CN104866712B - A kind of velocity correction method of new projection immersed Boundary Method - Google Patents
A kind of velocity correction method of new projection immersed Boundary Method Download PDFInfo
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Abstract
The present invention relates to a kind of velocity correction method of new projection immersed Boundary Method, belong to Fluid Mechanics Computation and its fluid structurecoupling analogue technique field.The present invention includes A, mesh generation module is called, using two nested grids：Flow field regions Eulerian mesh, solid boundaries region Lagrangian mesh；B, flow field velocity prediction module is called, try to achieve the predicted value of flow field regions；C, Eulerian mesh point determined property module is called, judge that Eulerian mesh point belongs to solid interior region or solids external region；D, call flow field velocity correction module, update flow field velocity；E, call result output module, will act at the solid borderline power of stream and information of flow is output to file, read and show for backstage；F, judge whether terminate calculate.The present invention overcomes conventional projection immersed Boundary Method near wall region speed interpolation arithmetic complicated when solving, and has saved computing resource, has improved computational efficiency.
Description
Technical field
The present invention relates to a kind of velocity correction method of new projection immersed Boundary Method, belong to Fluid Mechanics Computation and its stream
Gu coupled simulation technical field.
Background technology
One of difficult point of fluid structurecoupling problem is that fluid and solid use different mathematical description frameworks.Generally, fluid is transported
It is dynamic to use Eulerian configuration, and solids movement is described using Lagrange：Traditional immersed Boundary Method, solid boundaries region flow field speed
The correction of degree is obtained using linear (bilinearity) interpolation mostly, and often Interpolation Process calculates complex, and amount of calculation is big, meter
Calculate efficiency low.Therefore, the present invention proposes a kind of velocity correction method of new projection immersed Boundary Method, flow field regions are divided into
Pure flow field regions and time flow field regions, pure flow field regions speed are no longer corrected, and to secondary flow field regions, first carry out Eulerian mesh point category
Property judge, if belonging to solid interior, directly allow speed to be equal to zero, if belonging to solids external, further according to the solid border effect of stream
Force density is modified.Interpolation Process complicated when near wall region speed is solved is avoided, amount of calculation is substantially reduced, and improves meter
Calculate efficiency.
The content of the invention
The invention provides a kind of velocity correction method of new projection immersed Boundary Method, for overcoming tradition immersion side
Boundary's method calculates complex near wall region speed method for solving, amount of calculation is big, the problem of computational efficiency is low, it is to avoid near
Complicated Interpolation Process when wall area speed is solved, amount of calculation is substantially reduced, and improves computational efficiency.
What the velocity correction method of new projection immersed Boundary Method of the invention was realized in：The specific steps of methods described
It is as follows：
A, mesh generation module is called, using two nested grids：Flow field regions, solid boundaries region；Wherein flow field regions exist
Under Eulerian configuration using cartesian grid it is discrete, solid boundaries region Lagrange description under using fit curvilinear grid from
Dissipate, flow field regions include pure flow field regions and time flow field regions；
B, flow field velocity prediction module is called, using substep projecting method, solve the stream of incompressible viscous Newtonian fluid
Dynamic governing equation, tries to achieve the predicted value of flow field regions original variable；
C, Eulerian mesh point determined property module is called, judge that Eulerian mesh point belongs to outside solid interior region or solid
Portion region；
D, call flow field velocity correction module, update flow field velocity；
E, call result output module, the power and information of flow that will act in stream solid boundaries are output to file, supply
Background process software reads display；
F, judge whether terminate calculate：
If △ tn ＜ T, enter future time step, continue executing with step B, C, D, E and F；
If △ tn >=T, terminate whole calculating；
Wherein △ t are time step, and T is the total physical time for requiring to calculate, and n is time step number.
In the step A, the flow field regions include the area of space occupied by fluid and solid；Spatially by flow field
Region division is pure flow field regions and time flow field regions, and pure flow field regions refer to not to be influenceed and not comprising solid by solid wall boundary layer
Area of space inside, secondary flow field regions, which refer to, to be influenceed by solid wall boundary layer and completely includes the area of space including solid.
In the step A, flow field regions are divided under Eulerian configuration using cartesian grid, on its grid cell node
Flow field variable is referred to as euler variable, and by node coordinate information xjIt is output to file f cor.txt；Solid boundaries region is in glug
Lang descriptions are lower to be divided using fit curvilinear grid, and the variable on its grid node is referred to as lagrange's variable, corresponding grid section
Point coordinates information X (si) it is output to file scor.txt.
In the step B, flow field velocity prediction module refers to solve not using substep projecting method under first, boundary value condition
The Fluid Control Equation of compressible viscous Newtonian fluid, obtains the pressure of flow field regions, and then obtains the pre- of flow field regions and test the speed
Spend u ' (xj, t), and by routine interface, extract predetermined speed u ' (x on cartesian grid nodej, t), it is output to file
fvel.txt。
In the step C, Eulerian mesh point determined property module is comprised the following steps that：
C1, solid boundaries discrete nodes exterior normal direction solve module；To any solid boundaries discrete nodes X (si), its
Two neighboring node is respectively X (si-1) and X (si+1), make approximate this section of curve of a parabola by this 3 points, using s as ginseng
Number, the parabolic equation is expressed as
In formulaFor the coefficient of second-degree parabola equation (1), thus 3 points of coordinate is uniquely determined；
The exterior normal direction at any point on this section of curveIt is expressed as
Herein,X in x, the unit vector in y directions, formula is represented respectivelys,YsX (s) and Y (s) in (1) formula is represented respectively
First order derivative is asked to parameter s；
C2, any fluid grid node direction derivative solve module；To any fluid grid node xj, try to achieve nearest therewith
Solid boundaries discrete nodes X (smin), from solid boundaries discrete nodes X (smin) arrive fluid grid node xjDirectional derivativeIt is expressed as
According to formula (2), to solid boundaries discrete nodes X (smin), its exterior normal directionIt is expressed as
In formulaRepresent in (1) formula X (s) and Y (s) to parameter s first order derivative in discrete nodes X respectively
(smin) value；
C3, any fluid grid nodal community judge module；To any fluid grid node xj, definition
If δ >=0, then it is assumed that the fluid grid node is located at solids external, if δ<0, then it is assumed that the fluid grid section
Point is located at solid interior.
In the step D, comprising the following steps that for flow field velocity is updated：
D1, stream liquid/solid interface force densitySolve module；Pass through flow field sub-region speed u ' (xj, it is t) near with δ (x-X (s, t))
Speed u (X (s on the solid boundaries Lagrangian points obtained like smooth functioni) it is equal to the natural speed of given solid boundariesTo realize the solid border force density of streamSolution, and result is output to file sfor.txt；Wherein s is solid side
The initial configuration coordinate of boundary's discrete curve mesh point, t is the time, and variable subscript i and j represent solid boundaries discrete curve net respectively
J-th of unit of i-th of node of lattice and flow field regions Eulerian mesh；
D2, flow field regions velocity correction module；
If D2.1, fluid grid node xjPositioned at pure flow field regions, the node speed need not be corrected, i.e.,
u(xj, t)=u ' (xj,t) (6)
If D2.2, fluid grid node xjPositioned at secondary flow field regions, Eulerian mesh point determined property module is called：
If D2.2.1, fluid grid node xjPositioned at solid interior, fluid grid node xjU (x in speed modej, t) by
Following formula updates
u(xj, t)=0 (7)
If D2.2.2, fluid grid node xjPositioned at solids external, its velocity correction value Δ u (xj, t) it is：
Δ s in formulaiFor the area of i-th section of solid boundaries, the C in formulajiFor information transition matrix, it is defined as follows：
In formula, h is the grid spacing of flow field regions, and function phi is expressed as：
Fluid grid node xjSpeed u (xj, t) updated by following formula
u(xj, t)=u ' (xj,t)+Δu(xj,t) (11)
The beneficial effects of the invention are as follows：
1st, projection immersed Boundary Method avoids using Dynamic mesh, largely saves computing resource：It is traditional based on mobile network
The fluid structurecoupling method of lattice technology is, it is necessary to by Dynamic mesh, and for the solid with complex geometry profile, significantly
Solids movement often leads to the failure of flow field grid updating, and the present invention exactly makes up this major defect, in solid and fluid
Successfully avoid using Dynamic mesh during coupling.
2nd, the velocity correction method of projection immersed Boundary Method proposed by the present invention overcomes traditional immersed Boundary Method to solve closely
The complicated Interpolation Process of wall area speed, using suitable approximate smooth function, adaptability is stronger, using flowing the consistent bar of liquid/solid interface
Part, it is ensured that the fluid-structure coupling system conservation of energy, it is ensured that the validity that coupling is calculated.
3rd, flow field regions are divided into pure flow field regions and secondary flow field regions, velocity correction specific aim is stronger, greatly improves
Computational efficiency, makes it more effectively to predict the coupling of solid and fluid, in field of fluid mechanics and fluid structurecoupling field
It will be used widely.
Brief description of the drawings
Fig. 1 is the flow chart in the present invention；
Fig. 2 is the schematic diagram of the zoning of whole fluid-structure coupling system in the present invention；
Fig. 3, Fig. 4 is calculate the effect force density on the solid border of obtained a certain moment stream in the present invention；
Fig. 5 is calculates the VELOCITY DISTRIBUTION in obtained a certain moment flow field in the present invention.
Embodiment
Embodiment 1：As Figure 1-5, a kind of velocity correction method of new projection immersed Boundary Method, the tool of methods described
Body step is as follows：
A, mesh generation module is called, using two nested grids：Flow field regions, solid boundaries region；Wherein flow field regions exist
Under Eulerian configuration using cartesian grid it is discrete, solid boundaries region Lagrange description under using fit curvilinear grid from
Dissipate, flow field regions include pure flow field regions and time flow field regions；
B, flow field velocity prediction module is called, using substep projecting method, solve the stream of incompressible viscous Newtonian fluid
Dynamic governing equation, tries to achieve the predicted value of flow field regions original variable；
C, Eulerian mesh point determined property module is called, judge that Eulerian mesh point belongs to outside solid interior region or solid
Portion region；
D, call flow field velocity correction module, update flow field velocity；
E, call result output module, the power and information of flow that will act in stream solid boundaries are output to file, supply
Background process software reads display；
F, judge whether terminate calculate：
If △ tn ＜ T, enter future time step, continue executing with step B, C, D, E and F；
If △ tn >=T, terminate whole calculating；
Wherein △ t are time step, and T is the total physical time for requiring to calculate, and n is time step number.
In the step A, the flow field regions include the area of space occupied by fluid and solid；Spatially by flow field
Region division is pure flow field regions and time flow field regions, and pure flow field regions refer to not to be influenceed and not comprising solid by solid wall boundary layer
Area of space inside, secondary flow field regions, which refer to, to be influenceed by solid wall boundary layer and completely includes the area of space including solid.
In the step A, flow field regions are divided under Eulerian configuration using cartesian grid, on its grid cell node
Flow field variable is referred to as euler variable, and by node coordinate information xjIt is output to file f cor.txt；Solid boundaries region is in glug
Lang descriptions are lower to be divided using fit curvilinear grid, and the variable on its grid node is referred to as lagrange's variable, corresponding grid section
Point coordinates information X (si) it is output to file scor.txt.
In the step B, flow field velocity prediction module refers to solve not using substep projecting method under first, boundary value condition
The Fluid Control Equation of compressible viscous Newtonian fluid, obtains the pressure of flow field regions, and then obtains the pre- of flow field regions and test the speed
Spend u ' (xj, t), and by routine interface, extract predetermined speed u ' (x on cartesian grid nodej, t), it is output to file
fvel.txt。
In the step C, Eulerian mesh point determined property module is comprised the following steps that：
C1, solid boundaries discrete nodes exterior normal direction solve module；To any solid boundaries discrete nodes X (si), its
Two neighboring node is respectively X (si-1) and X (si+1), make approximate this section of curve of a parabola by this 3 points, using s as ginseng
Number, the parabolic equation is expressed as
In formulaFor the coefficient of second-degree parabola equation (1), thus 3 points of coordinate is uniquely determined；
The exterior normal direction at any point on this section of curveIt is expressed as
Herein,X in x, the unit vector in y directions, formula is represented respectivelys,YsX (s) and Y (s) in (1) formula is represented respectively
First order derivative is asked to parameter s；
C2, any fluid grid node direction derivative solve module；To any fluid grid node xj, try to achieve nearest therewith
Solid boundaries discrete nodes X (smin), from solid boundaries discrete nodes X (smin) arrive fluid grid node xjDirectional derivativeIt is expressed as
According to formula (2), to solid boundaries discrete nodes X (smin), its exterior normal directionIt is expressed as
In formulaRepresent in (1) formula X (s) and Y (s) to parameter s first order derivative in discrete nodes X respectively
(smin) value；
C3, any fluid grid nodal community judge module；To any fluid grid node xj, definition
If δ >=0, then it is assumed that the fluid grid node is located at solids external, if δ<0, then it is assumed that the fluid grid section
Point is located at solid interior.
In the step D, comprising the following steps that for flow field velocity is updated：
D1, stream liquid/solid interface force densitySolve module；Pass through flow field sub-region speed u ' (xj, it is t) near with δ (x-X (s, t))
Speed u (X (s on the solid boundaries Lagrangian points obtained like smooth functioni) it is equal to the natural speed of given solid boundariesTo realize the solid border force density of streamSolution, and result is output to file sfor.txt；Wherein s is solid side
The initial configuration coordinate of boundary's discrete curve mesh point, t is the time, and variable subscript i and j represent solid boundaries discrete curve net respectively
J-th of unit of i-th of node of lattice and flow field regions Eulerian mesh；
D2, flow field regions velocity correction module；
If D2.1, fluid grid node xjPositioned at pure flow field regions, the node speed need not be corrected, i.e.,
u(xj, t)=u ' (xj,t) (6)
If D2.2, fluid grid node xjPositioned at secondary flow field regions, Eulerian mesh point determined property module is called：
If D2.2.1, fluid grid node xjPositioned at solid interior, fluid grid node xjU (x in speed modej, t) by
Following formula updates
u(xj, t)=0 (7)
If D2.2.2, fluid grid node xjPositioned at solids external, its velocity correction value Δ u (xj, t) it is：
Δ s in formulaiFor the area of i-th section of solid boundaries, the C in formulajiFor information transition matrix, it is defined as follows：
In formula, h is the grid spacing of flow field regions, and function phi is expressed as：
Fluid grid node xjSpeed u (xj, t) updated by following formula
u(xj, t)=u ' (xj,t)+Δu(xj,t) (11)
Embodiment 2：As Figure 1-5, a kind of velocity correction method of new projection immersed Boundary Method, the tool of methods described
Body step is as follows：
A certain water turbine movable guide vane aerofoil profile is included in flow field regions, its wing chord line length is L, and maximum gauge is D, is calculated
Region is 15L × 10L, and the origin of coordinates is located at the midpoint of chord line.Flowing Reynolds number is defined as Re=ρ UbD/ μ=200, time
Step delta t=0.002, square column boundary discrete method uses spacing for 0.01L.
S1：Mesh generation
Flow field regions (including fluid and water turbine movable guide vane airfoil region) use cartesian grid under Eulerian configuration
Divide, grid is uniform quadrilateral mesh, grid spacing is h=0.01L.And flow field regions are divided into pure flow field regions and secondary
Time flow field regions are 1.4L × 1.4L in flow field regions, this example, and secondary flow field regions center is the origin of coordinates.And by secondary flow field regions
Mesh point coordinate information is output to file f cor.txt, and solid boundaries region uses fit grid under Lagrange description
Lattice are divided, and spacing is 0.01L, and respective mesh node message file is output to scor.txt files.
S2：Flow field regions prediction of speed
Boundary value condition：
The zoning left side is inlet boundary condition, is u=Ub, v=0 is up and down sliding without penetrating boundary condition, i.e. u
=Ub, v=0, the right is export boundary condition,
Initial condition：
Set flow field regions velocity original value u=Ub, v=0, fluid field pressure p=0.
Using substep projecting method, the Fluid Control Equation of the incompressible viscous Newtonian fluid of numerical solution, by solving
Pressure Poisson's equation, obtains the pressure of flow field regions, and then obtain predetermined speed u ' (x in flow fieldj, t), and connect by program
Mouthful, extract predetermined speed u ' (x on the cartesian grid node of flow fieldj, t), it is output to file f vel.txt.
S3：Eulerian mesh point determined property module
S3.1, solid boundaries discrete nodes exterior normal direction solve module.To any solid boundaries discrete nodes X (si),
Its two neighboring node is respectively X (si-1) and X (si+1), can make approximate this section of curve of a parabola by this 3 points, using s as
Parameter, the parabolic equation is represented by
In formulaFor the coefficient of second-degree parabola equation (1), can thus 3 points coordinate it is uniquely true
It is fixed.
The exterior normal direction at any point on this section of curveIt is represented by
Herein,X, the unit vector in y directions are represented respectively.X in formulas,YsX (s) and Y (s) in (1) formula is represented respectively
First order derivative is asked to parameter s.
S3.2, any fluid grid node direction derivative solve module.To any fluid grid node xj, try to achieve therewith most
Near solid boundaries discrete nodes X (smin), from solid boundaries discrete nodes X (smin) arrive fluid grid node xjDirection lead
NumberIt is represented by
According to formula (2), to solid boundaries discrete nodes X (smin), its exterior normal directionIt is represented by
In formulaRepresent in (1) formula X (s) and Y (s) to parameter s first order derivative in discrete nodes X respectively
(smin) value.
S3.3, any fluid grid nodal community judge module.To any fluid grid node xj, definition
If δ >=0, the fluid grid node is considered as positioned at solids external, if δ<0, it is considered as the fluid grid section
Point is located at solid interior.
S4：Velocity correction is calculated
S4.1, stream liquid/solid interface active force density are calculated
To meet stream liquid/solid interface without consistent boundary condition of the sliding without infiltration, pass through flow field regions speed u ' (xj, t) and δ
Speed u (X (the s on solid boundaries Lagrangian points that (x-X (s, t)) approximate smooth function is obtainedi) given consolidate should be equal to
The natural speed on body borderTo realize stream liquid/solid interface force densitySolution, and result is output to file
sfor.txt.Wherein s is the initial configuration coordinate of solid boundaries discrete curve mesh point, and t is time, variable subscript i and j difference
Represent j-th of unit of i-th of node of solid boundaries discrete curve grid and flow field regions Eulerian mesh.
S4.2：Flow field regions velocity correction.
If S4.2.1, fluid grid node xjPositioned at pure flow field regions, the node speed need not be corrected, i.e.,
u(xj, t)=u ' (xj,t) (6)
If S4.2.2, fluid grid node xjPositioned at secondary flow field regions, Eulerian mesh point determined property module is called.
If S4.2.2.1, fluid grid node xjPositioned at solid interior, fluid grid node xjU (x in speed modej,t)
It can be updated by following formula
u(xj, t)=0 (7)
If S4.2.2.2, fluid grid node xjPositioned at solids external, its velocity correction value Δ u (xj, t) it is：
Δ s in formulaiFor the area of i-th section of solid boundaries, the C in formulajiFor information transition matrix, it is defined as follows：
In formula, h is the grid spacing of flow field regions, and function phi is represented by：
Fluid grid node xjSpeed u (xj, can t) be updated by following formula
u(xj, t)=u ' (xj,t)+Δu(xj,t) (11)
S5：Call result output module, will act at the solid borderline power of stream and information of flow is output to file, for after
Handle software and read display.
Fig. 3, Fig. 4 show that n=10000 is walked, that is, the effect force density edge solid side of stream on stream solid border when calculating time t=20
The distribution of boundary's curve.Fig. 3 is stream liquid/solid interface force densityComponent in x directionsAlong the distribution (s of stator aerofoil profile boundary curvei
=1 is starting point, positioned at the trailing edge point of aerofoil profile, in the counterclockwise direction), Fig. 4 is stream liquid/solid interface force densityComponent in y directionsAlong the distribution of stator aerofoil profile boundary curve.
Fig. 5 is calculates obtained n=10000 steps in the present invention, that is, the VELOCITY DISTRIBUTION in flow field is equivalent when calculating time t=20
Line chart.
S6：Time stepping method
After the completion of being calculated in a time step, next time step is transferred to, repeat the above steps S2-S5, until meeting
Time requirement is calculated to stop calculating.This example takes time step Δ t=0.002s, calculates total time T=60s, altogether time step n=
30000。
Above in conjunction with accompanying drawing to the present invention embodiment be explained in detail, but the present invention be not limited to it is above-mentioned
Embodiment, can also be before present inventive concept not be departed from the knowledge that those of ordinary skill in the art possess
Put that various changes can be made.
Claims (5)
1. a kind of velocity correction method of new projection immersed Boundary Method, it is characterised in that：Methods described is comprised the following steps that：
A, mesh generation module is called, using two nested grids：Flow field regions, solid boundaries region；Wherein flow field regions are in Euler
Description is lower discrete using cartesian grid, and solid boundaries region is discrete using fit curvilinear grid under Lagrange description, stream
Field areas includes pure flow field regions and time flow field regions；
B, flow field velocity prediction module is called, using substep projecting method, solve the flowing control of incompressible viscous Newtonian fluid
Equation processed, tries to achieve the predicted value of flow field regions original variable；
C, Eulerian mesh point determined property module is called, judge that Eulerian mesh point belongs to solid interior region or solids external area
Domain, Eulerian mesh point determined property module is comprised the following steps that：
C1, solid boundaries discrete nodes exterior normal direction solve module；To any solid boundaries discrete nodes X (si), its adjacent two
Individual node is respectively X (si-1) and X (si+1), make approximate this section of curve of a parabola, using s as parameter, the throwing by this 3 points
Thing line equation is expressed as
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The exterior normal direction at any point on this section of curveIt is expressed as
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Number s seeks first order derivative；
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Body boundary discrete method nodes X (smin), from solid boundaries discrete nodes X (smin) arrive fluid grid node xjDirectional derivativeIt is expressed as
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<mi>y</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<mi>Y</mi>
<mo>(</mo>
<msub>
<mi>s</mi>
<mi>min</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>n</mi>
<mi>y</mi>
<mi>j</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<mi>Y</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>s</mi>
<mi>i</mi>
<mi>min</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<mi>X</mi>
<mo>(</mo>
<msub>
<mi>s</mi>
<mi>min</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<mi>Y</mi>
<mo>(</mo>
<msub>
<mi>s</mi>
<mi>min</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
According to formula (2), to solid boundaries discrete nodes X (smin), its exterior normal directionIt is expressed as
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>N</mi>
<mi>x</mi>
<mi>min</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mrow>
<mo>-</mo>
<msubsup>
<mi>Y</mi>
<mi>s</mi>
<mi>min</mi>
</msubsup>
</mrow>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>X</mi>
<mi>s</mi>
<mi>min</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>Y</mi>
<mi>s</mi>
<mi>min</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>N</mi>
<mi>y</mi>
<mi>min</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>X</mi>
<mi>s</mi>
<mi>i</mi>
</msubsup>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>X</mi>
<mi>s</mi>
<mi>min</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>Y</mi>
<mi>s</mi>
<mi>min</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formulaRepresent in (1) formula X (s) and Y (s) to parameter s first order derivative in discrete nodes X (s respectivelymin)
Value；
C3, any fluid grid nodal community judge module；To any fluid grid node xj, definition
<mrow>
<mi>&delta;</mi>
<mo>=</mo>
<msubsup>
<mi>n</mi>
<mi>x</mi>
<mi>j</mi>
</msubsup>
<mo>&CenterDot;</mo>
<msubsup>
<mi>N</mi>
<mi>x</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>n</mi>
<mi>y</mi>
<mi>j</mi>
</msubsup>
<mo>&CenterDot;</mo>
<msubsup>
<mi>N</mi>
<mi>y</mi>
<mi>min</mi>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
If δ >=0, then it is assumed that the fluid grid node is located at solids external, if δ<0, then it is assumed that the fluid grid node position
In solid interior；
D, call flow field velocity correction module, update flow field velocity；
E, call result output module, the power and information of flow that will act in stream solid boundaries are output to file, for backstage
Handle software and read display；
F, judge whether terminate calculate：
If △ tn ＜ T, enter future time step, continue executing with step B, C, D, E and F；
If △ tn >=T, terminate whole calculating；
Wherein △ t are time step, and T is the total physical time for requiring to calculate, and n is time step number.
2. a kind of velocity correction method of new projection immersed Boundary Method according to claim 1, it is characterised in that：It is described
In step A, the flow field regions include the area of space occupied by fluid and solid；Spatially flow field regions are divided into pure
Flow field regions and time flow field regions, pure flow field regions refer to not to be influenceed and not comprising the space region including solid by solid wall boundary layer
Domain, secondary flow field regions, which refer to, to be influenceed by solid wall boundary layer and completely includes the area of space including solid.
3. a kind of velocity correction method of new projection immersed Boundary Method according to claim 1, it is characterised in that：It is described
In step A, flow field regions are divided under Eulerian configuration using cartesian grid, and the flow field variable on its grid cell node is referred to as
Euler variable, and by node coordinate information xjIt is output to file f cor.txt；Solid boundaries region makes under Lagrange description
Divided with fit curvilinear grid, the variable on its grid node is referred to as lagrange's variable, respective mesh node coordinate information X
(si) it is output to file scor.txt.
4. a kind of velocity correction method of new projection immersed Boundary Method according to claim 1, it is characterised in that：It is described
In step B, flow field velocity prediction module refers to solve incompressible sticky ox using substep projecting method under first, boundary value condition
The Fluid Control Equation of fluid, obtains the pressure of flow field regions, and then obtain predetermined speed u ' (x of flow field regionsj, t), and
By routine interface, predetermined speed u ' (x on cartesian grid node are extractedj, t), it is output to file f vel.txt.
5. a kind of velocity correction method of new projection immersed Boundary Method according to claim 1, it is characterised in that：It is described
In step D, comprising the following steps that for flow field velocity is updated：
D1, stream liquid/solid interface force densitySolve module；Pass through flow field sub-region speed u ' (xj, t) the approximate light with δ (x-X (s, t))
The speed u (X (si)) on solid boundaries Lagrangian points that sliding function is obtained is equal to the natural speed of given solid boundariesTo realize the solid border force density of streamSolution, and result is output to file sfor.txt；Wherein s is solid
The initial configuration coordinate of boundary discrete method grid lattice point, t is the time, and variable subscript i and j represent solid boundaries discrete curve respectively
J-th of unit of i-th of node of grid and flow field regions Eulerian mesh；
D2, flow field regions velocity correction module；
If D2.1, fluid grid node xjPositioned at pure flow field regions, the node speed need not be corrected, i.e.,
u(xj, t)=u'(xj,t) (6)
If D2.2, fluid grid node xjPositioned at secondary flow field regions, Eulerian mesh point determined property module is called：
If D2.2.1, fluid grid node xjPositioned at solid interior, fluid grid node xjU (x in speed modej, t) by following formula
Update
u(xj, t)=0 (7)
If D2.2.2, fluid grid node xjPositioned at solids external, its velocity correction value Δ u (xj, t) it is：
<mrow>
<mi>&Delta;</mi>
<mi>u</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mi>i</mi>
</munder>
<msub>
<mi>C</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mi>F</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>X</mi>
<mi>B</mi>
<mi>i</mi>
</msubsup>
<mo>,</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>&Delta;s</mi>
<mi>i</mi>
</msub>
<mi>&Delta;</mi>
<mi>t</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mi>M</mi>
<mo>;</mo>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mi>N</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
Δ s in formulaiFor the area of i-th section of solid boundaries, the C in formulajiFor information transition matrix, it is defined as follows：
<mrow>
<msub>
<mi>C</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>X</mi>
<mi>B</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msup>
<mi>h</mi>
<mn>2</mn>
</msup>
</mfrac>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msubsup>
<mi>X</mi>
<mi>B</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</mrow>
<mi>h</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msubsup>
<mi>Y</mi>
<mi>B</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
</mrow>
<mi>h</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msubsup>
<mi>Z</mi>
<mi>B</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msub>
<mi>z</mi>
<mi>j</mi>
</msub>
</mrow>
<mi>h</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, h is the grid spacing of flow field regions, and function phi is expressed as：
<mrow>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>8</mn>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mo>|</mo>
<mi>r</mi>
<mo>|</mo>
<mo>+</mo>
<msqrt>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>4</mn>
<mrow>
<mo>|</mo>
<mi>r</mi>
<mo>|</mo>
</mrow>
<mo>-</mo>
<mn>4</mn>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>0</mn>
<mo>&le;</mo>
<mrow>
<mo>|</mo>
<mi>r</mi>
<mo>|</mo>
</mrow>
<mo><</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>8</mn>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>-</mo>
<mn>2</mn>
<mo>|</mo>
<mi>r</mi>
<mo>|</mo>
<mo>+</mo>
<msqrt>
<mrow>
<mo>-</mo>
<mn>7</mn>
<mo>+</mo>
<mn>12</mn>
<mrow>
<mo>|</mo>
<mi>r</mi>
<mo>|</mo>
</mrow>
<mo>-</mo>
<mn>4</mn>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>1</mn>
<mo>&le;</mo>
<mrow>
<mo>|</mo>
<mi>r</mi>
<mo>|</mo>
</mrow>
<mo><</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>2</mn>
<mo>&le;</mo>
<mrow>
<mo>|</mo>
<mi>r</mi>
<mo>|</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Fluid grid node xjSpeed u (xj, t) updated by following formula
u(xj, t)=u'(xj,t)+Δu(xj,t) (11)。
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