outflow of the mesh surface, whereas the thin method obtains the fluid volume outflow of the mesh surface by an analytical method. As shown in fig. 6(a) and 6(b), the thick solid line in the coordinate of fig. 6(a) represents a real physical interface, and the thick solid line in the coordinate of fig. 6(b) represents an interface of the THINC structure, that is, a hyperbolic tangent function, and if the flow field velocity and the time step are known, the fluid volume outflow rate of the grid surface can be obtained by integrating the hyperbolic tangent function.
The hyperbolic tangent function is expressed as follows:
where β is a quantity related to a normal vector, γ is a quantity related to a velocity direction, and xi-1/2Is the coordinates of the left interface of the grid,is the hopping center of the hyperbolic tangent function.
The expression of beta is:
βx＝2.3|nx|+0.01
βy＝2.3|ny|+0.01
the expression gamma is as follows:
the expression is as follows:
wherein phiiupFor the windward grid, take the right interface as an example, if ui+1/2<0, iup ═ i +1, otherwise iup ═ i;
it is to be noted that, in the original THINC algorithm, nx and ny are interface normal vectors obtained by a young method, and the symbolic distance function ladder normal vector constructed in the sixth step is adopted in the present invention.
Secondly, the hyperbolic tangent function is subjected to time integral, and the volume of the fluid flowing out of the grid surface within a certain time can be obtained.
Taking the grid right interface as an example, the volume of the fluid flowing out is:
where λ is a quantity related to the speed direction, and its expression is as follows:
the outflow volume of the left interface is the outflow volume of the right interface of the left grid, so the results can be substituted into a discrete VOF equation to obtain an updated VOF function.
And finally, splitting along the x direction, the y direction and the z direction by adopting a splitting algorithm, and updating the multidimensional VOF function.
The splitting algorithm expression is as follows:
the foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (4)

1. An improved CLSVOF method for quickly constructing a symbol distance function by a VOF function is characterized in that: comprises the following steps
The first step is as follows: defining initial VOF function
Defining a VOF function in a grid according to an actual physical interface, wherein the VOF function value of the interface grid is 0-1, the VOF function value of the grid in the interface is 1, and the VOF function value of the grid outside the interface is 0;
the second step is that: obtaining interface grid
Firstly, initializing a symbol distance function through a VOF function value of a grid, wherein the symbol distance function of the grid with the VOF value larger than 0.5 is positive, and the symbol distance function of the grid with the VOF value smaller than 0.5 is negative; secondly, judging whether the current grid is an interface grid or not by adopting a sub-grid technology, wherein the sub-grid technology determines whether the current grid is the interface grid or not by judging whether the symbol distance function values of the current grid and surrounding grids are different, if so, the motion interface is between the two grids, the grids are interface grids, otherwise, the grids are non-interface grids;
the third step: converting VOF function to symbol distance function
Because the VOF function and the symbol distance function represent the same interface, the heavisiside value of the symbol distance function at the interface grid is equal to the VOF function value, and the Newton iteration method is adopted to solve the equivalent relation, so that the symbol distance function of the interface grid, namely the symbol distance function value, can be obtained;
the fourth step: reconstructing a symbol distance function
Reconstructing the symbol distance function by adopting a fast scanning method, wherein the fast scanning method is a fast solution method for solving an Eikonal equation, and the reconstruction of the symbol distance function is equal to the solution of the Eikonal equation |. phi | ═ 1;
the fifth step: obtaining a symbol distance function gradient using a WENO format
After the symbol distance function is reconstructed, acquiring a gradient by adopting a high-precision WENO format;
and a sixth step: defining interface normal vectors by gradients of symbolic distance functions
When defining an interface normal vector, considering windward characteristics, if the flow field speed is negative, taking the right derivative of the sign distance function as the interface normal vector, and if the flow field speed is positive, taking the left derivative of the sign distance function as the interface normal vector;
the seventh step: and solving the VOF transmission equation.
2. The improved CLSVOF method for fast construction of a symbol distance function from a VOF function according to claim 1, wherein: the fourth step comprises the following steps
(1) Initializing; setting the grid state at the interface to be 0 and the non-interface grid state to be 1 according to the result given in the third step, initializing the non-interface grid to be a maximum value if the sign distance function value of the non-interface grid is positive, and initializing the non-interface grid to be a minimum value if the sign distance function value of the non-interface grid is negative;
(2) gauss Seidel iteration; scanning iteration is carried out on the whole calculation area along different directions according to a format given by a quick scanning method;
(3) updating the symbol distance function; and judging whether the symbol distance function needs to be updated or not according to the grid state given by initialization, if the grid state is '1', comparing the symbol distance function value after scanning iteration with the original symbol distance function value, and taking the minimum value, and if the grid state is '0', taking the original value.
3. The improved CLSVOF method for fast construction of a symbol distance function from a VOF function according to claim 2, wherein: the fifth step comprises the following steps
(1) Selecting an interpolation template, wherein the left derivative template is { I-2, I-1, I, I +1 and I +2}, and the right derivative template is { I +2, I +1, I, I-1 and I-2 };
(2) constructing three third-order approximations s1、s2、s3Taking the left derivative as an example, the interpolation templates are { I-2, I-1, I }, { I-1, I, I +1}, { I, I +1, I +2 };
(3) three non-linear weights ω are defined1、ω2、ω3；
(4) Defining three smoothing factors β1、β2、β3；
(5) A non-linear convex combination of three third-order approximations is constructed.
4. The improved CLSVOF method for fast construction of a symbol distance function from a VOF function according to claim 3, wherein: the seventh step comprises the following steps
(1) According to the interface speed direction, defining lambda and an upwind grid iup;
(2) calculating a hop center of a hyperbolic tangent function
(3) Calculating the volume outflow f of the fluid on the grid surfacei+1/2、fi-1/2；
(4) The one-dimensional results are split into multiple dimensions.
CN201610545217.XA 2016-07-12 2016-07-12 Improved CLSVOF method for quickly building signed distance function by VOF function Pending CN106445882A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201610545217.XA CN106445882A (en) 2016-07-12 2016-07-12 Improved CLSVOF method for quickly building signed distance function by VOF function

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201610545217.XA CN106445882A (en) 2016-07-12 2016-07-12 Improved CLSVOF method for quickly building signed distance function by VOF function

Publications (1)

Publication Number Publication Date
CN106445882A true CN106445882A (en) 2017-02-22

Family

ID=58183524

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201610545217.XA Pending CN106445882A (en) 2016-07-12 2016-07-12 Improved CLSVOF method for quickly building signed distance function by VOF function

Country Status (1)

Country Link
CN (1) CN106445882A (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111177965A (en) * 2019-12-25 2020-05-19 南京航空航天大学 Multi-resolution WENO format fixed-point fast scanning method based on solving of constancy problem
CN113178011A (en) * 2021-04-28 2021-07-27 哈尔滨工程大学 Cut grid THINC method for solving VOF convection equation
CN116011264A (en) * 2023-03-27 2023-04-25 北京适创科技有限公司 Thermal stress calculation method and device, electronic equipment and storage medium
CN117993328A (en) * 2024-03-29 2024-05-07 中国空气动力研究与发展中心超高速空气动力研究所 Method for characterizing appearance of two-dimensional flow field barrier

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111177965A (en) * 2019-12-25 2020-05-19 南京航空航天大学 Multi-resolution WENO format fixed-point fast scanning method based on solving of constancy problem
CN111177965B (en) * 2019-12-25 2022-06-17 南京航空航天大学 Multi-resolution WENO format fixed-point fast scanning method based on solving of constancy problem
CN113178011A (en) * 2021-04-28 2021-07-27 哈尔滨工程大学 Cut grid THINC method for solving VOF convection equation
CN116011264A (en) * 2023-03-27 2023-04-25 北京适创科技有限公司 Thermal stress calculation method and device, electronic equipment and storage medium
CN117993328A (en) * 2024-03-29 2024-05-07 中国空气动力研究与发展中心超高速空气动力研究所 Method for characterizing appearance of two-dimensional flow field barrier
CN117993328B (en) * 2024-03-29 2024-05-28 中国空气动力研究与发展中心超高速空气动力研究所 Method for characterizing appearance of two-dimensional flow field barrier

Similar Documents

Publication Publication Date Title
CN106445882A (en) Improved CLSVOF method for quickly building signed distance function by VOF function
CN110069800B (en) Three-dimensional structure topology optimization design method and equipment with smooth boundary expression
Chen et al. Point cloud resampling using centroidal Voronoi tessellation methods
CN104036095B (en) Coupling high accuracy complex appearance flow field fast algorithm based on Region Decomposition
CN109726465B (en) Three-dimensional non-adhesive low-speed streaming numerical simulation method based on non-structural curved edge grid
Dai et al. A novel fast method for L∞ problems in multiview geometry
Bank et al. Superconvergent derivative recovery for Lagrange triangular elements of degree p on unstructured grids
Gao et al. A residual-based procedure for hp-adaptation on 2-d hybrid meshes
CN117473655B (en) Aircraft simulation driving design method and device based on edge collapse grid optimization
Chen et al. Stability and accuracy of adapted finite element methods for singularly perturbed problems
CN103279985B (en) A kind of intelligent Modeling method of complicated landform structural system three-dimensional finite element model
Badshah et al. On two multigrid algorithms for modeling variational multiphase image segmentation
Collins et al. A penalty-free Shifted Boundary Method of arbitrary order
CN109165402B (en) Method for solving general power function-shaped hydraulic optimal section of open channel
Gerace et al. A model-integrated localized collocation meshless method (MIMS)
Loseille et al. Developments on the P^ 2 cavity operator and Bézier Jacobian correction using the simplex algorithm.
CN112989679B (en) Structure-guided hexahedral mesh geometric optimization method
Hao et al. Surface reconstruction based on CAD model driven priori templates
Liu et al. An improved Poisson surface reconstruction algorithm based on the boundary constraints
CN110188498B (en) Optimal non-design space partitioning method based on topological optimization variable density method
Pons et al. A Lagrangian approach to dynamic interfaces through kinetic triangulation of the ambient space
CN109308382B (en) Analysis method for contact stress near singular point
Lin et al. Trivariate B-spline solid construction by pillow operation and geometric iterative fitting
CN108073776B (en) Complex river network trunk and branch intersection grid drawing and river center continent grid processing method
CN116529774A (en) Model optimization method, device and storage medium for additive manufacturing

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20170222

RJ01 Rejection of invention patent application after publication