CN111008489B - Grid unit particle number optimization method in rarefied airflow numerical simulation - Google Patents
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Abstract
The invention discloses a method for optimizing the particle number of grid units in rarefied airflow numerical simulation, which comprises the following steps: in the process of carrying out numerical simulation on the rarefied airflow by adopting the DSMC, judging whether the number of simulation particles in any grid unit is within a set range, and if the number of the simulation particles is within the set range, optimizing the number of particles in the grid unit is not needed; if the number of the simulation particles exceeds the upper limit value of the set range, repeatedly executing particle fusion operation according to particle fusion criteria so that the number of the simulation particles in each grid unit is in the set range; if the number of the simulated particles is lower than the lower limit value of the set range, the particle separation operation is repeatedly executed according to the particle separation criterion, so that the number of the simulated particles in each grid cell is in the set range. And controlling the particle number of each grid cell in the analog domain, so that the simulated particle number in each grid cell does not change greatly along with the cell density and the cell size, and balancing the distribution of the simulated particles on different grid cells.
Description
Technical Field
The invention relates to the technical field of rarefied airflow numerical simulation, in particular to a grid unit particle number optimization method in rarefied airflow numerical simulation.
Background
In recent years, the method of numerically simulating the lean airflow using the monte carlo Direct Simulation Method (DSMC) has attracted more and more attention due to the failure of the continuous medium assumption of the N-S equation in the lean airflow region.
DSMC is a discrete particle simulation method of probability theory. The DSMC method uses a small number of simulated particles to represent a large number of real gas molecules in a computer, the space coordinates, the speed, the internal energy and the like of the simulated particles are stored in the computer and change along with time due to the movement, the collision and the interaction with a boundary of the particles, and a molecular speed distribution function is restored by sampling the simulated particles.
Generally, for a lean gas stream supersonic flow, the fluid density increases significantly on the shock wave; furthermore, if the wall temperature is low, the fluid density will increase further towards the boundary layer region. Assuming uniform grid cells are used in the simulation, the number of particles per cell in the simulation will increase from free-flow cells to boundary layer cells due to the significant increase in flow density from free-flow to boundary layer regions. Thus, if the free-flow cell has about 10-20 particles, the cells near the boundary layer may have more than several hundred particles. As previously mentioned, this would make the simulation time long and inefficient. In contrast, if this number is too small, the simulation results may be inaccurate due to the inability to solve for collisions in each analog cell, according to physical problems.
Disclosure of Invention
Aiming at the problems and the defects in the prior art, the invention provides a grid unit particle number optimization method in the rarefied airflow numerical simulation, which carries out self-adaptive adjustment and optimization on the number of simulated particles in a grid unit, thereby obviously improving the precision and the efficiency of the rarefied airflow numerical calculation.
The invention solves the technical problems through the following technical scheme:
the invention provides a method for optimizing the particle number of grid cells in rarefied airflow numerical simulation, which is characterized by comprising the following steps of:
in the process of carrying out numerical simulation on the rarefied airflow by adopting the DSMC, judging the relation between the number of simulation particles in any grid unit and a set range to judge whether to execute particle fusion operation or particle separation operation, if the number of the simulation particles is in the set range, optimizing the number of the particles of the grid unit is not needed, namely, the particle fusion operation or the particle separation operation is not executed; if the number of the simulation particles exceeds the upper limit value of the set range, repeatedly executing particle fusion operation according to particle fusion criteria so that the number of the simulation particles in each grid unit is in the set range; if the number of the simulated particles is lower than the lower limit value of the set range, the particle separation operation is repeatedly executed according to the particle separation criterion, so that the number of the simulated particles in each grid cell is in the set range.
Preferably, in the numerical simulation of the lean airflow by adopting the DSMC, the particles with the particle mass larger than the average particle mass in any grid unit are defined as large particles, the particles with the particle mass smaller than or equal to the average particle mass are defined as small particles, the particles in the grid unit are numbered, and the number NB and the number NS of the large particles and the small particles in the grid unit are counted;
the particle fusion criterion is used for judging the relationship between the number of simulation particles containing large particles and small particles in the grid unit and a set range so as to judge whether to execute particle fusion operation, and comprises the following steps:
if the number NB + NS of the simulated particles exceeds the upper limit value of the set range, then:
a) if NB is larger than or equal to the upper limit value of the set range, adjusting the grid size to ensure that the number NB of large particles in the adjusted grid unit is smaller than the upper limit value of the set range;
a1) if the number of the simulated particles in the adjusted grid unit is within the set range, the particle fusion operation or the particle separation operation is not executed;
a2) if the number of the simulated particles in the adjusted grid unit still exceeds the upper limit value of the set range, judging whether the distance between any two small particles is smaller than the set distance and whether the particle fusion judgment condition is met or not in the adjusted grid unit
If so, fusing two small particles into one large particle, otherwise, adjusting the grid size, renumbering the particles in the adjusted grid unit, counting the number NB of the large particles and the number NS of the small particles, and judging whether to execute particle fusion or separation operation again;
b) if NB is less than the upper limit value of the set range, in the grid unit, the distance between any two small particles is judged to be less than the set distance and whether the particle fusion judgment condition is satisfied
If so, fusing the two small particles into one large particle, otherwise, adjusting the size of the grid, renumbering the particles in the grid unit after adjustment, counting the number NB of the large particles and the number NS of the small particles, and judging whether to execute particle fusion or separation operation again;
in steps a2) and b), judging whether the number of the simulated particles in the grid cell after the two small particle fusion operations are executed is within a set range every time the two small particle fusion operations are executed, and if not, continuing the two small particle fusion operations;
wherein,
is the average mass of large particles around two small particles,
is the average mass of the two small particles,
is the number of large particles surrounding two small particles,
is the number of small particles that are present,
is an artificial threshold;
particle fusion follows conservation of mass and momentum:
wherein m is1、m2Mass of two small particles, v1、v2The velocities of the two small particles are respectively, m and v are respectively the mass and velocity of the fused large particle, and the position of the fused large particle is the midpoint of the positions of the two small particles before fusion.
Preferably, the mean free path of small particles is set at a distance of 0.5 times.
Preferably, the determining the particle separation criterion determines the relationship between the number of simulated particles containing large particles and small particles in the grid cell and the set range to determine whether to perform the particle separation operation includes:
if the number NB + NS of the simulated particles is lower than the lower limit value of the set range:
c) if NB =0, adjusting the grid size of the grid unit so that the number NB of macro-particles in the adjusted grid unit is more than 0;
c1) if the number of the simulated particles in the adjusted grid unit is within the set range, the particle fusion operation or the particle separation operation is not executed;
c2) if the adjusted grid cellIf the number of middle simulation particles is still lower than the lower limit value of the set range, judging whether any single large particle meets the particle separation judgment condition or not in the adjusted grid unit
If so, separating a single large particle into two small particles, otherwise, adjusting the grid size, and judging whether to execute particle fusion or separation operation;
d) if NB is greater than 0, in the grid unit, judging whether any single large particle meets the particle separation judgment condition
If so, separating a single large particle into two small particles, otherwise, adjusting the grid size, and judging whether to execute particle fusion or separation operation;
in steps c2) and d), each time the macro-particle separating operation is executed, judging whether the number of the simulated particles in the grid unit after the macro-particle separating operation is executed is within a set range, and if not, continuing the macro-particle separating operation;
wherein,
is the mass of the individual large particles,
is the average mass of small particles surrounding a single large particle,
is the number of large particles and is,
is the number of small particles surrounding a single large particle,
is an artificial threshold;
particle separation follows conservation of mass and momentum:
wherein,
the mass of the two separated small particles is respectively,
respectively the speed of the two separated small particles,
the mass and speed of the large particles before separation are respectively, and the positions of the two small particles after separation are as follows:
wherein p is1、p2The positions of two small particles after separation are respectively shown, p is the position of a single large particle before separation, and h is a set threshold value.
Preferably, h is taken as the radius r of the separated small particles.
Preferably, the setting range is 10-20.
On the basis of the common knowledge in the field, the above preferred conditions can be combined randomly to obtain the preferred embodiments of the invention.
The positive progress effects of the invention are as follows:
1. and controlling the particle number of each grid cell in the analog domain, so that the simulated particle number in each grid cell does not change greatly along with the cell density and the cell size, and balancing the distribution of the simulated particles on different grid cells.
2. The calculation amount of numerical simulation is controlled, the simulation efficiency is improved, and the simulation precision is improved.
Drawings
FIG. 1 is a schematic view of particle fusion according to a preferred embodiment of the present invention.
FIG. 2 is a schematic view of particle separation according to a preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The embodiment provides a method for optimizing the particle number of grid cells in a rarefied airflow numerical simulation, which comprises the following steps of:
in the numerical simulation of the thin airflow by adopting the DSMC, judging the relationship between the number of simulation particles in any grid unit and a set range (such as 10-20) to judge whether to execute particle fusion operation or particle separation operation, if the number of the simulation particles is within the set range (10-20), optimizing the number of particles of the grid unit is not needed, namely, the particle fusion operation or the particle separation operation is not executed; if the number of the simulated particles exceeds the upper limit value (20) of the set range, repeatedly executing particle fusion operation according to particle fusion criteria so that the number of the simulated particles in each grid cell is within the set range (10-20); if the number of the simulated particles is lower than the lower limit value (10) of the set range, the particle separation operation is repeatedly executed according to the particle separation criterion so that the number of the simulated particles in each grid cell is within the set range (10-20).
In the numerical simulation of the thin gas flow by adopting the DSMC, the particles with the particle mass larger than the average particle mass in any grid unit are defined as large particles, the particles with the particle mass smaller than or equal to the average particle mass are defined as small particles, the particles in the grid unit are numbered, and the number NB and the number NS of the large particles and the small particles in the grid unit are counted.
(1) The particle fusion criterion is used for judging the relationship between the number of simulation particles containing large particles and small particles in the grid unit and a set range so as to judge whether to execute particle fusion operation, and comprises the following steps:
fusing small particles in a region with more large particles to obtain larger particles. When large particles are mostly present around two small particles and the two small particles are very close to each other, the particles are fused, the new fused particle mass is the sum of the two small particle masses, and the position is the midpoint of the positions of the two particles before fusion.
If the number NB + NS of the simulated particles exceeds the upper limit value of the set range, then:
a) if NB is larger than or equal to the upper limit value of the set range, adjusting the grid size to enable the number NB of large particles in the adjusted grid unit to be smaller than the upper limit value of the set range.
For example: if NB + NS in the grid cell is 24 (20 set upper limits), where NB is 22, the number NB of large particles in the grid cell exceeds 20 set upper limits, and at this time, the number of simulated particles in the grid cell cannot be within the set range even if the particle fusion operation is performed. At this time, the grid size of the grid unit needs to be adjusted, so that the number NB of large particles in the adjusted grid unit is less than the upper limit value 20 of the set range, and at this time, the number of simulated particles in the grid unit may be in the set range through the particle fusion operation.
a1) And if the number of the simulated particles in the adjusted grid unit is within the set range, not executing the particle fusion operation or the particle separation operation. For example: if the number NB of large particles in the adjusted grid cell is 18 and the number of small particles in the adjusted grid cell is 2, the number of simulated particles in the adjusted grid cell is 20, and is within the set range, and then it is not necessary to perform the particle fusion operation or the particle separation operation.
a2) If the number of the simulated particles in the adjusted grid cell still exceeds the upper limit value of the set range, judging whether the distance between any two small particles is smaller than the set distance (the small particle mean free path which is 0.5 times) and whether the particle fusion judgment condition is met in the adjusted grid cell
If so, two granulesAnd (3) merging the particles into a large particle (see figure 1), otherwise, adjusting the grid size, renumbering the particles in the grid unit after adjustment, counting the number NB of the large particles and the number NS of the small particles, and judging whether to execute particle merging or separation operation again.
For example: if the number NB of large particles in the adjusted grid unit is 19 and the number of small particles is 2, the number 21 of simulated particles in the adjusted grid unit still exceeds the upper limit value 20 of the set range, at this time, it is determined whether the distance between any two small particles is smaller than the set distance and the particle fusion determination condition is satisfied, if so, two small particles are fused into one large particle, so that the number of simulated particles in the adjusted grid unit is 20 and is within the set range, and then, there is no need to perform the particle fusion operation or the particle separation operation.
b) If NB is less than the upper limit value of the set range, in the grid unit, the distance between any two small particles is judged to be less than the set distance and whether the particle fusion judgment condition is satisfied
If so, fusing two small particles into one large particle (see fig. 1), otherwise, adjusting the grid size, renumbering the particles in the adjusted grid unit, counting the number NB of the large particles and the number NS of the small particles, and judging whether to execute particle fusion or separation operation again.
In steps a2) and b), each time two small particle fusion operations are executed, whether the number of simulated particles in the grid cell after the two small particle fusion operations are executed is within a set range is judged, and if not, the two small particle fusion operations are continued.
Wherein,
is the average mass of large particles around two small particles,
is the average mass of the two small particles,
is the number of large particles surrounding two small particles,
is the number of small particles that are present,
is an artificial threshold (γ = 1).
Particle fusion follows conservation of mass and momentum:
wherein m is1、m2Mass of two small particles, v1、v2The velocities of the two small particles are respectively, m and v are respectively the mass and velocity of the fused large particle, and the position of the fused large particle is the midpoint of the positions of the two small particles before fusion.
(2) The particle separation criterion is used for judging the relationship between the number of simulation particles containing large particles and small particles in the grid unit and a set range so as to judge whether to execute particle separation operation, and comprises the following steps:
when large particles are mixed in a small particle region, a separation mechanism opposite to fusion is added. When there are many cases of small particles around a single large particle, the large particle is divided into smaller particles. The velocity and position of the two small particles separated are determined from conservation of energy and conservation of momentum.
If the number NB + NS of the simulated particles is lower than the lower limit (10) of the set range:
c) if NB =0, adjusting the grid size of the grid unit so that the number of macro-particles NB in the adjusted grid unit is greater than 0. If NB =0, the particle separating operation cannot be performed, and the simulated particle data in the mesh cell cannot be made to be within the set range, so the particle separating operation is performed on the premise that NB > 0.
c1) And if the number of the simulated particles in the adjusted grid unit is within the set range, not executing the particle fusion operation or the particle separation operation.
c2) If the number of the simulated particles in the adjusted grid unit is still lower than the lower limit value of the set range, judging whether any single large particle meets the particle separation judgment condition or not in the adjusted grid unit
If so, separating a single large particle into two small particles, otherwise, adjusting the grid size, and judging whether to execute particle fusion or separation operation;
d) if NB is greater than 0, in the grid unit, judging whether any single large particle meets the particle separation judgment condition
If so, separating a single large particle into two small particles, otherwise, adjusting the grid size, and judging whether to execute particle fusion or separation operation;
in steps c2) and d), each time the macro-particle separating operation is executed, judging whether the number of the simulated particles in the grid unit after the macro-particle separating operation is executed is within a set range, and if not, continuing the macro-particle separating operation;
wherein,
is the mass of the individual large particles,
is the average mass of small particles surrounding a single large particle,
is the number of large particles and is,
is the number of small particles surrounding a single large particle,
is an artificial threshold;
particle separation follows conservation of mass and momentum:
wherein,
the mass of the two separated small particles is respectively,
respectively the speed of the two separated small particles,
the mass and speed of the large particles before separation are respectively, and the positions of the two small particles after separation are as follows:
wherein p is1、p2The positions of two small particles after separation, p the position of a single large particle before separation, h a set threshold, the size of h generally affects the distance between two small particles after separation, and is not recommended to be too large, and herein, the radius r of a small particle is taken.
The invention provides a grid unit particle number optimization method in rarefied airflow numerical simulation, which is used for adaptively adjusting and optimizing the number of simulation particles in each grid unit in a simulation domain, so that the number of the simulation particles in each grid unit is in a set range, the number of the simulation particles in each grid unit is not greatly changed along with the unit density and the unit size, the distribution of the simulation particles on different grid units is balanced, and the accuracy and the efficiency of rarefied airflow numerical calculation can be obviously improved.
While specific embodiments of the invention have been described above, it will be appreciated by those skilled in the art that these are by way of example only, and that the scope of the invention is defined by the appended claims. Various changes and modifications to these embodiments may be made by those skilled in the art without departing from the spirit and scope of the invention, and these changes and modifications are within the scope of the invention.
Claims (5)
1. A method for optimizing the particle number of grid cells in a rarefied airflow numerical simulation is characterized by comprising the following steps of:
in the process of carrying out numerical simulation on the rarefied airflow by adopting the DSMC, judging the relation between the number of simulation particles in any grid unit and a set range to judge whether to execute particle fusion operation or particle separation operation, if the number of the simulation particles is in the set range, optimizing the number of the particles of the grid unit is not needed, namely, the particle fusion operation or the particle separation operation is not executed; if the number of the simulation particles exceeds the upper limit value of the set range, repeatedly executing particle fusion operation according to particle fusion criteria so that the number of the simulation particles in each grid unit is in the set range; if the number of the simulated particles is lower than the lower limit value of the set range, repeatedly executing particle separation operation according to the particle separation criterion so as to enable the number of the simulated particles in each grid unit to be in the set range;
in the numerical simulation of the thin airflow by adopting the DSMC, defining the particles with the particle mass larger than the average particle mass in any grid unit as large particles and the particles with the particle mass smaller than or equal to the average particle mass as small particles, numbering the particles in the grid unit, and counting the number NB and NS of the large particles and the small particles in the grid unit;
the particle fusion criterion is used for judging the relationship between the number of simulation particles containing large particles and small particles in the grid unit and a set range so as to judge whether to execute particle fusion operation, and comprises the following steps:
if the number NB + NS of the simulated particles exceeds the upper limit value of the set range, then:
a) if NB is larger than or equal to the upper limit value of the set range, adjusting the grid size to ensure that the number NB of large particles in the adjusted grid unit is smaller than the upper limit value of the set range;
a1) if the number of the simulated particles in the adjusted grid unit is within the set range, the particle fusion operation or the particle separation operation is not executed;
a2) if the number of the simulated particles in the adjusted grid unit still exceeds the upper limit value of the set range, judging whether the distance between any two small particles is smaller than the set distance and whether the particle fusion judgment condition is met or not in the adjusted grid unit
If so, fusing two small particles into one large particle, otherwise, adjusting the size of the grid, renumbering the particles in the grid unit after adjustment, counting the number NB of the large particles and the number NS of the small particles, and judging whether to execute particle fusion or separation operation again;
b) if NB is less than the upper limit value of the set range, in the grid unit, the distance between any two small particles is judged to be less than the set distance and whether the particle fusion judgment condition is satisfied
If so, fusing the two small particles into one large particle, otherwise, adjusting the size of the grid, renumbering the particles in the grid unit after adjustment, counting the number NB of the large particles and the number NS of the small particles, and judging whether to execute particle fusion or separation operation again;
in steps a2) and b), judging whether the number of the simulated particles in the grid cell after the two small particle fusion operations are executed is within a set range every time the two small particle fusion operations are executed, and if not, continuing the two small particle fusion operations;
wherein m isbigIs the average mass of large particles around two small particles, msmaIs the average mass of two small particles, NbigIs the number of large particles surrounding two small particles, NsmaIs the number of small particles, γ is the artificial threshold;
particle fusion follows conservation of mass and momentum: m is m1+m2，m1＝m2，v＝v1＝v2
Wherein m is1、m2The mass of each of the two small particles,v1、v2the velocities of the two small particles are respectively, m and v are respectively the mass and velocity of the fused large particle, and the position of the fused large particle is the midpoint of the positions of the two small particles before fusion.
2. The method for optimizing the particle count of grid cells in a lean flow numerical simulation of claim 1, wherein a mean free path of small particles is set at a distance of 0.5 times.
3. The method of claim 1, wherein the particle separation criterion for determining the relationship between the number of simulated particles containing large particles and small particles in the grid cell and a set range to determine whether to perform a particle separation operation comprises:
if the number NB + NS of the simulated particles is lower than the lower limit value of the set range:
c) if NB is 0, adjusting the grid size of the grid unit so that the number NB of large particles in the adjusted grid unit is more than 0;
c1) if the number of the simulated particles in the adjusted grid unit is within the set range, the particle fusion operation or the particle separation operation is not executed;
c2) if the number of the simulated particles in the adjusted grid unit is still lower than the lower limit value of the set range, judging whether any single large particle meets the particle separation judgment condition or not in the adjusted grid unit
If so, separating a single large particle into two small particles, otherwise, adjusting the grid size, and judging whether to execute particle fusion or separation operation;
d) if NB>0, judging whether any single large particle meets the particle separation judgment condition or not in the grid unit
If so, the single large particle is separated into two small particles, otherwise, the net is adjustedGrid size, judging whether to execute particle fusion or separation operation;
in steps c2) and d), each time the macro-particle separating operation is executed, judging whether the number of the simulated particles in the grid unit after the macro-particle separating operation is executed is within a set range, and if not, continuing the macro-particle separating operation;
wherein m'bigIs the mass of individual macroparticles, m'smaIs the average mass of small particles surrounding a single large particle, N'bigIs the number of macroparticles, N'smaIs the number of small particles surrounding a single large particle, γ' is the artificial threshold;
particle separation follows conservation of mass and momentum: m '═ m'1+m′2，m′1＝m′2，
Wherein m'1、m′2Respectively the mass v 'of the two separated small particles'1、v′2The speeds of the two small particles after separation are respectively, m 'and v' are respectively the mass and the speed of the large particle before separation, and the positions of the two small particles after separation are as follows:
wherein p is1、p2The positions of two small particles after separation are respectively shown, p is the position of a single large particle before separation, and h is a set threshold value.
4. The method of optimizing the particle count of grid cells in a lean flow numerical simulation of claim 3, wherein h is taken as the radius r of the separated small particles.
5. The method for optimizing the particle count of grid cells in a lean airflow numerical simulation of claim 1, wherein the setting range is 10 to 20.
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