Adomian Decomposition Based Numerical Scheme for Flow Simulations

TL;DR

This paper introduces a novel numerical scheme combining Adomian decomposition for time discretization with DG techniques for space, specifically applied to Euler equations, demonstrating efficiency through numerical tests against exact solutions and Runge-Kutta DG methods.

Contribution

The paper presents a new numerical method integrating Adomian decomposition with DG techniques for Euler equations, enhancing computational efficiency and accuracy.

Findings

The scheme accurately approximates solutions of Euler equations.

Numerical tests show improved efficiency over traditional methods.

The method is validated against exact solutions and Runge-Kutta DG results.

Abstract

This paper proposes a numerical method based on the Adomian decomposition approach for the time discretization, applied to Euler equations. A recursive property is demonstrated that allows to formulate the method in an appropriate and efficient way. To obtain a fully numerical scheme, the space discretization is achieved using the classical DG techniques. The efficiency of the obtained numerical scheme is demonstrated through numerical tests by comparison to exact solution and the popular Runge-Kutta DG method results.