A method for repairing ill-conditioned flow field based on flow characteristic feedback

Abstract

The application discloses a kind of ill-conditioned flow field repair methods based on flow characteristic feedback, belong to aerodynamics and numerical simulation field, including the following steps: step 1, identify the ill-conditioned flow field microelement of calculation error in numerical iteration process;Step 2, find the reference microelement corresponding to ill-conditioned microelement based on flow field parameter dependence relationship;Step 3, calculate the conservation variable on reference microelement;Step 4, based on the conservation variable on reference microelement, interpolation calculation ill-conditioned microelement's conservation variable;Step 5: by the conservation variable on ill-conditioned microelement, obtain the new original variable reset flow field parameter on ill-conditioned microelement, complete repair.This method can effectively guarantee the conservation characteristics of flow field, more universal realization ill-conditioned flow field repair;While this method finds reference microelement from flow field parameter dependence relationship, can guarantee the stability of numerical calculation to the greatest extent.

Description

Technical Field

[0001] This invention relates to the fields of aerodynamics and numerical simulation, and in particular to a method for repairing ill-conditioned flow fields based on flow characteristic feedback. Background Technology

[0002] High-speed aircraft can reach speeds of several times the speed of sound and possess excellent maneuverability, enabling them to reach any location on Earth within hours to perform missions. High-speed flow numerical simulation technology can lay the foundation for the design and development of high-speed aircraft, reusable launch vehicles, and other aircraft, and is highly valued by major spacefaring nations worldwide.

[0003] In high-speed flow numerical simulations, the flow field parameters vary complexly and drastically in different spatial regions and at different times, often by several orders of magnitude. Due to factors such as the quality of the discrete mesh and numerical iteration errors, local instantaneous pressure, gas density, or flow field temperature may exhibit non-physical negative values, leading to errors in iterative calculations, forced termination of the numerical simulation, and invalidation of the simulation results.

[0004] To avoid this situation, the numerical iteration process needs to repair the "ill-conditioned" regions where the flow field calculations have failed, ensuring that the numerical iteration can proceed normally. Similar flow field correction techniques are introduced in the theoretical manual of the commercial software CFD3D, but because they only correct pressure, they cannot effectively solve the ill-conditioned flow field problem caused by iteration errors. Therefore, it is still necessary to develop a more universal method for repairing ill-conditioned flow fields. Summary of the Invention

[0005] The purpose of this invention is to provide a method for repairing ill-conditioned flow fields based on flow characteristic feedback, which addresses the above-mentioned shortcomings. This method solves the problem in the prior art that, due to factors such as discrete grid quality and numerical iteration errors, the local instantaneous pressure, gas density, or flow field temperature may exhibit non-physical negative values, leading to errors in iterative calculations, forced termination of numerical simulations, and invalidation of simulation results.

[0006] This invention is achieved through the following scheme: A method for repairing ill-conditioned flow fields based on flow characteristic feedback includes the following steps: Step 1: Identify ill-conditioned flow field elements that have computational errors during the numerical iteration process; Step 2: Find the reference element corresponding to the ill-conditioned element based on the flow field parameter dependencies: Step 3, calculate the conserved variables on the reference infinitesimal element: Step 4: Based on the conserved variables on the reference infinitesimal element, interpolate to calculate the conserved variables of the ill-conditioned infinitesimal element: Step 5: Obtain the new original variables on the ill-conditioned infinitesimal from the conserved variables on the ill-conditioned infinitesimal, reset the flow field parameters, and complete the repair.

[0007] Step 1 includes the following steps: During the iterative solution of the flow control equations, the gas density on each grid element is extracted. Gas pressure and gas temperature Mesh element number , Let be the total number of infinitesimal elements; if or or If so, then the infinitesimal element is an ill-conditioned mesh element; , and These are the allowable gas density, pressure, and temperature limits in the flow field, selected based on actual operating conditions.

[0008] , and The selection principle, based on actual operating conditions, is as follows: in the bottom region of high-speed leeward flow or in the rarefied flow region at high altitudes, the gas density and pressure are very low, approaching a vacuum. and The value is set to 0; in ground wind tunnel tests, the incoming flow temperature for high-speed flow tests is very low, as low as around 20K, therefore Set the value to 10K~20K.

[0009] Step 2 includes the following steps: For each ill-conditioned micro-element, extract the nearest neighbor in its upstream region. A non-pathological infinitesimal element is used as a reference infinitesimal element. .

[0010] Step 2 specifically includes the following steps: The velocity direction on the ill-conditioned infinitesimal element is the unit vector. ,Pick and smallest A non-pathological infinitesimal element is used as a reference infinitesimal element. Let be the vector pointing from the ill-conditioned element to the surrounding non-ill-conditioned elements. The angle between the upstream and downstream regions. The value range is (0, 90]; if only one is found in the upstream region indivual( If a non-ill-conditioned infinitesimal satisfies the above conditions, then the rest... For each infinitesimal element, the nearest non-obsessive infinitesimal element is selected; if the velocity on an obsessive infinitesimal element is zero, then the nearest non-obsessive infinitesimal element is selected. A non-pathological infinitesimal is used as a reference infinitesimal.

[0011] Specifically, The value range is [1, 6]. The value range is [45°, 60°]. If enough non-illness elements cannot be found in the upstream region or the velocity is 0, then the nearest non-illness element can only be found around it. If no non-illness element can be found in the entire watershed, it means that the numerical iteration has completely failed and there is no feasibility or necessity for repair calculation.

[0012] Step 3 includes the following steps: for Each reference infinitesimal element is used to calculate the conserved variables for the current iteration, including but not limited to the gas mass conservation variable. Momentum conservation variables and energy conservation variables , , It is a velocity vector. Energy per unit mass of gas.

[0013] The interpolation method in step 4 is the direct averaging method, the volume weighting method, the inverse distance weighting method, or a hybrid method.

[0014] The direct averaging method is as follows: ; The volume-weighted method is as follows: ; The inverse distance weighted method is as follows: ; The hybrid method is specifically as follows:

[0015] here These are conserved variables, such as gas mass conservation variables, momentum conservation variables, and energy conservation variables; Let be the distance from the j-th reference infinitesimal to the corresponding ill-conditioned infinitesimal; Let j be the size of the region occupied by the j-th reference element. These are mixed parameters.

[0016] Step 5 includes the following steps: The new gas density on the ill-conditioned infinitesimal element is calculated from the conserved variables on that element. ,speed ,temperature ,pressure Wait for the original variables to complete the repair.

[0017] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This method finds reference infinitesimal elements based on the dependence of flow field parameters, which can maximize the stability of numerical calculations.

[0018] 2. This method effectively ensures the conservation characteristics of mass, momentum, and energy in the flow field, and can better guarantee the effectiveness of the repair calculation.

[0019] 3. This method has no restrictions on flow control equations, gas models, grid types, or computational dimensions, and has good universality. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0021] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0022] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0023] In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a predetermined orientation, or be constructed and operated in a predetermined orientation. Therefore, they should not be construed as limitations on this invention.

[0024] Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity indicated. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature.

[0025] Example 1 like Figure 1 As shown, the present invention provides a technical solution: A method for handling the floating default components in high-temperature nonequilibrium flow simulation: This method first identifies ill-conditioned flow field elements with calculation errors during the numerical iteration process; secondly, it finds their reference elements based on the flow field parameter dependencies; then, it interpolates and calculates the conserved variables of the ill-conditioned elements by combining the flow field conservation characteristics; finally, it obtains new original variables on the ill-conditioned elements to reset the flow field parameters.

[0026] Specifically, it includes the following steps: Step 1, Identify ill-conditioned flow field micro-elements: During the iterative solution of the flow control equations, extract the gas density on each grid micro-element. Gas pressure and gas temperature Mesh element number , Let be the total number of infinitesimal elements; if or or If so, then the infinitesimal element is an ill-conditioned mesh element; , and These represent the allowable gas density, pressure, and temperature limits in the flow field, and must be selected based on actual operating conditions.

[0027] Step-by-step instructions: Numerical simulations of hypersonic flow typically employ iterative solutions to the governing equations of the flow field. During the iteration process, factors such as the quality of the discrete mesh and numerical iteration errors can lead to excessively low gas density, pressure, and temperature values, or even unphysical negative values, exceeding the effective calculation range of the gas reaction model, transport coefficient model, and gas internal energy model. This forces the numerical simulation to terminate, rendering the simulation results invalid. Therefore, it is crucial to identify and correct such "ill-conditioned" regions during numerical iteration to obtain gas density, pressure, temperature, velocity, and other parameters that closely resemble physical realities, ensuring the successful execution of numerical calculations.

[0028] , and The selection must be based on actual operating conditions. Suggested values ​​are provided here, but the invention is not limited to these: because in the bottom region of high-speed flowing leeward or in high-altitude rarefied flow regions, gas density and gas pressure can be very small and approach a vacuum, therefore... and It is recommended to set it to 0; in ground wind tunnel tests, the incoming flow temperature for high-speed flow tests can be very low, even as low as around 20K, therefore It is recommended to use 10K~20K to ensure the universality of the recognition method.

[0029] Step 2, determine the reference element corresponding to the ill-conditioned element: For each ill-conditioned element, extract the reference element that is closest to its upstream region. A non-pathological infinitesimal element is used as a reference infinitesimal element. Set by humans, .

[0030] The specific implementation method is as follows: taking the velocity direction on the ill-conditioned infinitesimal element as the unit vector. ,Pick and smallest A non-pathological infinitesimal element is used as a reference infinitesimal element. Let be the vector pointing from the ill-conditioned element to the surrounding non-ill-conditioned elements. The angle between the upstream and downstream regions. The value range is (0, 90], which is set manually. If only one is found in the upstream region... indivual( If a non-ill-conditioned infinitesimal satisfies the above conditions, then the rest... For each infinitesimal element, the nearest non-obsessive infinitesimal element is selected. If the velocity on an obsessive infinitesimal element is zero, then the nearest non-obsessive infinitesimal element is selected. A non-pathological infinitesimal is used as a reference infinitesimal; Step-by-step instructions: Since ill-conditioned infinitesimal elements do not conform to physical reality, they must be corrected. There are generally two types of correction methods: one is to correct the parameters based on the ill-conditioned infinitesimal element, combining the basic principles of fluid mechanics and numerical simulation, such as changing the discretization scheme or reducing the iteration amplitude to achieve parameter preservation; the other is to reset the parameters on the ill-conditioned infinitesimal element. Each method has its advantages and disadvantages: the former cannot guarantee that the ill-conditioned flow field will be completely repaired, and the flow field may still eventually diverge as iterations continue; while the latter depends on the appropriateness of the parameter reset.

[0031] As is known from the basic principles of fluid mechanics, the local parameters of flow are mainly affected by upstream parameters. Therefore, when resetting ill-conditioned infinitesimal elements, the reference cell for resetting parameters should preferably be the nearest one in its upstream region. A non-pathological microelement. This invention proposes a method that is manually set, with no upper limit, and considers both computational efficiency and accuracy. The value range is [1,6], but is not limited to this. The angle between the upstream and downstream regions is set manually. The value range is (0, 90]. This invention suggests... The value range is [45°, 60°], but not limited to this. If enough non-ill-conditioned infinitesimals cannot be found in the upstream region or the velocity is 0, then the nearest non-ill-conditioned infinitesimal can only be found in its vicinity. If no non-ill-conditioned infinitesimals can be found in the entire watershed, it indicates that the numerical iteration has completely failed, and there is neither the feasibility nor the necessity for repair calculation.

[0032] Step 3, calculate the conserved variables on the reference infinitesimal element: For Each reference infinitesimal element is used to calculate the conserved variables for the current iteration, including but not limited to the gas mass conservation variable. Momentum conservation variables and energy conservation variables , , It is a velocity vector. Energy per unit mass of gas.

[0033] Step-by-step instructions: The repair of ill-conditioned infinitesimal elements first requires ensuring the conservation of mass, momentum, and energy. For its reference element, this invention first calculates the conservation variables on each reference infinitesimal element, and then repairs the ill-conditioned infinitesimal element using these conservation variables to minimize deviations of the reset parameters from conservation. Since gases may contain multiple components and gas energy may consider the conservation of multiple energy modes (e.g., in thermochemical non-equilibrium, conservation equations need to consider multiple gas components and multiple energy modes of molecules), the conservation variables include, but are not limited to, the gas mass conservation variable. Momentum conservation variables and energy conservation variables .

[0034] Step 4: Based on the conserved variables on the reference infinitesimal element, interpolate to calculate the conserved variables on the ill-conditioned infinitesimal element. ; There are many existing interpolation methods, and this invention applies to all of them. Four types of processing methods are provided here, but are not limited to these: 1. Direct averaging method:

[0035] 2. Volume-weighted method:

[0036] 3. Distance-inverse weighted method:

[0037] 4. Mixed method:

[0038] here These are conserved variables, such as gas mass conservation variables, momentum conservation variables, and energy conservation variables. Let be the distance from the j-th reference infinitesimal to the corresponding ill-conditioned infinitesimal; Let j be the size of the region occupied by the j-th reference element. These are mixed parameters.

[0039] Step-by-step instructions: There are many existing interpolation methods, and this invention applies to all of them. This invention provides four common processing methods, each with its own advantages and disadvantages, the physical meaning of which is as follows: (1) The direct averaging method is equivalent to providing an equal amount of gas to each of j reference micro-elements, mixing them to ensure that mass, momentum, and energy are conserved and reach equilibrium. This is a physically real state, so the gas density, temperature, and pressure must be positive, and it can be used to repair diseased micro-elements. The direct averaging method has small calculations, but ignores the position and morphological characteristics of each micro-element.

[0040] (2) The volume weighting method is equivalent to providing gas with the actual volume of the j reference micro-elements for each micro-element, mixing to ensure that mass, momentum, and energy are conserved to reach an equilibrium state, which is also a physically real state. Therefore, the gas density, temperature, and pressure must be positive, and it can be used to repair ill micro-elements. The volume weighting method considers the morphological characteristics of each micro-element, with larger micro-elements having greater weights, but it ignores the positional characteristics of the micro-elements.

[0041] (3) The reciprocal distance method is equivalent to providing a component for each of j reference infinitesimals. The mixture of gases ensures the conservation of mass, momentum, and energy, reaching an equilibrium state, which is also a physically real state. Therefore, the gas density, temperature, and pressure must be positive, making it suitable for repairing pathological micro-elements. The volume-weighted method considers the positional characteristics of micro-elements, with closer micro-elements having greater weights, but it ignores the morphological characteristics of each micro-element.

[0042] (4) The hybrid method can consider both the positional and morphological characteristics of the micro-element, but it has artificial parameters. Uncertainty.

[0043] Step 5: Calculate the new gas density on the ill-conditioned infinitesimal element using the conserved variables. ,speed ,temperature ,pressure Wait for the original variables to complete the repair.

[0044] Step-by-step instructions: The method for calculating the original variables from the conserved variables has been introduced in many public documents, so I will not repeat it here.

[0045] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for repairing ill-conditioned flow fields based on flow characteristic feedback, characterized in that: Includes the following steps: Step 1: Identify ill-conditioned flow field elements that have computational errors during the numerical iteration process; Step 2: Find the reference element corresponding to the ill-conditioned element based on the flow field parameter dependency; Step 2 includes the following steps: For each ill-conditioned micro-element, extract the nearest neighbor in its upstream region. A non-pathological infinitesimal element is used as a reference infinitesimal element. ; Specifically, the velocity direction on the ill-conditioned infinitesimal element is taken as the unit vector. ,Pick and smallest A non-pathological infinitesimal element is used as a reference infinitesimal element. Let be the vector pointing from the ill-conditioned element to the surrounding non-ill-conditioned elements. The angle between the upstream and downstream regions. The value range is (0, 90]; if only one is found in the upstream region A non-pathological infinitesimal element that meets the conditions, among which Then the rest For each infinitesimal element, the nearest non-obstructed infinitesimal element is selected; if the velocity on an obstructed infinitesimal element is zero, then the nearest non-obstructed infinitesimal element is selected. Each non-pathological infinitesimal is a reference infinitesimal. Step 3: Calculate the conserved variables on the reference infinitesimal element; Step 3 includes the following steps: for Each reference infinitesimal element is used to calculate the conserved variables for the current iteration, including the gas mass conservation variable. Momentum conservation variables and energy conservation variables , , It is a velocity vector. Energy per unit mass of gas; Step 4: Based on the conserved variables on the reference infinitesimal element, interpolate to calculate the conserved variables of the ill-conditioned infinitesimal element; Step 5: Obtain the new original variables on the ill-conditioned infinitesimal from the conserved variables on the ill-conditioned infinitesimal, reset the flow field parameters, and complete the repair.

2. The method for repairing ill-conditioned flow fields based on flow characteristic feedback as described in claim 1, characterized in that: Step 1 includes the following steps: During the iterative solution of the flow control equations, the gas density on each grid element is extracted. Gas pressure and gas temperature Mesh element number , Let be the total number of infinitesimal elements; if or or If so, then the infinitesimal element is an ill-conditioned mesh element; , and These are the allowable gas density, pressure, and temperature limits in the flow field, selected based on actual operating conditions.

3. The method for repairing ill-conditioned flow fields based on flow characteristic feedback as described in claim 2, characterized in that: , and The selection should be based on actual operating conditions, with the following principle: in the bottom region of the leeward side of high-speed flow or in the rarefied flow region at high altitude. and Set to 0; in ground wind tunnel tests, Set the value to 10K~20K.

4. The method for repairing ill-conditioned flow fields based on flow characteristic feedback as described in claim 3, characterized in that: Specifically, The value range is [1, 6]. The value range is [45°, 60°]; if enough non-pathological infinitesimals cannot be found in the upstream region or the velocity is 0, then the nearest non-pathological infinitesimal can only be found around it; If no non-illness-prone infinitesimal element can be found in the entire watershed, it indicates that the numerical iteration has completely failed and there is neither the feasibility nor the necessity for repair calculation.

5. The method for repairing ill-conditioned flow fields based on flow characteristic feedback as described in claim 1, characterized in that: The interpolation method in step 4 is the direct averaging method, the volume weighting method, the inverse distance weighting method, or a hybrid method.

6. The method for repairing ill-conditioned flow fields based on flow characteristic feedback as described in claim 5, characterized in that: The direct averaging method is as follows: ； The volume-weighted method is as follows: ； The inverse distance weighted method is as follows: ； The hybrid method is specifically as follows: here These are conserved variables, such as gas mass conservation variables, momentum conservation variables, and energy conservation variables; Let be the distance from the j-th reference infinitesimal to the corresponding ill-conditioned infinitesimal; Let j be the size of the region occupied by the j-th reference element. These are mixed parameters.

7. The method for repairing ill-conditioned flow fields based on flow characteristic feedback as described in claim 1, characterized in that: Step 5 includes the following steps: The new gas density on the ill-conditioned infinitesimal element is calculated from the conserved variables on that element. ,speed ,temperature ,pressure The original variables were restored, and the repair was completed.

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