A Real-Space Discrete Inverse Renormalization Group Method

TL;DR

This paper develops a numerical real-space inverse renormalization group method and tests it on the heat equation, aiming to apply it to fully developed turbulence in the future.

Contribution

It introduces a real-space inverse renormalization group technique and demonstrates its effectiveness on the heat equation, with plans for turbulence applications.

Findings

Successfully tested on the random-forced heat equation

Revealed scaling behavior at short scales

Provides a foundation for turbulence studies

Abstract

A numerical real-space version of the Inverse Renormalization Group proposed by Gawedzky et al is developed. It has been tested to obtain the scaling behaviour of the random-forced heat equation in the short scales limit. Prospectives are described, and the most important target for the procedure is fully developed turbulence.