CN112820356B - Method for quickly applying molecular dynamics boundary conditions based on geometric boundary operation - Google Patents
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Abstract
The invention discloses a method for quickly applying a molecular dynamics boundary condition based on geometric boundary operation, which comprises the following steps: extracting a geometric boundary of the molecular dynamics simulation model according to the molecular dynamics simulation model, finding out boundary particles through geometric boundary operation, and acquiring position information of each boundary particle in a boundary domain; and (3) endowing each boundary particle with reasonable speed and force, so that the macroscopic physical quantity of the boundary particle is consistent with the microscopic state, and the complete molecular dynamics boundary condition is obtained. The invention provides a general scheme for rapidly applying boundary conditions on a complex molecular dynamics system; the velocity boundary condition and the stress boundary condition of smooth transition are applied, the velocity distribution and the potential energy distribution of boundary particles are consistent with the local micro dynamic state of the system, the state fluctuation near the boundary is limited to a lower level, the problem of heavy task of applying the boundary condition is solved, and the boundary oscillation is greatly reduced.
Description
Technical Field
The invention relates to the technical field of molecular dynamics computational simulation, in particular to a method for quickly applying molecular dynamics boundary conditions based on geometric boundary operation.
Background
With the development of computer technology and numerical simulation theory, molecular Dynamics (MD) methods are becoming more and more interesting. The molecular dynamics is a numerical simulation method which obtains the phase trajectory of a system by numerically solving the mechanical motion equation of a molecular system and counts the structural characteristics and properties of the system. The method is widely applied to biological calculation, microfluid and micro-nano engineering simulation.
Molecular dynamics is a particle-based computational method, and the application of boundary conditions is a very difficult task. In a traditional grid-based computing method, such as a finite element method, boundary conditions are applied to a geometric boundary, and the traditional grid-based computing method can be conveniently operated in a graphical interaction mode and the like. However, molecular dynamics, as a discrete particle system, must impose boundary effects on all boundary particles. The selection and manipulation of a large number of boundary particles can be a very burdensome task. Especially for the computation region with complex shape, the fast operation of boundary particles still lacks an effective general processing method.
In addition, in a molecular dynamics system, the motion states of particles, including position, velocity, and potential energy, form a specific distribution. The motion state of the boundary particles must be adapted to the local distribution function, and the boundary effect cannot be simply averaged to the boundary particles, otherwise the oscillation of the system state is caused, the calculation error is increased, and even the calculation is not converged.
At present, the molecular dynamics calculation scale is larger and larger, the calculation region shape is more and more complex, and the calculation requirements on unsteady and non-uniform systems are more and more. How to use a visualization method to quickly establish a calculation model and apply corresponding molecular dynamics boundary conditions is an important challenge facing modern molecular dynamics simulation. The following difficulties mainly need to be solved:
(1) The fast selection and manipulation of boundary particles, for large scale molecular dynamics calculations, the number of boundary particles is very large, in the order of millions, which can be a very burdensome task.
(2) The proper speed and potential energy are given to each boundary particle, the action among molecular dynamic particles is very strong, if the motion state of the particles does not correspond to the distribution function, violent oscillation is possible to occur, instantaneous deviation can occur between the local condition and the target state, and boundary effects such as density fluctuation and the like are easy to occur.
Disclosure of Invention
The invention aims to provide a method for quickly applying a molecular dynamics boundary condition based on geometric boundary operation, which is used for solving the problem of heavy task of applying the boundary condition in the prior art.
In order to realize the task, the invention adopts the following technical scheme:
a molecular dynamics boundary condition rapid application method based on geometric boundary operation comprises the following steps:
extracting a geometric boundary of the molecular dynamics simulation model according to the molecular dynamics simulation model, finding out boundary particles through geometric boundary operation, and acquiring position information of each boundary particle in a boundary domain;
and (3) endowing each boundary particle with reasonable speed and force, so that the macroscopic physical quantity of the boundary particle is consistent with the microscopic state, and the complete molecular dynamics boundary condition is obtained.
Further, the finding out the boundary particle through the geometric boundary operation to obtain the position information of each boundary particle in the boundary domain includes:
constructing a solid model of the geometric boundary according to the geometric characteristics of the boundary;
acquiring the geometric information of the boundary abstraction according to the entity model, and performing discrete operation on the entity model according to the geometric information of the boundary model to obtain discrete particles; and distinguishing the position relation between the discrete particles and the boundary by adopting an intersection method according to the geometric characteristics of the boundary so as to determine the boundary particles and the simulation domain particles and finally obtain the complete position information of the boundary particles.
Further, in the process of constructing the solid model of the geometric boundary according to the geometric features of the boundary, a bias method is adopted for obtaining the more regular geometric boundary, and Boolean operation is used for obtaining the more complex boundary.
Further, the endowing of each boundary particle with a reasonable speed includes:
for all boundary particles, based on a speed correction mode, correcting the speed of the boundary particles by using a relaxation factor, so that the speed of the boundary particles is changed slowly towards the direction of the analog domain, wherein the speed correction formula is as follows:
V i '＝V i +h(x i )(u-V i ) Formula 1
In formula 1, i represents the ith boundary particle; v i ' is the corrected velocity of the boundary particle; v i Is the initial velocity of the boundary particle; h (x) i ) Is a relaxation factor with a value of 0 to h 0 Change within the interval; x is the number of i A certain coordinate value which is changed from 0 to A along the normal direction of the analog domain for the particle; u is the expected speed of the boundary particles in the target state of the molecular dynamics simulation system, A is the boundary domain along the normal vector n directionOf the display device.
Furthermore, a normal vector n of the boundary domain towards the direction of the simulation domain is determined based on the geometric characteristics of the boundary, and the speed is sequentially given to all the boundary particles along the direction of the normal vector according to the position information of the boundary particles in a numerical calculation mode of the speed correction formula.
Further, the imparting of reasonable force to each boundary particle includes:
in practical simulations, to apply boundary forces within the boundary domain, it is assumed that there are some external particles outside the boundary domain that exert an action potential on the boundary particle, the external particles being at the cutoff radius R C Effective action potentials exist on the boundary particles within the range, and the sum of the action potentials forms effective boundary action force; assuming that any boundary particle is surrounded by a shell outside the boundary domain, the force of the single shell on any boundary particle within the boundary domain is first determined, followed by the total force exerted by the outer particle on any boundary particle within the boundary domain.
Further, the determining the acting force of the monolayer thin shell on any boundary particle in the boundary domain comprises:
the number of particles in the shell can be expressed as: ρ g (r) S (r) dr, the force of the particles in the shell to the boundary particles, along the normal direction of the simulation domain, the force of the particles in any thin shell to any particle in the boundary domain is:
wherein rho is the particle density in the molecular dynamics simulation system;
g (r) is the radial distribution function of the particles; s (r) is the area of the shell; t (r) is the projection of the thin shell area on the outer layer of the boundary domain; v (r) is the action potential of the particles in a single shell to any particle in the boundary domain; dr is the thickness of the shell.
Further, the total force exerted by the external particle on any boundary particle within the boundary domain is expressed as:
in the above formula, Φ is the stress tensor; p is Viry pressure; t (r, x) is the projection of the thin shell area on the outer layer of the boundary domain when the boundary particle has the coordinate x.
Further, for the boundary particle i, at its cutoff radius R c Within the range, the acting force of any external particle j outside the boundary domain is F ij The effective acting force F exerted on the boundary particle i by all the particles within the truncation radius range outside the boundary domain is obtained by calculating by using the formula 2 by assuming that the periphery of any boundary particle outside the boundary domain is wrapped by a thin shell m Finally, the application of the appropriate boundary force for all boundary particles is achieved.
Compared with the prior art, the invention has the following technical characteristics:
1. the method can quickly find out boundary particles and apply reasonable boundary conditions, solve the problem of heavy task of applying the boundary conditions, and greatly reduce boundary oscillation.
2. The invention provides a general scheme for rapidly applying boundary conditions on a complex molecular dynamics system; and applying a speed boundary condition and a stress boundary condition of smooth transition, and the speed distribution and the potential energy distribution of boundary particles are consistent with the local micro dynamic state of the system, so that the state fluctuation near the boundary is limited to a lower level.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of the boundary particle acquisition principle of the present invention;
FIG. 3 is a schematic diagram of the velocity imparted to boundary particles by the present invention;
FIG. 4 is a schematic diagram of the present invention applied boundary particle forces.
Detailed Description
Referring to fig. 1, the invention provides a method for rapidly applying a molecular dynamics boundary condition based on geometric boundary operation, which first finds boundary particles rapidly through geometric boundary operation on a molecular dynamics simulation model, and obtains position information of each boundary particle in a boundary domain; and secondly, endowing each boundary particle with reasonable speed and acting force, so that the macroscopic physical quantity of the boundary particles is consistent with the microscopic state, and thus, the complete molecular dynamics boundary condition is obtained.
Specifically, the method for rapidly applying the molecular dynamics boundary condition of the invention comprises three processes, which are specifically described as follows:
1. boundary particle acquisition from given geometric boundaries
The step is the most basic step when boundary conditions are applied, and mainly obtains molecular dynamics boundary particle information through dispersion according to geometric boundaries in a molecular dynamics simulation model to construct a boundary model. The method comprises the following specific steps:
1.1 construction of solid models of geometric boundaries
Extracting a geometric boundary of the molecular dynamics simulation model according to the molecular dynamics simulation model, and constructing an entity model of the geometric boundary according to the geometric characteristics of the boundary; in the process, a bias method can be adopted to obtain a more regular geometric boundary, and a Boolean operation can be used to obtain a more complex boundary; for a solid model, a straight line in a two-dimensional model or a plane in a three-dimensional model may be considered as a relatively regular geometric boundary.
As shown in fig. 2 (a), in the example given in fig. 2, for the geometric features of the more regular molecular dynamics model boundary, the bias method may be directly adopted to bias the model b along the X direction and a along the Y direction, so as to obtain the boundary solid model; as shown in fig. 2 (b), when the boundary of the simulation model is irregular or is a complex curved surface, the boundary model may be obtained by performing boolean operations on two or more models.
1.2 building a geometric boundary particle model
After the step 1.1 is completed, acquiring the abstract geometric information of the boundary according to the entity model of the geometric boundary, and performing discrete operation on the entity model according to the geometric information of the boundary model; after the discrete particles are obtained, the position relation between the discrete particles and the boundary is judged by adopting an intersection method according to the geometric characteristics of the boundary, so that the boundary particles and the particles in the analog domain are determined, as shown in fig. 2, the position information of the complete boundary particles is finally obtained, and a boundary particle model is constructed.
2. Imparting reasonable velocities to boundary particles
The boundary conditions applied to molecular dynamics simulation systems are largely divided into two parts, velocity and force. In the step, the speed is given to the boundary particles, the speed needs to meet the Dirichlet boundary condition, and meanwhile, the microscopic state of the molecular dynamics simulation system particles is consistent with the macroscopic physical quantity. In order to avoid the large deviation of the particle speed in the boundary domain and the simulated domain, which causes the system oscillation, the particle speed in the boundary domain must be changed slowly, i.e. the speed is in 'soft transition'; the specific implementation manner of the step is as follows:
for all boundary particles, based on a speed correction mode, adopting a relaxation factor in the form of a bell-shaped function to correct the speed of the boundary particles, so that the speed of the boundary particles changes slowly towards the direction of the simulation domain, wherein the speed correction formula is as follows:
V i '＝V i +h(x i )(u-V i ) Formula 1
In formula 1, i represents the ith boundary particle; v i ' is the corrected velocity of the boundary particle; v i Is the initial velocity of the boundary particle; h (x) i ) Is a relaxation factor, and has a value of 0 to h 0 Within a range of variation, h 0 The specific value of (a) depends on the specific molecular dynamics simulation model, e.g. h in general 0 Can take on a value of 1; x is the number of i A certain coordinate value which is the change of the particle from 0 to A (the width of the boundary domain along the direction of the normal vector n) along the normal direction of the analog domain; u is the expected velocity of the boundary particle in the molecular dynamics simulation system target state.
The speed value of the boundary particles from the boundary to the normal vector n direction of the simulation domain is slowly changed from u, the introduced relaxation factor function satisfies h '(0) =0, h' (A) =0, and the relaxation factor is tightly supported in the boundary domain, so that the boundary action is limited in the boundary domain, and the introduction of the relaxation factor function depends on a specific molecular dynamics simulation model.
As shown in fig. 3, a normal vector n of the boundary domain toward the simulation domain is determined based on the geometric features of the boundary, and based on the position information of the boundary particles obtained in step 1.2, velocities are sequentially given to all the boundary particles along the normal vector direction by the numerical calculation method of formula 1.
After the relaxation factor is introduced and a speed correction formula is adopted, reasonable boundary particle speed can be obtained quickly, so that the boundary particle speed meets Dirichlet boundary conditions, the microscopic state of a simulation system is met, and system oscillation is reduced.
3. Applying appropriate forces to the boundary particles
In order to ensure that the boundary particles are consistent with the internal stress and the microscopic action potential of the simulation system in the microscopic state, the boundary action force is introduced to ensure the continuity of the internal stress of the system and adapt to the local particle distribution function. According to the local particle distribution function, virtual 'external particles' are introduced, the action of the external boundary on the internal boundary particles is reconstructed, and the additional acting force applied to the boundary particles is deduced based on the Viry theorem. The specific implementation mode is as follows:
in a practical simulation, to apply a boundary force within the boundary domain, it may be assumed that there are some foreign particles outside the boundary domain that have an action potential on the boundary particle, the foreign particle being at the cutoff radius R C Effective potentials exist within the range for the boundary particles, and the sum of these potentials constitutes the effective boundary force. The action potential among all particles in the molecular dynamics simulation model is always limited to the truncation radius R C In scope, therefore, it can be assumed that any boundary particle is surrounded by a shell outside the boundary region, the radius R of the shell being x (the distance from the particle in the boundary region to the boundary in the normal direction) to R C And (c) within a range.
The number of particles within the shell can be expressed as: ρ g (r) S (r) dr, the force of the particles in the shell to the boundary particles, along the normal direction of the simulation domain, the force of the particles in any thin shell to any particle in the boundary domain is:
wherein rho is the particle density in the molecular dynamics simulation system;
g (r) is the radial distribution function of the particles; s (r) is the area of the shell; t (r) is the projection of the thin shell area on the outer layer of the boundary domain; v (r) is the action potential of the particles in a single shell to any particle in the boundary domain; dr is the thickness of the shell.
After the acting force of the single-layer thin shell on any boundary particle in the boundary domain is determined, the total acting force applied by the external particle on any boundary particle in the boundary domain can be obtained as follows:
in the above formula, Φ is the stress tensor; p is Viry pressure; t (r, x) is the projection of the thin shell area on the outer layer of the boundary domain when the boundary particle has the coordinate x.
As shown in FIG. 4, for the boundary particle i, at its cutoff radius R c Within the range, the acting force of any external particle j outside the boundary domain is F ij The effective acting force F exerted on the boundary particle i by all the particles in the cutoff radius range outside the boundary domain is obtained by the integral calculation of the formula 2 by adopting the thin shell method m Finally, the proper boundary acting force is applied to all the boundary particles, so that the macroscopic physical quantity of the boundary particles is consistent with the microscopic state, and the complete molecular dynamics boundary condition is obtained.
The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present application and are intended to be included within the scope of the present application.
Claims (5)
1. A molecular dynamics boundary condition rapid application method based on geometric boundary operation is characterized by comprising the following steps:
extracting the geometric boundary of the molecular dynamics simulation model according to the molecular dynamics simulation model, finding out boundary particles through geometric boundary operation, and acquiring the position information of each boundary particle in the boundary domain, wherein the method comprises the following steps:
constructing a solid model of the geometric boundary according to the geometric characteristics of the boundary;
acquiring the geometric information of the boundary abstraction according to the entity model, and performing discrete operation on the entity model according to the geometric information of the boundary model to obtain discrete particles; judging the position relation between the discrete particles and the boundary by adopting an intersection method according to the geometric characteristics of the boundary so as to determine the boundary particles and the simulation domain particles and finally obtain the complete position information of the boundary particles;
endowing each boundary particle with reasonable speed and acting force, so that the macroscopic physical quantity of the boundary particle is consistent with the microscopic state, and thus obtaining a complete molecular dynamics boundary condition;
the method for endowing each boundary particle with reasonable speed comprises the following steps:
for all the boundary particles, based on a speed correction mode, correcting the speed of the boundary particles by using a relaxation factor, so that the speed of the boundary particles is slowly changed towards the direction of an analog domain, wherein a speed correction formula is as follows:
V i '＝V i +h(x i )(u-V i ) Formula 1
In formula 1, i represents the ith boundary particle; v i ' is the corrected velocity of the boundary particle; v i Is the initial velocity of the boundary particle; h (x) i ) Is a relaxation factor with a value of 0 to h 0 Change within the interval; x is a radical of a fluorine atom i A certain coordinate value which is changed from 0 to A along the normal direction of the analog domain for the particle; u is the expected speed of the boundary particles in the target state of the molecular dynamics simulation system, and A is the width of the boundary domain along the direction of the normal vector n;
the method for endowing each boundary particle with reasonable acting force comprises the following steps:
in a practical simulation, to apply a boundary force within the boundary domain, it is assumed that there are some foreign particles outside the boundary domain that have an action potential on the boundary particle, the foreign particles being at the cutoff radius R C Within range for the presence of boundary particlesEffective potentials, the sum of which constitutes an effective boundary force; assuming that a layer of thin shell is wrapped around any boundary particle outside the boundary domain, firstly determining the acting force of the single-layer thin shell on any boundary particle in the boundary domain, and then determining the total acting force of an external particle applied to any boundary particle in the boundary domain;
the determination of the acting force of the single-layer thin shell on any boundary particle in the boundary domain comprises the following steps:
the number of particles within the shell can be expressed as: ρ g (r) S (r) dr, the action force of the particles in the shell to the boundary particles, along the normal direction of the simulation domain, the action force of the particles in any thin shell to any particle in the boundary domain is as follows: - ρ g (r) T (r) V (r) dr; wherein rho is the particle density in the molecular dynamics simulation system; g (r) is the particle radial distribution function; s (r) is the area of the shell; t (r) is the projection of the shell area on the outer layer of the boundary domain; v (r) is the action potential of a particle in a single shell to any particle in the boundary domain; dr is the thickness of the shell.
2. The method for rapidly applying the molecular dynamics boundary condition based on the geometric boundary operation of claim 1, wherein in the process of constructing the solid model of the geometric boundary according to the geometric characteristics of the boundary, the more regular geometric boundary is obtained by a bias method, and the more complex boundary is obtained by a Boolean operation.
3. The method of claim 1, wherein a normal vector n of the boundary domain toward the simulation domain is determined based on the geometric features of the boundary, and the velocity is sequentially assigned to all the boundary particles along the normal vector direction by the numerical calculation of the velocity correction formula according to the position information of the boundary particles.
4. The method for rapidly applying boundary conditions of molecular dynamics based on geometric boundary operations according to claim 1, wherein the total force applied by the external particle to any boundary particle in the boundary domain is expressed as:
in the above formula, Φ is the stress tensor; p is Viry pressure; t (r, x) is the projection of the thin shell area on the outer layer of the boundary domain when the boundary particle has the coordinate x.
5. The method of claim 4, wherein the boundary particle i is truncated at its truncation radius R c Within the range, the acting force of any external particle j outside the boundary domain is F ij The effective acting force F exerted on the boundary particle i by all the particles within the truncation radius range outside the boundary domain is obtained by calculating by using the formula 2 by assuming that the periphery of any boundary particle outside the boundary domain is wrapped by a thin shell m The final realization is to apply the appropriate boundary forces for all boundary particles.
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