Work

Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators

Year: 2026

Type: preprint

Abstract: We present new fully discrete Cartesian grid Active Flux methods for the two-dimensional Euler equations of gas dynamics. A key component of these methods is the evolution operator used to evolve point-value degrees of freedom. Therefore, we derive several new, third-order accurate, multidimensional evolution operators for point-value updates of the linearized Euler equations using the method of bicharacteristics. We also investigate how the reconstruction and choice of approximate evolution operator affect the accuracy and stability of the resulting methods.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.34669

Authors: Helzel, Christiane, Lukáčová-Medvid'ová, Mária, Porfetye, Amelie, Tang, Zhuyan

Institutions: Heinrich Heine University Düsseldorf, Johannes Gutenberg University Mainz

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: Zufällige kompressible Euler Gleichungen: Numerik und ihre Analysis, G3044548687, Active Flux Verfahren für die Euler Gleichungen

OpenAlex ID: W7214770413

Cites: 5

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Related to: 10