CN110659447B - Implicit solution method based on influence factor residual sorting - Google Patents
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Abstract
The invention relates to the field of an implicit equation set acceleration solution based on residual sorting, and discloses an implicit solution based on influence factor residual sorting. Establishing an initial flow field matrix equation according to an object to be detected; setting restrictive flow field conditions, and performing residual error calculation on each unit of the flow field; then establishing a residual error influence factor transmission scalar equation, and calculating to obtain residual error influence factors of all units; and sequencing and calculating the product of the residual error and the influence factor to a calculation unit to obtain a final result. The influence of the product of the residual error and the influence factor on the calculation result is subjected to sequencing calculation, so that unit priority calculation with large influence can be realized; moreover, because the influence factor equation is much simpler than the adjoint equation, and the calculation of the product of the influence factor and the residual error is also simpler than the calculation of the product of the adjoint matrix and the residual error, the additional overhead of sequencing calculation can be greatly reduced, and the calculation efficiency can be further improved; meanwhile, all calculations are guaranteed to be effective.
Description
Technical Field
The invention relates to the field of an implicit equation set acceleration solution based on residual sorting, in particular to an implicit solution based on influence factor residual sorting.
Background
In the field of Computational Fluid Dynamics (CFD), most computational models can be solved with the following matrix equations:
Ax+b＝0。 (1)
wherein the matrix A is a matrix representing a control equation, b represents a boundary condition, and x is a vector to be solved.
Generally, the method for solving the flow field control equation (1) is to set an initial value x _0 for a vector x to be solved by using a time correlation method, and experience a time-varying process:
finally, a solution of formula (1) is obtained, wherein R is the residual error.
The general process of CFD computation is to set the initial flow field, with the residual of the flow field region outside the object plane (or other restrictive boundary) at or near 0, with non-zero residual near the restrictive boundary, bounded by boundary conditions, and diffusing outward, reflecting at the boundary, and possibly oscillating during the computational iteration, and then gradually decreasing in amplitude and going toward 0. The variation of the residual error is actually representative of the propagation and interaction process of the perturbation signal generated by the restrictive boundary conditions under the control of the flow equation.
In a supersonic/hypersonic flow field, a limited disturbance area (usually shock waves are used as a boundary) exists, the influence of disturbance is limited in the disturbance area, and the flow field outside the disturbance area is invariable; meanwhile, the directivity of signal propagation exists, and downstream changes cannot influence an upstream area beyond the Mach cone. Based on these characteristics, some methods are proposed to reduce unnecessary computation outside the disturbance influence area, such as defining the computation domain based on pre-analysis, or simplifying the control equation into a parabolic form (PNS), performing space-marching computation, and the like.
For a subsonic flow field, the influence of disturbance can be spread to the whole flow field, but the rules of the propagation direction and attenuation still exist, and correspondingly, an acceleration method aiming at signal propagation directivity such as alternating direction scanning (ADI) exists.
However, these methods have limitations. The computational domain definition cannot be made the most efficient for all computational states with one scheme; the PNS changes the equation, influences the precision and can only be applied to the supersonic velocity area; ADI also has a certain blindness, does not accurately track the propagation path of the signal, and has a large degree of redundancy in computation. In the calculation process, the situation that local region oscillation convergence in the flow field is poor, so that the full flow field is subjected to long-time iterative calculation is also often caused, convergence is judged by using a full flow field convergence criterion, but a large deviation still exists locally. These greatly affect the computational efficiency and accuracy.
And (4) carrying out sequencing management on the residual errors of all grids of the full flow field based on an implicit solution of residual error sequencing, and preferentially calculating a unit with the highest residual error sequencing. The method has the advantages that the calculation of the unit with the residual error sequencing in the front can ensure that all the calculation is effective calculation; along with the propagation process of the signals, the calculation area can be ensured to cover the signal propagation path all the time, and the redundant calculation amount is reduced to the maximum extent; the calculation domain is always driven by the propagation of disturbance signals, the effective region and the ineffective region are automatically distinguished, one method can adapt to all calculation states, and special processing is not needed to be carried out on different calculation states; the method only controls the calculation domain, has no restriction and special requirements on the algorithm layer, can be suitable for any algorithm, and does not sacrifice the precision or limit the application range of the algorithm.
The effect of residuals from different regions in the flow field on the final calculation is not the same. Particularly in a supersonic flow field, the influence of disturbance cannot be propagated upstream, the downstream residual has no influence on the calculation result, the calculation is not necessary, and the repeated calculation of the part cannot be completely avoided by using the residual sorting.
Based on an implicit solution method accompanied with residual sorting, the influence quantity of each unit residual on the final calculation result is obtained by utilizing an accompanying matrix, the calculation sorting is carried out according to the influence quantity of the residual,
for equation (1), let the adjoint matrix Λ be satisfied
From equation (3), an estimated expression of the variation of each unit residual with respect to the variation of the calculation result can be obtained:
the final calculation convergence result is compared with the current state, and the residual error has the variable quantity of
δR＝-R
Therefore, the estimated variation of the final result and the current result is the same
δF＝ΛR
If the calculation model object surface is outside the influence area of a certain unit, the flow field change disturbance of the calculation model object surface has no influence on the flow field near the object surface, and the adjoint matrix value of the unit is equal to 0, so that the invalid calculation of a downstream area which does not influence the calculation result in the supersonic flow field can be effectively reduced based on the solution of adjoint residual sorting.
The aerodynamic force calculation F often contains multiple components,
the method is also a complex matrix, so that the solution of the equation (3) is complex, the calculation cost is high, and the effect of calculation acceleration is weakened to a certain extent. If the adjoint matrix is used only for rough estimation of residual influence quantity, data correction and calculation accuracy improvement are not required to be performed by using the adjoint matrix, and the requirement on calculation accuracy can be reduced. Even so, the adjoint equation itself is complex, and the product of the adjoint matrix and the residual involves a matrix operation, which also introduces additional overhead.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the existing problems, an implicit solution based on influence factor residual sorting is provided.
The technical scheme adopted by the invention is as follows: an implicit solution method based on influence factor residual sorting specifically comprises the following processes:
step S1: establishing an initial flow field matrix equation according to an object to be measured;
step S2: setting restrictive flow field conditions, and performing residual calculation on each unit of the flow field;
and step S3: defining a residual error influence factor according to a flow field residual error change influence propagation mechanism, establishing a residual error influence factor propagation scalar equation, and calculating to obtain each unit residual error influence factor;
and step S4: defining the product result of the residual error of each unit and the influence factor as the characteristic value of the influence quantity, sequencing each unit to obtain a sequencing queue, calculating according to the sequence of the queue, and dynamically adjusting the sequence of the queue according to the characteristic value of the influence quantity until the maximum characteristic value of the influence quantity is reduced by one order of magnitude;
step S5: and repeating the step S3 and the step S4 until a final result is obtained.
Further, in step S1, the flow field matrix equation is:
Ax+b＝0
the matrix A is a matrix representing a control equation, b represents a boundary condition established according to an object to be measured, and x is a vector to be solved and represents a flow field parameter to be solved.
Further, in step S2, the residual equation is calculated as:
an initial value x0 is set for a vector x to be solved by adopting a time correlation method, and a value of R is obtained after a process of changing along with time, wherein R is a residual error.
Further, in step S2, the flow field conditions are specifically boundary conditions and initial flow field conditions.
Further, in step S3, the specific process is as follows: defining a residual influence factor xi according to a flow field residual change influence propagation mechanism, and establishing an influence factor propagation scalar equation of each unit i:
∑(ξ i -ξ j )S ij max(1+M nij ,0)＝0
and calculating to obtain scalar influence factors xi of each unit, wherein j is taken as all adjacent units of the unit i, sij is the area of the common plane between the unit i and the unit j, mnij is the normal Mach number of the airflow on the common plane of the unit i and the unit j, the speed is directed from i to j and is positive, the influence factor xi is taken as 1 on the object plane, and the influence factor xi is taken as 0 on the boundary of the non-object plane.
Further, in the step S4, the specific process is as follows: step S41, calculating the product of the influence factor and the residual modulus of each unit as the characteristic value of the influence quantity; step S42, establishing a solving queue for the cell arrangement according to the size of the influence quantity characteristic value, wherein the cell with the largest influence quantity characteristic value is positioned at the head of the queue; s43, taking out the cell with the maximum influence quantity characteristic value from the head of the queue, and carrying out iterative solution on a control equation until the influence quantity characteristic value is smaller than the current head of the queue cell; step S44, calculating and updating residual errors and influence quantity characteristic values of adjacent cells of the current cell, and putting the current cell and the cells influenced by the change of the current cell and the change of the residual errors into corresponding positions in a queue according to the size of the influence quantity characteristic values; step S45, repeating steps S43 and S44 until the maximum residual eigenvalue decreases by one order of magnitude.
Further, in the step S5, the specific process is as follows: and repeating the step S3 and the step S4 until the total residual influence quantity estimated value is smaller than a preset convergence criterion value, and obtaining a final flow field calculation convergence result.
Compared with the prior art, the beneficial effects of adopting the technical scheme are as follows: the influence of the product of the residual error and the influence factor on the calculation result is used for carrying out sequencing calculation, and unit priority calculation with large influence can be achieved. Particularly for the supersonic flow field, because the influence of disturbance cannot be propagated upstream, the change of the flow field of the downstream unit has no influence on the calculation result, the corresponding adjoint matrix is 0, the influence quantity of residual errors obtained by the adjoint matrix is used for calculation sequencing, redundant calculation on the unit without influence can be completely avoided, and the calculation efficiency is improved to the maximum extent. Meanwhile, the influence factor equation is much simpler than the adjoint equation, and the calculation of the product of the influence factor and the residual error is also simpler than the calculation of the product of the adjoint matrix and the residual error, so that the additional overhead of sequencing calculation can be greatly reduced, and the calculation efficiency can be further improved.
Drawings
FIG. 1 is a schematic flow chart of an implicit solution method based on impact factor residual sorting according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in the flowchart of fig. 1, an implicit solution based on impact factor residual sorting includes:
(1) Step S1: establishing an initial flow field matrix equation according to an object to be detected;
in step S1, a flow field matrix equation is established for the object to be measured
Ax+b＝0；
The matrix A is a matrix representing a control equation, b is a vector and represents a boundary condition established according to an object to be measured, and x is a vector to be solved and represents a flow field parameter to be solved.
In the field of Computational Fluid Dynamics (CFD), most computational models can be solved using the above-described flow field matrix equations.
(2) Step S2: setting restrictive flow field conditions, and performing residual calculation on each unit of the flow field;
the restrictive flow field conditions are specifically flow field boundary conditions and initial flow field conditions, and generally, each cell under the initial flow field conditions does not satisfy a given matrix equation and has a certain degree of residual error.
In step S2, the calculation residual equation is:
an initial value x0 is set for a vector x to be solved by adopting a time correlation method, and a value of R is obtained after a process of changing along with time, wherein R is a residual error.
(3) And step S3: defining a residual error influence factor according to a flow field residual error change influence propagation mechanism, establishing a residual error influence factor propagation scalar equation, and calculating to obtain each unit residual error influence factor;
in the CFD field, the CFD calculation process is to set an initial flow field, a residual error of a flow field region outside a restrictive boundary is 0 or close to 0, and a non-0 residual error is generated near the restrictive boundary due to the limitation of a boundary condition, and the non-0 residual error is diffused outwards in the calculation iteration process, reflected on the boundary, possibly having an oscillation process, and finally gradually reducing the amplitude and tending to 0. According to the mechanism of the flow field residual variation influence propagation, a residual influence factor xi is defined, and an influence factor propagation scalar equation of each unit i is established:
∑(ξ i -ξ j )S ij max(1+M nij ,0)＝0
and calculating to obtain scalar influence factors xi of each unit, wherein j is used for acquiring all adjacent units of the unit i, sij is the area of the common plane between the unit i and the unit j, mnij is the normal Mach number of the airflow on the common plane of the unit i and the unit j, the speed is positive from the direction of i to j, the influence factor of the object plane is 1, and the influence factor of the boundary of the non-object plane is 0.
Thus, the influence factor of each unit residual error, namely the relative estimation of the influence degree of the final calculation result can be obtained. If the calculation model object plane is outside the influence area of a unit, the flow field change disturbance of the calculation model object plane has no influence on the flow field near the object plane, and the influence factor of the unit is equal to 0.
(4) And step S4: defining the product result of the residual error of each unit and the influence factor as an influence quantity characteristic value, sequencing each unit to obtain a sequencing queue, calculating according to the sequence of the queue, and dynamically adjusting the sequence of the queue according to the size of the influence quantity characteristic value until the maximum influence quantity characteristic value is reduced by one order of magnitude; in step S4:
step S41, calculating the product of the influence factor and the residual modulus of each unit as the characteristic value of the influence quantity;
step S42, establishing a solving queue for the cell arrangement according to the size of the influence quantity characteristic value, wherein the cell with the largest influence quantity characteristic value is positioned at the head of the queue;
step S43, taking out the cell with the maximum influence quantity characteristic value from the head of the queue to carry out iterative solution on a control equation until the influence quantity characteristic value is smaller than the current head of the queue cell;
step S44, calculating and updating residual errors and influence quantity characteristic values of cells adjacent to the current cell, and putting the current cell and the cells influenced by the change of the current cell and the residual errors into corresponding positions in a queue according to the size of the influence quantity characteristic values;
step S45, repeating step S43 and step S44 until the maximum influence amount characteristic value decreases by one order of magnitude.
(5) Step S5: and repeating the step S3 and the step S4 until the total influence quantity characteristic value is smaller than a preset convergence criterion value, and obtaining a final flow field calculation convergence result.
The invention has the advantages that: ensuring that all calculations are valid; along with the propagation process of the signals, the calculation area can be ensured to cover the signal propagation path all the time, and the redundant calculation amount is reduced to the maximum extent; the calculation domain is always driven by the propagation of disturbance signals, and an effective region and an ineffective region are automatically distinguished; particularly for the calculation of the supersonic flow field, as the disturbance is not propagated upstream, the invalid calculation of the downstream area which does not influence the calculation result can be effectively reduced; all the calculation states can be adapted to, and special processing is not needed for different calculation states; the method only controls the calculation domain, has no restriction and special requirements on the algorithm layer, can be suitable for any algorithm, and does not sacrifice the precision or limit the application range of the algorithm. Meanwhile, the influence factor equation is much simpler than the adjoint equation, and the calculation of the product of the influence factor and the residual error is also simpler than the calculation of the product of the adjoint matrix and the residual error, so that the additional overhead of sequencing calculation can be greatly reduced, and the calculation efficiency can be further improved.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed. Those skilled in the art to which the invention pertains will appreciate that insubstantial changes or modifications can be made without departing from the spirit of the invention as defined by the appended claims.
Claims (5)
1. An implicit solver based on impact factor residual ordering, comprising:
step S1: establishing an initial flow field matrix equation according to an object to be detected;
step S2: setting restrictive flow field conditions, and performing residual error calculation on each unit of the flow field;
and step S3: defining a residual error influence factor according to a mechanism that flow field residual error change influences propagation, establishing an influence factor propagation scalar equation, and calculating to obtain each unit residual error influence factor;
and step S4: defining the product result of the residual error of each unit and the influence factor as the characteristic value of the influence quantity, sequencing each unit to obtain a sequencing queue, calculating according to the sequence of the queue, and dynamically adjusting the sequence of the queue according to the characteristic value of the influence quantity until the maximum characteristic value of the influence quantity is reduced by one order of magnitude;
step S5: repeating the step S3 and the step S4 until the total influence quantity characteristic value is smaller than a preset convergence criterion value, and obtaining a final flow field calculation convergence result;
the step S4 includes: step S41, calculating the product of the influence factor and the residual modulus of each unit as the characteristic value of the influence quantity; step S42, establishing a solving queue for each cell according to the size of the influence quantity characteristic value, wherein the cell with the largest influence quantity characteristic value is positioned at the head of the queue, and recording the maximum value of the influence quantity characteristic value; step S43, taking out the cell with the maximum influence quantity characteristic value from the head of the queue, and carrying out iterative solution on a control equation until the influence quantity characteristic value is smaller than the current head of the queue cell; step S44, calculating and updating residual errors and influence quantity characteristic values of cells adjacent to the current cell, and putting the current cell and the cells influenced by the change of the current cell and the residual errors into corresponding positions in a queue according to the size of the influence quantity characteristic values; step S45, repeating steps S43 and S44 until the maximum residual eigenvalue decreases by one order of magnitude.
2. The implicit solution based on influence factor residual sorting according to claim 1, wherein in step S1, the flow field matrix equation is:
the matrix A is a matrix representing a control equation, b represents a boundary condition established according to an object to be measured, and x is a vector to be solved and represents a flow field parameter to be solved.
3. The implicit solution based on influence factor residual sorting according to claim 1, wherein in step S2, the residual equation is calculated as:
an initial value x0 is set for a vector x to be solved by adopting a time correlation method, and a time-varying process is carried out to obtain a value R, wherein R is a residual error.
4. The implicit solution based on impact factor residual sorting according to claim 3, wherein in the step S2, the flow field conditions are specifically a boundary condition and an initial flow field condition.
5. The implicit solution method based on impact factor residual sorting according to claim 1, wherein in step S3, the specific process is: defining a residual influence factor xi according to a flow field residual change influence propagation mechanism, and establishing an influence factor propagation scalar equation of each unit i:
and calculating to obtain scalar influence factors xi of each unit, wherein j is taken as all adjacent units of the unit i, sij is the area of the common plane between the unit i and the unit j, mnij is the normal Mach number of the airflow on the common plane of the unit i and the unit j, the speed is directed from i to j and is positive, the influence factor xi is taken as 1 on the object plane, and the influence factor xi is taken as 0 on the boundary of the non-object plane.
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