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A Structure-Preserving Finite Volume Scheme for a Hyperbolic Reformulation of the Navier–Stokes–Korteweg Equations.
- Source :
-
Mathematics (2227-7390) . Feb2023, Vol. 11 Issue 4, p876. 25p. - Publication Year :
- 2023
-
Abstract
- In this paper, we present a new explicit second-order accurate structure-preserving finite volume scheme for the first-order hyperbolic reformulation of the Navier–Stokes–Korteweg equations. The model combines the unified Godunov-Peshkov-Romenski model of continuum mechanics with a recently proposed hyperbolic reformulation of the Euler–Korteweg system. The considered PDE system includes an evolution equation for a gradient field that is by construction endowed with a curl-free constraint. The new numerical scheme presented here relies on the use of vertex-based staggered grids and is proven to preserve the curl constraint exactly at the discrete level, up to machine precision. Besides a theoretical proof, we also show evidence of this property via a set of numerical tests, including a stationary droplet, non-condensing bubbles as well as non-stationary Ostwald ripening test cases with several bubbles. We present quantitative and qualitative comparisons of the numerical solution, both, when the new structure-preserving discretization is applied and when it is not. In particular for under-resolved simulations on coarse grids we show that some numerical solutions tend to blow up when the curl-free constraint is not respected. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 162136656
- Full Text :
- https://doi.org/10.3390/math11040876