Higher-Order Multilevel Framework for ADER Scheme in Computational Aeroacoustics

TL;DR

This paper introduces a multilevel framework for the ADER scheme that enhances computational efficiency in solving hyperbolic PDEs in aeroacoustics while maintaining high accuracy through a novel cycling approach.

Contribution

It presents a new multilevel framework for the ADER scheme that reduces computational cost without sacrificing accuracy in aeroacoustic simulations.

Findings

Achieves high-order accuracy with reduced computational cost.

Validates the framework on benchmark aeroacoustic problems.

Demonstrates effectiveness in both time and frequency domains.

Abstract

The versatile Arbitrary-DERivative (ADER) scheme is cast in a multilevel framework (ML-ADER) for fast solution of system of linear hyperbolic partial differential equations. The solution is cycled through spatial operators of varying accuracy while retaining highest-order accuracy by the use of a forcing function. Accuracy analysis of the multilevel framework including in the ML-ADER form is carried out in time-domain as well as frequency-domain. Results are obtained for benchmark problems in computational aeroacoustics at a much reduced computational cost.