CN101944151A - Wall boundary simulation method in molecular dynamics simulation - Google Patents
Wall boundary simulation method in molecular dynamics simulation Download PDFInfo
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Abstract
The invention discloses a wall boundary simulation method in molecular dynamics simulation. The method integrates the advantages of a total reflection method and a random reflection method, can truly reflect the motion state of a particle after colliding with a wall and is also called as a semi-reflection method. The method comprises the following steps of: (1) defining a data structure of the particle in the molecular dynamics simulation; (2) determining the current position A (x0, y0, z0, u0, v0, w0) of the particle in a channel; (3) determining the motion direction of the particle according to the current position of the particle and information of acting force by other particles of the particle, and judging whether the particle can move to other positions beyond the wall boundary in a next step or not according to the current position and the acting force information of the particle; and (4) if the particle moves to a position beyond the wall boundary, reflecting the particle through the wall to a next reflection position B (x, y, z, u, v, w), wherein if the wall exists in the x direction, y is equal to y', z is equal to z', x is equal to 2*x' (which is the coordinate of the wall in the x direction), and the speed direction of the particle is random. In the simulation of the invention, physical conditions of wall constant temperature and wall roughness can be reflected, the position of the reflected particle can be more truly reflected, and the method also can be applied to an irregular nano channel to simplify the calculating method of a velocity vector.
Description
Technical field
The present invention relates to the method in a kind of molecular dynamics simulation, especially the method for the movement locus of simulation particle under wall boundary condition.
Background technology
The dynamics that now increasing scientist is flowed with fluid and nanochannel inner fluid in the molecular dynamics method simulation parallel flat.Along with going deep into of research, scientists begins the non-straight nanochannel is studied and adopted the molecular dynamics method that this passage is simulated, as: people such as Xi-Jun Fan adopt the non equilibrium molecular dynamics method to simulate the flow characteristics of simple fluid in the periodicity jet pipe; Roughness flows to the microchannel endosome and the influence of boundary slip character in order to study, and people such as Cao's handle sun have studied argon gas flowing in zigzag platinum passage; People such as J.Castillo-Tejas simulate at the flow process in 4: 1: 4 contraction-extended channels linear polymerization chain and Newtonian fluid respectively.Simulate between two flat boards and during the flow characteristics of nanochannel inner fluid using the molecular dynamics method, in the document in the past virtual thermal wall (Virtualthermal wall) situation lower wall surface simulation of boundary condition there are two kinds of methods, a kind of is Allen, M.P.and D.J.Tildesley, the total reflection method that in document Computer Simulation of Liquids., proposes, total reflection method is regarded wall as smooth mirror surface, direct reflection takes place in particle on wall, adopt the movement locus of total reflection method simulation particle under wall boundary condition referring to Fig. 1 (a), when particle when the A point moves to B ', because the existence of virtual wall, particle can not occur in the position of B ', particle can move to the B point after wall generation total reflection, B and B ' point are about the wall symmetry, remain unchanged with the velocity of wall parallel coordinates direction, remain unchanged with the velocity size of wall vertical coordinate direction, direction is reverse; Though total reflection method can reflect the position of particle after launching truly, but total reflection method can not simulate particle at the movement locus of deciding under the rough condition of wall temperature and wall, if and in the non-straight nanochannel, if adopt total reflection method to come track under the wall boundary condition of simulation particle, then also have certain degree of difficulty aspect the computing velocity vector; Another kind is Raraport, D.C. in document The art of molecular dynamics simulation., the random reflected method has been proposed, the random reflected method is corresponding with casual emission physically, adopt the movement locus of random reflected method simulation particle under wall boundary condition referring to Fig. 1 (b), particle reflexes to B ' does vertical some B from vertical line to wall, velocity magnitude determines that by wall surface temperature direction at random.Though the random reflected method can simulate the physical condition that wall is rough and decide wall temperature, but the random reflected method since the position after the particle reflection in the unicity of wall vertical direction, therefore in the process of simulation particle movement locus, there is certain untrue property, can not truly reflects the position after particle reflects.
Therefore, how the motion state of real simulation particle under wall boundary condition becomes the technical matters that the researchist in this area is badly in need of solving.
Summary of the invention
At the prior art above shortcomings, the invention provides a kind of in molecular dynamics simulation, when particle is in wall boundary condition following time, comprehensively total reflection method and random reflected method advantage, the wall boundary condition simulation method of the motion state of real embodiment particle under wall boundary condition.
In order to realize the foregoing invention purpose, the present invention takes following technical scheme: the analogy method on wall border in the molecular dynamics simulation is characterized in that described analogy method comprises following steps:
A) data structure of particle in the definition molecular dynamics simulation, particle is represented the motion state of particle in the molecular dynamics simulation passage by six information in three-dimensional model, described six information are respectively x direction coordinate, y direction coordinate, z direction coordinate, x direction speed, y direction speed and z direction speed; Wherein x direction coordinate is the wall horizontal ordinate, and y direction coordinate is the wall ordinate, and the z direction is the direction vertical with the XY plane;
B) determine the current location A (x of particle in passage
0, y
0, z
0, u
0, v
0, w
0), x wherein
0The current position coordinates of expression particle on the x direction, y
0The current position coordinates of expression particle on the y direction, z
0The current position coordinates of expression particle on the z direction, u
0The current location speed of expression particle on the x direction, v
0The current location speed of expression particle on the y direction, w
0The current location speed of expression particle on the z direction;
C) be subjected to the acting force information of other particle according to particle current location and particle, determine the direction of motion of particle, and according to the particle current location and be subjected to force information to judge particle whether next step can move to the wall border with external position; If particle does not move to the wall border with external position, then particle can move along the direction of motion of determining, arrive next step assigned address B ' (x ', y ', z ', u ', v ', w '), wherein x ' is the assigned address coordinate of particle on the x direction, the assigned address coordinate of y ' expression particle on the y direction, the assigned address coordinate of z ' expression particle on the z direction, the assigned address speed of u ' expression particle on the x direction, the assigned address speed of v ' expression particle on the y direction, the assigned address speed of w ' expression particle on the z direction;
D) if particle movement is arrived the wall border with external position, particle can not arrive next step appointed positions B ', and particle is according to the temperature of wall, reflection arrives next step reflection position B (x, y, z through wall, u, v, w), when there is wall in the x direction, y=y ' wherein then, z=z ', the coordinate-x ' of x=2* wall x direction
The particle's velocity direction at random; When there is wall in the y direction, x=x ' wherein then, z=z ', the coordinate-y ' of y=2* wall y direction,
The particle's velocity direction at random; When there is wall in the z direction, x=x ' wherein then, y=y ', the coordinate-z ' of z=2* wall z direction,
The particle's velocity direction at random.
In the above-mentioned formula, (document The art of moleculardynamics simulation (D.C.Rapaport is adopted in obtaining of this random number to a for the random number between-1～1, Second Edition, Cambridge University Press, 2004) program in is calculated, be not described in detail at this), k
BBe Boltzmann constant, T is a Current Temperatures, m is a quality, x represents the reflection position coordinate of particle on the x direction, y represents the reflection position coordinate of particle on the y direction, and z represents the reflection position coordinate of particle on the z direction, and u is the reflection position speed of particle on the x direction, v is the reflection position speed on the particle y direction, and w is the reflection position speed of particle on the z direction.
The analogy method on wall border in the molecular dynamics simulation of the present invention, its cardinal principle are to have considered the influence of wall roughness to particle rapidity on the direct reflection basis, and therefore, the inventive method can be called the half reflection method again.
Generally, the macroscopic quantity of statistical system can be by the motion state of particle, promptly in the inventive method by particle respectively at x, y, coordinate on the z direction and particle are respectively at x, y, the speed of z direction reflects the motion state of particle, when the particle movement state changes, and x, y, coordinate on the z direction and particle be respectively at x, y, and the speed of z direction all can change.When adopting the half reflection method particle to be in movement locus under the wall boundary condition to simulate, it had both considered the randomness of particle, and promptly particle is after running into wall and reflecting, its reflection position speed (u, v w) can be relevant according to the temperature of wall, and its reflection position x, y, z direction coordinate (x, y, z) then do not meet the x of next step predetermined assigned address of wall with particle, y, z direction coordinate (x ', y ', z ') relevant.Therefore this method is not only considered the temperature of wall when next step position of simulation particle, considered that also particle reflects through wall after, its position must with particle relation is not arranged through the position of reflection.
The beneficial effect that the present invention produces:
(1) the inventive method not only can embody permanent wall temperature condition and the rough physical condition of wall in molecular dynamics simulation, and can truly reflect the position after the particle reflection in molecular dynamics simulation.It has solved in the random reflected method can not reflect the problem of position afterwards by the actual response particle.
(2) the inventive method can also be simplified the velocity computing method in irregular nanochannel, thereby is convenient to calculate.Solved that the total reflection boundary method can not be simulated the problem of the real motion state of particle under permanent wall temperature condition and the rough condition of wall and in irregular nanochannel, total reflection method can not be simplified the problem of velocity computing method.
(3) the inventive method can be used for the motion conditions of simulation particle after outside various different passages move to virtual wall border, thereby for research particle motion state in different passages, provides technical support.
Description of drawings
Fig. 1 is the particle movement track synoptic diagram in the molecular dynamics simulation; Wherein (a) is for adopting the movement locus synoptic diagram of total reflection method simulation particle under wall boundary condition; Wherein (b) is for adopting the movement locus synoptic diagram of random reflected method simulation particle under wall boundary condition;
Fig. 2 is that the particle in the molecular dynamics simulation reflects synoptic diagram under two kinds of boundary conditions: (a) half reflection particle trajectory motion synoptic diagram wherein; (b) random reflected particle trajectory motion synoptic diagram;
Fig. 3 is the variable cross section access diagram in the molecular dynamics simulation; Wherein (a) is three-dimensional variable cross section access diagram; (b) be three-dimensional variable cross section passage front elevational schematic;
Fig. 4 is that population density distributes with the comparison diagram to the wall distance in the molecular dynamics simulation;
Fig. 5 is a potential energy change curve in time in the inventive method simulation variable cross section nanochannel.
Embodiment
Below in conjunction with the drawings and specific embodiments the present invention is done explanation in further detail.
A kind of new wall boundary condition disposal route---half reflection method that combines total reflection method and random reflected method advantage is proposed herein.When particle A point moves to B ', as Fig. 1 (a), because the existence of wall, particle arrives the B point through wall reflection back, and coordinate position is identical with total reflection method particle reflection back, but velocity magnitude is determined by wall surface temperature, direction at random, promptly definite method of velocity is identical with the random reflected method.When simulation non-straight micro-nano passage, such as non-45 ° of ramp ways, if wall adopts total reflection boundary condition treatment method, after the particle reflection, velocity define certain degree of difficulty.The random reflected method has implied two conditions with respect to total reflection method: (1) wall constant temperature; (2) wall is rough, and is more approaching with truth.But the random reflected method has certain untrue property when the simulation nanochannel.As shown in Figure 2, the x direction is a flow direction, when regional A is arrived in particle movement, if adopt the random reflected method, see Fig. 2 (b), particle B is in and appears at B ' after optional position among the A is regulated through coordinate, can not go out the coordinate position of particle movement by actual response.If but adopted half reflection boundary condition analogy method, as Fig. 2 (a), particle B would appear at the optional position among the regional A, can appear at the corresponding B ' point arbitrarily of B after employing half reflection method is regulated through coordinate, thereby more approaching with the real motion position of particle.
Present embodiment is by in the molecular dynamics simulation process, adopt random reflected method, total reflection method and three kinds of wall boundary condition analogy methods of half reflection to simulate argon process fluid flow in the parallel flat respectively, thereby further specify the difference of the inventive method and existing random reflected method and total reflection method.Concrete enforcement is as follows:
Adopt in the ar atmo simulation NVT system, with speed revised law control system temperature, interaction between atoms adopts the 12-6LJ Potential Model, the equation of motion adopts the Verlet numerical integrating, time step is 1fs, and simulated time is 100000fs, and simulation is of a size of 6nm * 6nm * 1.5nm, population is 648, and density is 1g/cm
3. in the present embodiment, true origin is defined as 0 point, x and y direction adopt periodic boundary condition, (the Z direction is meant direction vertical with the xy plane in the three-dimensional channel when the z direction, particle only may exceed the wall border of z direction, because x and y direction adopt periodic boundary condition, so all be unlimited the extension in this embodiment, do not have wall) be 0 o'clock, the xy plane is a lower wall surface, when z was 1.5nm, the xy plane was a upper wall surface, adopted three kinds of different wall boundary condition analogy methods to obtain the motion state of particle below respectively:
Random reflected method: x=x '; Y=y '; Z=0;
Total reflection method: x=x '; Y=y '; Coordinate-the z ' of z=2* wall z direction; U=u '; V=v '; W=-w '
Half reflection method: x=x '; Y=y '; Coordinate-the z ' of z=2* wall z direction;
In the above-mentioned formula, a is the random number between-1～1, k
BBe Boltzmann constant, T is a Current Temperatures, m is a quality, x represents the reflection position coordinate of particle on x direction coordinate, y represents the reflection position coordinate of particle on y direction coordinate, and z represents the reflection position coordinate of particle on z direction coordinate, and u is the reflection position speed of particle on x direction coordinate, v is the reflection position speed of particle on y direction coordinate, and w is the reflection position speed of particle on z direction coordinate." * " herein is multiplication sign, and "-" is minus sign.
From the simulation of adopting random reflected method, total reflection method and the half reflection method situation of being rebuffed in flowing of the argon fluid the parallel flat under given conditions, when adopting the simulation of random reflected method, referring to Fig. 1 (b) particle A (x
0, y
0, z
0, u
0, v
0, w
0) when exceeding the simulated domain border in motion process, particle can not arrive next step assigned address B ' (x ', y ', z ', u ', v ', w ') along given line, is vertical some B of vertical line, x=x ' and can reflex to B ' along particle to wall; Y=y '; The coordinate of z=wall z direction; Velocity magnitude is definite by wall surface temperature,
Direction at random; Total reflection method is analog when adopting, referring to Fig. 1 (a), and particle A (x
0, y
0, z
0, u
0, v
0, w
0) when in motion process, exceeding the simulated domain border, particle not can along given line arrive next step assigned address B ' (x ', y ', z ', u ', v ', w '), particle can move to B (x, y, z after wall generation total reflection, u, v, w) point, B (x, y, z, u, v, w) and B ' (x ', y ', z ', u ', v ', w ') about the wall symmetry, remain unchanged with the velocity of wall parallel coordinates direction, remain unchanged with the velocity magnitude of wall vertical coordinate direction, velocity reversal is reverse; When adopting the simulation of half reflection method, particle A (x
0, y
0, z
0, u
0, v
0, w
0) when in motion process, exceeding the simulated domain border, particle not can along given line arrive next step assigned address B ' (x ', y ', z ', u ', v ', w '), and can on virtual wall border, reflect, arrive reflection position B (x, y, z, u, v, w), its reflection back position B both with particle do not take place reflex time assigned address B ' (x ', y ', z ', u ', v ', w ') relevant, also relevant with the temperature of the wall of particle generation reflex time, i.e. x=x '; Y=y '; Coordinate-the z ' of z=2* wall z direction;
Velocity reversal after the particle reflection at random, thereby obtain position after the particle reflection.Because the speed after the particle reflection and the speed component u of three directions, v is relevant with w, and therefore, the velocity magnitude after the particle reflection is
And the direction of speed is velocity reversal synthetic of three speed components, and speed component has and just has negatively, so synthetic velocity reversal also is that all angles all have, thereby the velocity reversal after the particle reflection is at random.In this instructions, the coordinate of the coordinate of the coordinate of wall x direction, wall y direction and wall z direction is meant the coordinate of wall in three-dimensional cartesian coordinate system, because the initial point of three-dimensional system of coordinate can be 0 point in actual application, it also can not be 0 point, therefore, this coordinate in three-dimensional system of coordinate of wall is relevant with being provided with of three-dimensional system of coordinate initial point.
2) after simulation finishes, added up the situation that population density distributes under three kinds of wall boundary condition analogy method situations, as shown in Figure 4.
The comparative result explanation: the result 100% who adopts half reflection boundary condition simulation and adopt the simulation of total reflection boundary condition simulation to obtain coincide, and has very strong practicality.Thereby show that the inventive method when the motion state of simulation particle under wall boundary condition, not only can embody permanent wall temperature condition and the rough physical condition of wall, and can in molecular dynamics simulation, truly reflect the position after the particle reflection.
Half reflection boundary method and random reflected boundary method and the total reflection boundary method similarities and differences see Table 1 and table 2:
Table 1 half reflection boundary method and random reflected boundary method and total reflection boundary method characteristic comparison sheet
Table 2 half reflection boundary method and random reflected boundary method and total reflection boundary method identical point
| The random reflected boundary condition | The total reflection boundary condition | |
| Reflection back particle position | Different | Identical |
| The size of reflection back particle rapidity | Identical | Different |
| The direction of reflection back particle rapidity | Identical | Different |
From table 1 and table 2 as can be seen, half reflection boundary condition analogy method had both combined the advantage of considering wall surface temperature and smooth degree in the simulation of random reflected boundary condition, the variation of particle physical location in also simulating in conjunction with the total reflection boundary condition, therefore, it is simulated with the total reflection boundary condition with the simulation of random reflected boundary condition and compares, and more can reflect the variation of the motion state after being rebuffed of particle.
Embodiment 2: adopt half reflection boundary condition analogy method, adopt the flow process of tygon fluid in the molecular dynamics simulation variable cross section passage.Concrete steps are as follows:
1) adopt the present invention's simulation to carry out in the variable cross section channel architecture, the flow process of tygon molecule is referring to Fig. 3.With speed revised law control system temperature, the equation of motion adopts the Verlet numerical integrating, and time step is 1fs, and simulated time is 320000fs, and density is 0.2588g/cm
3
2) after simulation finishes, added up the potential energy of different time dot system, as shown in Figure 5.Potential energy is potential energy, is one of sign physical quantity of system's macrostate.When adopting random device commonly used, find to move to when surpassing optional position, xy and xz plane passages outside simultaneously at next step when particle, all can only be after particle is launched in 16 somes appearance fixing, this and actual conditions are not inconsistent; And when adopting total reflection method commonly used, when next step moves to above border, passage inclined-plane when particle, be difficult to the velocity after definite particle reflects, at this moment, adopting the inventive method (half reflection method) is a kind of authentic and valid mode, because adopt method of the present invention, after particle is launched, can appear at the optional position in the passage really, and be easy to calculate velocity.
Analog result explanation: the present invention can be applied in the process of molecular dynamics simulation example, and the motion state that reflects can the real simulated particle takes place after running into virtual wall, is a kind of authentic and valid numerical simulation calculation method.
The inventive method can be used for the motion state after the multiple passage of simulation particle runs into wall, when the real motion state of simulation particle in passage, both needed to consider the proper motion state of particle, it is the motion state that particle is not run into virtual wall, (analogy method of this normal condition has been ripe prior art, do not do at this patent yet and to elaborate), need to consider the improper motion state of particle again, it is particle motion state after running into virtual wall, in simulation to this motion state, prior art has proposed total reflection method and random reflected method, but because these two kinds of defectives that method self is intrinsic, thereby can not effectively simulate effective status after particle is rebuffed really, thereby the applicant proposes " half reflection method ", this method has overcome the defective of total reflection method and random reflected method, can be authentic and valid simulate motion state after particle is rebuffed.The proposition of this method be effectively the statistics particle in the position at each quarter, velocity magnitude, and further count the temperature of system, macroscopical physical parameters such as kinetic energy, potential energy, thereby be the motion state technical supports of the different particles of research in different passages.
The inventive method can be simulated the motion state after different particles are rebuffed in different passages, such as: the argon process fluid flow, other situation such as tygon process fluid flow in hydrone flow process and the various passage, need to prove especially if analog channel is when being circular channel, after coordinate transformation became cylindrical coordinates or polar coordinates, the inventive method stood good.
Claims (1)
1. the analogy method on wall border in the molecular dynamics simulation is characterized in that, described analogy method comprises following steps:
A) data structure of particle in the definition molecular dynamics simulation, particle is represented the motion state of particle in the molecular dynamics simulation passage by six information in three-dimensional model, described six information are respectively x direction coordinate, y direction coordinate, z direction coordinate, x direction speed, y direction speed and z direction speed; Wherein x direction coordinate is the wall horizontal ordinate, and y direction coordinate is the wall ordinate, and the z direction is the direction vertical with the xy plane;
B) determine the current location A (x of particle in passage
0, y
0, z
0, u
0, v
0, w
0), x wherein
0The current position coordinates of expression particle on the x direction, y
0The current position coordinates of expression particle on the y direction, z
0The current position coordinates of expression particle on the z direction, u
0The current location speed of expression particle on the x direction, v
0The current location speed of expression particle on the y direction, w
0The current location speed of expression particle on the z direction;
C) be subjected to the acting force information of other particle according to particle current location and particle, determine the direction of motion of particle, and according to the particle current location and be subjected to force information to judge particle whether next step can move to the wall border with external position; If particle does not move to the wall border with external position, then particle can move along the direction of motion of determining, arrive next step assigned address B ' (x ', y ', z ', u ', v ', w '), wherein x ' is the assigned address coordinate of particle on the x direction, the assigned address coordinate of y ' expression particle on the y direction, the assigned address coordinate of z ' expression particle on the z direction, the assigned address speed of u ' expression particle on the x direction, the assigned address speed of v ' expression particle on the y direction, the assigned address speed of w ' expression particle on the z direction;
D) if particle movement is arrived the wall border with external position, particle can not arrive next step appointed positions B ', and particle is according to the temperature of wall, reflection arrives next step reflection position B (x, y, z through wall, u, v, w), when there is wall in the x direction, y=y ' wherein then, z=z ', the coordinate-x ' of x=2* wall x direction
The particle's velocity direction at random; When there is wall in the y direction, x=x ' wherein then, z=z ', the coordinate-y ' of y=2* wall y direction,
The particle's velocity direction at random; When there is wall in the z direction, x=x ' wherein then, y=y ', the coordinate-z ' of z=2* wall z direction,
The particle's velocity direction at random;
In the above-mentioned formula, a is the random number between-1～1, k
BBe Boltzmann constant, T is a Current Temperatures, m is a quality, x represents the reflection position coordinate of particle on the x direction, y represents the reflection position coordinate of particle on the y direction, and z represents the reflection position coordinate of particle on the z direction, and u is the reflection position speed of particle on the x direction, v is the reflection position speed of particle on the y direction, and w is the reflection position speed of particle on the z direction.
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