Differences of Dimensions in Analysis

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Zero-dimensional models treat a system as a single point with no spatial variation, while one-dimensional models incorporate variations along a single axis, allowing for more complexity in analysis. Quasi-one-dimensional models bridge the gap by simplifying multi-dimensional systems into a one-dimensional framework while retaining some spatial characteristics. The choice of dimensionality impacts the accuracy and applicability of thermochemical analyses, particularly in combustion modeling, where zero-dimensional models may overlook critical spatial dynamics. Understanding these differences is essential for effectively applying mathematical models to gaseous systems and improving predictive capabilities in thermochemical studies.
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When analyzing/studying thermochemistry or any system with gases, i.e., combustion, fusion, fuel cells, often time in the literature the system is derived or modeled as being zero-dimensional or quasi-one dimensional.
Can anyone provide a good explanation as to the differences between 0, 1, and quasi-1 dimensions or explain what the use of this mathematics gains you in analyzing/studying gaseous systems?

As an example: concerning combustion modeling using turbulent kenetic energy densities and fuel concentrations where the author is using a zero-dimension for analysis.

"...this formulation based on the k-ε model commonly used in three-dimensional simulations is not particularly suitable for zero-dimensional models."

Again, can anyone provide a good explanation as to the differences between 0, 1, and quasi-1 dimensions or explain what the use of this mathematics gains you in analyzing/studying gaseous systems?
 
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