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

0495265 - MÚ 2019 RIV DE eng J - Článek v odborném periodiku
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
GRANT EU: European Commission(XE) 320078 - MATHEF
Institucionální podpora: RVO:67985840
Klíčová slova: compressible Navier-Stokes * finite difference method * positivity preserving * energy stability
Obor OECD: Pure mathematics
Impakt faktor: 3.107, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0288264