Volume 58, 2017LMLFN 2015 – Low Velocity Flows – Application to Low Mach and Low Froude regimes
|Page(s)||27 - 39|
|Published online||08 November 2017|
A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *
1 Department of Mathematics, Würzburg University, Germany
2 Heidelberg Institute for Theoretical Studies, Germany
3 Heidelberg University, Germany
In order to perform simulations of low Mach number flow in presence of gravity the technique from  is found insufficient as it is unable to cope with the presence of a hydrostatic equilibrium. Instead, a new modification of the diffusion matrix in the context of Roe-type schemes is suggested. We show that without gravity it is able to resolve the incompressible limit, and does not violate the conditions of hydrostatic equilibrium when gravity is present. These properties are verified by performing a formal asymptotic analysis of the scheme. Furthermore, we study its von Neumann stability when subject to explicit time integration and demonstrate its abilities on numerical examples.
© EDP Sciences, SMAI 2017
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.