Versatile mixed methods for weakly-compressible flows

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Miller, Edward A., Williams, David M.
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915409749344256
author Miller, Edward A.
Williams, David M.
author_facet Miller, Edward A.
Williams, David M.
contents Versatile mixed finite element methods were originally developed by Chen and Williams for isothermal incompressible flows in "Versatile mixed methods for the incompressible Navier-Stokes equations," Computers & Mathematics with Applications, Volume 80, 2020. Thereafter, these methods were extended by Miller, Chen, and Williams to non-isothermal incompressible flows in "Versatile mixed methods for non-isothermal incompressible flows," Computers & Mathematics with Applications, Volume 125, 2022. The main advantage of these methods lies in their flexibility. Unlike traditional mixed methods, they retain the divergence terms in the momentum and temperature equations. As a result, the favorable properties of the schemes are maintained even in the presence of non-zero divergence. This makes them an ideal candidate for an extension to compressible flows, in which the divergence does not generally vanish. In the present article, we finally construct the compressible extension of the methods. In addition, we demonstrate the excellent performance of the resulting methods for weakly-compressible flows that arise near the incompressible limit, as well as moderately-compressible flows that arise near Mach 0.5.
format Preprint
id arxiv_https___arxiv_org_abs_2402_18660
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Versatile mixed methods for weakly-compressible flows
Miller, Edward A.
Williams, David M.
Numerical Analysis
76M10, 65M12, 65M60, 76D05
Versatile mixed finite element methods were originally developed by Chen and Williams for isothermal incompressible flows in "Versatile mixed methods for the incompressible Navier-Stokes equations," Computers & Mathematics with Applications, Volume 80, 2020. Thereafter, these methods were extended by Miller, Chen, and Williams to non-isothermal incompressible flows in "Versatile mixed methods for non-isothermal incompressible flows," Computers & Mathematics with Applications, Volume 125, 2022. The main advantage of these methods lies in their flexibility. Unlike traditional mixed methods, they retain the divergence terms in the momentum and temperature equations. As a result, the favorable properties of the schemes are maintained even in the presence of non-zero divergence. This makes them an ideal candidate for an extension to compressible flows, in which the divergence does not generally vanish. In the present article, we finally construct the compressible extension of the methods. In addition, we demonstrate the excellent performance of the resulting methods for weakly-compressible flows that arise near the incompressible limit, as well as moderately-compressible flows that arise near Mach 0.5.
title Versatile mixed methods for weakly-compressible flows
topic Numerical Analysis
76M10, 65M12, 65M60, 76D05
url https://arxiv.org/abs/2402.18660