CN110674607B - Implicit solution method based on residual magnitude ordering - Google Patents
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Abstract
The invention discloses an implicit solution method based on residual magnitude ordering, which relates to the field of numerical calculation and comprises the steps of establishing a flow field matrix equation aiming at an object to be measured; setting boundary conditions and initial flow field conditions, and calculating residual errors of all the cells; defining a residual error module, and establishing a plurality of solving queues according to the magnitude of the residual error module; taking out a cell from the non-empty queue with the maximum residual magnitude to perform control equation iteration until the modulus of the residual decreases by one magnitude; calculating and updating the residual error of the cell influenced by the change of the current cell and the change of the residual error, and putting the current cell and the cell influenced by the change of the current cell and changed by the change of the residual error into corresponding queues according to the magnitude of a residual error model; and (4) obtaining a final flow field calculation convergence result until the residual queues larger than the convergence criterion magnitude are all empty. The method only controls the calculation domain, can be applied to any algorithm, does not sacrifice precision or limit the algorithm, can effectively reduce the calculation resources required by sequencing and improves the calculation efficiency.
Description
Technical Field
The invention relates to the field of numerical calculation, in particular to an implicit solution based on residual magnitude ordering.
Background
The invention relates to an implicit equation set acceleration solution based on residual sorting, which is mainly applied to solving of a fluid mechanics equation and can also be applied to solving of other physical field equations or wider linear or nonlinear equation sets, so that the solving efficiency is improved.
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.
The invention aims to reduce repeated calculation amount and improve equation solving efficiency. Particularly in the CFD field, how to calculate equations in optimal calculation steps and order is studied to accelerate the convergence process of the equations to the maximum extent.
The method for solving the flow field control equation (1) usually adopts a time correlation method, and an initial value x is set for a vector x to be solved 0 Over a time-varying course
Finally, a solution of formula (1) is obtained, wherein R is the residual.
The objective of the steady state calculation is to make the residual tend to 0, and obtain the flow field target solution, and the size of R is the main sign of flow field convergence. 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 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.
For a supersonic/hypersonic flow field, a limited influence area of disturbance (usually shock waves are used as a boundary) exists, the influence of the disturbance is limited in the influence area, and the flow field outside the influence 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 a computation domain based on pre-analysis, or simplifying a control equation into a parabolic model (PNS), performing space-driven 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 can greatly affect computational efficiency and computational 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 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.
However, the sorting of the residuals is resource consuming, and frequent sorting operations may partially offset the effect of improving the computational efficiency. In fact, the influence of the units with the same residual magnitude on the calculation result is considerable, and the calculation sequence cannot generate a great improvement effect on the calculation efficiency. In view of this, a CFD calculation method based on residual magnitude ordering is now proposed.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: and only according to the order of magnitude classification of the residual errors, the residual errors with the same order of magnitude are treated equally, the additional overhead caused by sorting is reduced, and the total calculation efficiency of the existing CFD calculation program is improved by 1-2 orders of magnitude.
The invention provides an implicit solution method based on residual magnitude ordering, which comprises the following steps:
step 1: establishing a flow field matrix equation aiming at an object to be detected;
step 2: setting boundary conditions and initial flow field conditions, and calculating residual errors of all the cells;
and 3, step 3: defining a residual error module, and establishing a plurality of solving queues according to the magnitude classification of the residual error module;
and 4, step 4: taking out a cell from the non-empty queue with the maximum residual magnitude to carry out iterative solution on a control equation until the modulus of the residual decreases by one magnitude;
and 5: calculating and updating the residual error of the cell influenced by the change of the current cell and the change of the residual error, and putting the current cell and the cell influenced by the change of the current cell and changed by the change of the residual error into corresponding queues according to the magnitude of a residual error model;
and 6: and (5) repeating the step (4) and the step (5) until all residual queues larger than the preset convergence criterion magnitude are empty, and obtaining a final flow field calculation convergence result.
Because the method only controls the calculation domain and has no restriction and special requirements on the algorithm layer, the method can be applied to any algorithm without sacrificing the precision or limiting the application range of the algorithm. Meanwhile, the units with the same order of residual errors are not sequenced any more, so that the computing resources required by frequent sequencing are reduced, and the computing efficiency is further improved.
Further, the flow field matrix equation established in step 1 is Ax + b =0; wherein A is a control equation matrix; b is a vector representing a boundary condition established according to the object to be measured; x is a vector and represents a flow field parameter to be solved; the method for calculating the residual error in the step 2 is to set an initial value x for the vector x to be solved 0 Establishing an equation
And solving an equation to obtain a residual error R.
The mode of defining the residual error is based on the sum of the squares of the components of the residual error vector.
The method can ensure that the calculation area always covers the signal transmission path along with the signal transmission process, thereby reducing the redundant calculation amount 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 for different calculation states.
By adopting the technical scheme, the invention has the beneficial effects that: the unit with the maximum residual magnitude is calculated every time, so that all calculation can be guaranteed to be 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; and 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, as the units with the same magnitude of residual errors are not sorted any more, the calculation resources required by frequent sorting are reduced, and the calculation efficiency is further improved.
Detailed Description
All of the features disclosed in this specification, or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
The invention firstly provides a calculation method based on residual sorting, and the algorithm has universal applicability and is almost suitable for all solution models which can be equivalently Ax + b = 0. The method specifically comprises the following steps:
step 1: establishing a flow field matrix equation Ax + b =0 for an object to be measured; wherein A is a matrix of a governing equation; b is a vector representing a boundary condition established according to the object to be measured; and x is a vector and represents a flow field parameter to be solved.
And 2, step: boundary conditions and initial flow field conditions are set, generally, each unit cell under the initial flow field conditions does not meet a given matrix equation and has a certain degree of residual error. The residual error of each cell is calculated.
And step 3: the modulus of the residual is defined in some way, such as the sum of the squares of the components of the residual vector, and a plurality of solution queues are built sorted by the magnitude of the residual modulus.
And 4, step 4: and taking out a cell from the head of the non-empty queue with the maximum residual error magnitude to carry out iterative solution on the control equation until the modulus of the residual error is reduced by one magnitude.
And 5: and calculating and updating the residual error of the adjacent cell of the current cell, and putting the current cell and the cell influenced by the change of the current cell and changed by the residual error into corresponding queues according to the magnitude of the residual error module.
Step 6: and (5) repeating the step (4) and the step (5) until all residual queues larger than the preset convergence criterion magnitude are empty, and obtaining a final flow field calculation convergence result.
The invention has the advantages that the unit with the front-ranked residual error is always calculated, so that the calculation is guaranteed to be effective; 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 be used for adapting to all calculation states, 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, as the units with the same magnitude of residual errors are not sorted any more, the calculation resources required by frequent sorting are reduced, and the calculation efficiency is 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 to any novel method or process steps or any novel combination of steps disclosed.
Claims (3)
1. An implicit solution based on residual magnitude ordering, comprising:
step 1: establishing a flow field matrix equation aiming at an object to be detected;
and 2, step: setting boundary conditions and initial flow field conditions, and calculating residual errors of all the cells;
and step 3: defining a residual error module, and establishing a plurality of solving queues according to the magnitude classification of the residual error module;
and 4, step 4: taking out a cell from the non-empty queue with the maximum residual magnitude to carry out iterative solution on a control equation until the modulus of the residual decreases by one magnitude;
and 5: calculating and updating the residual error of the cell influenced by the change of the current cell and the change of the residual error, and putting the current cell and the cell influenced by the change of the current cell and changed by the change of the residual error into corresponding queues according to the magnitude of a residual error model;
step 6: and (5) repeating the step (4) and the step (5) until all residual queues larger than the preset convergence criterion magnitude are empty, and obtaining a final flow field calculation convergence result.
2. The implicit solution based on residual magnitude ranking of claim 1, wherein the flow field matrix equation established in step 1 is Ax + b =0; wherein A is a control equation matrix; b is a vector representing a boundary condition established according to the object to be measured; x is a vector and represents a flow field parameter to be solved; the method for calculating the residual error in the step 2 is to set an initial value x for the vector x to be solved 0 Establishing an equation
And solving an equation to obtain a residual error R.
3. An implicit solution based on residual magnitude ordering according to claim 1, characterised in that the mode defining the residual is based on the sum of the squares of the components of the residual vector.
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