scholarly journals Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities

2019 ◽  
Vol 80 (2) ◽  
pp. 924-956
Author(s):  
Christophe Berthon ◽  
Arnaud Duran ◽  
Françoise Foucher ◽  
Khaled Saleh ◽  
Jean De Dieu Zabsonré
Keyword(s):  
Fully Discrete ◽  
Reconstruction Scheme ◽  
Entropy Inequalities

scholarly journals RELAXATION OF FLUID SYSTEMS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250014 ◽  
Author(s):  
FRÉDÉRIC COQUEL ◽  
EDWIGE GODLEWSKI ◽  
NICOLAS SEGUIN
Keyword(s):  
Numerical Method ◽  
Weak Solutions ◽  
Equilibrium Model ◽  
Numerical Approximation ◽  
Natural Extension ◽  
Fluid Models ◽  
Relaxation System ◽  
Fluid Systems ◽  
Relaxation Procedure ◽  
Entropy Inequalities

We propose a relaxation framework for general fluid models which can be understood as a natural extension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The numerical method is particularly simple in the case of a fully degenerate relaxation system for which the solution of the Riemann problem is explicit. Indeed, the Godunov solver for the homogeneous relaxation system results in an HLLC-type solver for the equilibrium model. Discrete entropy inequalities are established under a natural Gibbs principle.

scholarly journals Discontinuous finite volume element method of two-dimensional unsaturated soil water movement problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fan Chen ◽  
Zhixiao Xu
Keyword(s):  
Soil Water ◽  
Finite Volume ◽  
Unsaturated Soil ◽  
Water Movement ◽  
Optimal Error Estimate ◽  
Two Dimensional ◽  
Fully Discrete ◽  
Volume Method ◽  
Movement Problem ◽  
Soil Water Movement

AbstractIn this paper, a numerical approximation method for the two-dimensional unsaturated soil water movement problem is established by using the discontinuous finite volume method. We prove the optimal error estimate for the fully discrete format. Finally, the reliability of the method is verified by numerical experiments. This method is not only simple to calculate, but also stable and reliable.

Sign in / Sign up

Export Citation Format

Share Document