Stability and consistency of a finite difference scheme for compressible viscous isentropic flow in multi-dimension

0495265 - MÚ 2019 RIV DE eng J - Journal Article
Hošek, Radim - She, Bangwei
Stability and consistency of a finite difference scheme for compressible viscous isentropic flow in multi-dimension.
Journal of Numerical Mathematics. Roč. 26, č. 3 (2018), s. 111-140. ISSN 1570-2820. E-ISSN 1569-3953
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : compressible Navier-Stokes * finite difference method * positivity preserving * energy stability
OECD category: Pure mathematics
Impact factor: 3.107, year: 2018
https://www.degruyter.com/view/j/jnma.2018.26.issue-3/jnma-2017-0010/jnma-2017-0010.xml

Motivated by the work of Karper [29], we propose a numerical scheme to compressible Navier-Stokes system in spatial multi-dimension based on finite differences. The backward Euler method is applied for the time discretization, while a staggered grid, with continuity and momentum equations on different grids, is used in space. The existence of a solution to the implicit nonlinear scheme, strictly positivity of the numerical density, stability and consistency of the method for the whole range of physically relevant adiabatic exponents are proved. The theoretical part is complemented by computational results that are performed in two spatial dimensions.
Permanent Link: http://hdl.handle.net/11104/0288264