RECORD
Corrected Navier-Stokes equations for compressible flows
Fluid Dynamics · Submitted 24 Dec 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For the first time, the NS equations have been capable of accurately solving shock structure and rarefied gas flows.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
For gas flows, the Navier-Stokes (NS) equations are established by mathematically expressing conservations of mass, momentum and energy. The advantage of the NS equations over the Euler equations is that the NS equations have taken into account the viscous stress caused by the thermal motion of molecules. The viscous stress arises from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress is proportional to the gradient of velocity1. Thus, the assumption is the only empirical element in the NS equations, and this is actually the reason why the NS equations perform poorly under special circumstances. For example, the NS equations cannot describe rarefied gas flows and shock structure. This work proposed a correction to the NS equations with an argument that the viscous stress is proportional to the gradient of momentum when the flow is under compression, with zero additional empirical parameters. For the first time, the NS equations have been capable of accurately solving shock structure and rarefied gas flows. In addition, even for perfect gas, the accuracy of the prediction of heat flux rate is greatly improved. The corrected NS equations can readily be used to improve the accuracy in the computation of flows with density variations which is common in nature.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | For gas flows, the Navier-Stokes (NS) equations are established by mathematically expressing conservations of mass, momentum and energy. | background 1.00 | 0.06 | 0.02 | asserted 1.00 |
| s1 | The advantage of the NS equations over the Euler equations is that the NS equations have taken into account the viscous stress caused by the thermal motion of molecules. | background 1.00 | 0.06 | 0.03 | asserted 1.00 |
| s2 | The viscous stress arises from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress is proportional to the gradient of velocity1. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s3 | Thus, the assumption is the only empirical element in the NS equations, and this is actually the reason why the NS equations perform poorly under special circumstances. | background 0.65 | 0.21 | 0.04 | asserted 1.00 |
| s4 | For example, the NS equations cannot describe rarefied gas flows and shock structure. | background 0.48 | 0.10 | 0.03 | asserted 1.00 |
| s5 | This work proposed a correction to the NS equations with an argument that the viscous stress is proportional to the gradient of momentum when the flow is under compression, with zero additional empirical parameters. | contribution 0.90 | 0.94 | 0.42 | asserted 0.99 |
| s6 | For the first time, the NS equations have been capable of accurately solving shock structure and rarefied gas flows. | result 0.96 | 0.87 | 0.72 | asserted 1.00 |
| s7 | In addition, even for perfect gas, the accuracy of the prediction of heat flux rate is greatly improved. | result 1.00 | 0.83 | 0.09 | asserted 1.00 |
| s8 | The corrected NS equations can readily be used to improve the accuracy in the computation of flows with density variations which is common in nature. | interpretation 0.92 | 0.48 | 0.14 | asserted 0.76 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
For gas flows, the Navier-Stokes (NS) equations are established by mathematically expressing conservations of mass, momentum and energy. The advantage of the NS equations over the Euler equations is that the NS equations have taken into account the viscous stress caused by the thermal motion of molecules. The viscous stress arises from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress is proportional to the gradient of velocity1. Thus, the assumption is the only empirical element in the NS equations, and this is actually the reason why the NS equations perform poorly under special circumstances. For example, the NS equations cannot describe rarefied gas flows and shock structure. This work proposed a correction to the NS equations with an argument that the viscous stress is proportional to the gradient of momentum when the flow is under compression, with zero additional empirical parameters. For the first time, the NS equations have been capable of accurately solving shock structure and rarefied gas flows. In addition, even for perfect gas, the accuracy of the prediction of heat flux rate is greatly improved. The corrected NS equations can readily be used to improve the accuracy in the computation of flows with density variations which is common in nature.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.