A new discretization of the Euler equation via the finite operator theory

TL;DR

This paper introduces a novel discretization method for the Euler equation using Galois differential algebras and finite operator calculus, enabling the creation of a discrete model that preserves certain exact solutions of the continuous equation.

Contribution

The paper presents a new discretization approach for the Euler equation based on advanced algebraic theories, offering a systematic way to retain exact solutions in the discrete model.

Findings

New discretization procedure for Euler equation

Discrete model inherits exact solutions from continuous case

Algorithmic construction of the discretization method

Abstract

We propose a novel discretization procedure for the classical Euler equation based on the theory of Galois differential algebras and the finite operator calculus developed by G.C. Rota and collaborators. This procedure allows us to define algorithmically a new discrete model that inherits from the continuous Euler equation a class of exact solutions.