Exact solutions of a nonlinear diffusion equation with absorption and production

TL;DR

This paper derives exact closed-form solutions for a nonlinear diffusion equation modeling turbulent kinetic energy transport within a single-equation turbulence model.

Contribution

It presents the first explicit solutions to this specific nonlinear diffusion equation with absorption and production terms.

Findings

Closed-form solutions for the turbulence energy equation.

Enhanced understanding of turbulence modeling dynamics.

Potential applications in fluid dynamics simulations.

Abstract

We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.