What is a limit of structure-preserving numerical methods for compressible flows?

2024/01/30 by Mária Lukáčová-Medviďová, Lukacova-Medvidova, Maria, Bangwei She +3 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2401.16763

openalex publication_date 2024/01/30 · openalex created_date 2024/02/01 · openalex updated_date 2026/07/28

Abstract

We present an overview of recent developments on the convergence analysis of numerical methods for inviscid multidimensional compressible flows that preserve underlying physical structures. We introduce the concept of generalized solutions, the so-called dissipative solutions, and explain their relationship to other commonly used solution concepts. In numerical experiments we apply K-convergence of numerical solutions and approximate turbulent solutions together with the Reynolds stress defect and the energy defect.

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