TY - JOUR

T1 - Influence of discrete model on derivatives in kinetic theory

AU - Prozorova, Evelina V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The aim of this work is to clarify the mathematical models describing the mechanics of rarefied gas and continuous mechanics, and to study the errors that arise when describing a rarefied gas by the framework of a continuous medium through the distribution function. We also trace the errors of numerical calculations. In conservation laws for space coordinates, averaging is fulfilled but for times it is not. So we have laws that are not symmetric relative to time and space. It should be noted that for the kinetic theory (the Boltzmann equation), the law of conservation of angular momentum does not hold. However, writing conservation laws via delta functions, the same classical definition is obtained. Proposed analysis for derivative is to consider the difference between the time derivatives as a limit (the ratio of the increment of the function to the small increment of the argument). In a rarefied gas, we have end values of the mean free path and time. The results of the analysis show which effects are lost when the discrete medium is approximated by a distribution function. As an example of the solutions, a formula is given for calculating the distance of flow of a jet of gas at large non-calculative supersonic flow upstream.

AB - The aim of this work is to clarify the mathematical models describing the mechanics of rarefied gas and continuous mechanics, and to study the errors that arise when describing a rarefied gas by the framework of a continuous medium through the distribution function. We also trace the errors of numerical calculations. In conservation laws for space coordinates, averaging is fulfilled but for times it is not. So we have laws that are not symmetric relative to time and space. It should be noted that for the kinetic theory (the Boltzmann equation), the law of conservation of angular momentum does not hold. However, writing conservation laws via delta functions, the same classical definition is obtained. Proposed analysis for derivative is to consider the difference between the time derivatives as a limit (the ratio of the increment of the function to the small increment of the argument). In a rarefied gas, we have end values of the mean free path and time. The results of the analysis show which effects are lost when the discrete medium is approximated by a distribution function. As an example of the solutions, a formula is given for calculating the distance of flow of a jet of gas at large non-calculative supersonic flow upstream.

KW - angular momentum

KW - Boltzmann equations

KW - Chapman-Enskog method

KW - Conjugate problem to the Navier-Stokes

KW - Conservation laws

KW - Non-symmetrical stress tensor

UR - http://www.scopus.com/inward/record.url?scp=85069719391&partnerID=8YFLogxK

U2 - 10.17654/HM017010001

DO - 10.17654/HM017010001

M3 - Article

AN - SCOPUS:85069719391

VL - 17

SP - 1

EP - 19

JO - JP Journal of Heat and Mass Transfer

JF - JP Journal of Heat and Mass Transfer

SN - 0973-5763

IS - 1

ER -