Hybrid iteration method for gas energy inversion thermodynamic temperature

Abstract

The invention discloses a hybrid iteration method for gas energy inversion thermodynamic temperature. The method is mainly used for a sub-iterative inversion calculation process of gas modal energy (translational energy, rotational energy, vibration energy, electron energy and combination of the translational energy, the rotational energy, the vibration energy and the electron energy) to corresponding gas thermodynamic temperature in a hypersonic non-equilibrium flow numerical simulation process. According to the method, on the basis of a Newton iteration method, gas energy inversion characteristics are combined, a local dichotomy is introduced to correct a calculation criterion, and the Newton iteration method and the dichotomy are combined to form a hybrid iterative calculation method. According to the method, the advantage that convergence is fast when an iteration initial value approaches a true value of a Newton iteration method is reserved, the calculation efficiency is high, theadvantage that a dichotomy has high stability for a monotonic function is absorbed, and the divergence problem of the Newton iteration method under extreme conditions is avoided.

Description

technical field [0001] The invention relates to the field of numerical simulation calculations, in particular to an iterative calculation method for reversing the corresponding thermodynamic temperature of each modal energy of gas when various thermodynamic temperature models are used. Background technique [0002] In the process of numerical simulation of hypersonic non-equilibrium flow, since the mixture of multiple gas components is involved and the energy levels and energy characteristics of molecules (or atoms) of each component are quite different, the modal energy of each gas mixture ( Translational kinetic energy, rotational energy, vibration energy, electronic energy (single, multiple or combined equivalent energy) often cannot be directly analytically calculated to obtain the equivalent thermodynamic temperature of the corresponding mode, often relying on iterative calculation methods for inversion. [0003] At present, the most commonly used iterative methods for ...

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Problems solved by technology

Its disadvantage is that the scope of application is limited to a certain extent. When the energy function changes in the local area are complex and sharp (such as the electron binding energy of heavy particles) or the initial value of the temperature is far from the true value, the calculation results may oscillate, do not converge, or even diverge.

In order to ensure better convergence of the Newton iterative method, artificial parameters such as relaxation factors are often introduced to adjust the relaxation iteratively. On the one hand, this increases the amount of calculation. On the other hand, it cannot completely guarantee the convergence of the results.

[0005] The advantage of the dichotomy method is that it has good stability for monotone functions (energy functions are generally monotonically increasing functions of thermodynamic temperature), thus ensuring the stable convergence of energy inversion temperature; its disadvantage is that it cannot inherit the temperature of most regions of the flow field. The initial value is close to the true value", each inversion calculation needs to go through many iterations from the upper and lower limits of the calculated temperature range, and gradually approach the true value, so the calculation efficiency is low

At the same time, when using the dichotomy method, the true value must be within the calculated temperature range, and the given calculation range must be sufficiently "broad". It is necessary to estimate the upper and lower limits of each modal temperature in the full flow field, and give out enough redundancy, which will further reduce computational efficiency

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