Physlib.FluidDynamics.ThermodynamicCauchyFlow.Isentropic

Isentropic thermodynamic Cauchy flows

i. Overview

This module defines the isentropic predicate for thermodynamic Cauchy flows.

ii. Key results

- `ThermodynamicCauchyFlow.IsIsentropic` : A thermodynamic Cauchy flow whose entropy is materially conserved.

iii. Table of contents

A. Thermodynamic-flow predicates

iv. References

A. Thermodynamic-flow predicates

1 declaration

definition

Isentropic condition for a thermodynamic Cauchy flow ( $\frac{Ds}{Dt} = 0$ )

#IsIsentropic

For a thermodynamic Cauchy flow in $d$ -dimensional space, the property of being isentropic is defined as the material derivative of the entropy field $s$ being zero at all times $t$ and positions $x$ with respect to the underlying velocity field $\mathbf{u}$ . Mathematically, this is expressed as: $\frac{Ds}{Dt} = \frac{\partial s}{\partial t} + (\mathbf{u} \cdot \nabla)s = 0$