Abstract

Citation

Researchers should cite this work as follows:

• Vladimir Riabov (2022). 4-065-GasInjection-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/9QG8-MP36

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Article Context

Description

The uniform second-order accuracy is obtained for functions and derivatives in this approach. The methodology is widely applied to practical studies of boundary layers with gas injection and combustion.

This case study promotes the development of numerical methods for solving singular (ordinary or partial) differential equations with small coefficients for the highest derivative terms. This singularity leads to the formation of regions with small linear dimensions where gradients of functions are large, thus making numerical steps unsteady. (The analytical analyses of these zones do not provide reliable quantitative data estimations).

The numerical analysis of such problems by traditional box-schemes is restricted by non-uniform convergence or even divergence of numerical solutions. In this case study, students will find the numerical solutions of the model’s singular ordinary differential equation evaluated for the linear boundary value problem.

The developed numerical method (based on exponential box-schemes) can be used for the analysis of gas flow parameters in boundary layers and viscous shock layers under the conditions of gas injection from the body surface.

The practical applications of this methodology include the active heat protection methods for spacecraft and analyses of supersonic hydrogen combustion regimes in engines of modern hypersonic vehicles.