Viscous–capillary traveling waves associated with classical and nonclassical shocks in van der Waals fluids

2018 ◽  
Vol 41 ◽  
pp. 107-127 ◽  
Author(s):  
Nguyen Huu Hiep ◽  
Mai Duc Thanh ◽  
Nguyen Dinh Huy
Keyword(s):  
Traveling Waves ◽  
Van Der Waals ◽  
Van Der Waals Fluids

Existence of traveling waves in van der Waals fluids with viscosity and capillarity effects

2014 ◽  
Vol 95 ◽  
pp. 743-755 ◽  
Author(s):  
Mai Duc Thanh ◽  
Nguyen Dinh Huy ◽  
Nguyen Huu Hiep ◽  
Dao Huy Cuong
Keyword(s):  
Traveling Waves ◽  
Van Der Waals ◽  
Van Der Waals Fluids

NON-MONOTONIC TRAVELING WAVES IN VAN DER WAALS FLUIDS

2005 ◽  
Vol 03 (04) ◽  
pp. 419-446 ◽  
Author(s):  
N. BEDJAOUI ◽  
C. CHALONS ◽  
F. COQUEL ◽  
P. G. LeFLOCH
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Van Der Waals ◽  
Traveling Wave Solutions ◽  
Left Hand ◽  
Wave Solutions ◽  
Nonlinear Viscosity ◽  
Classical Trajectories ◽  
Parameter Values ◽  
Van Der Waals Fluids

We investigate the existence and properties of traveling wave solutions for the hyperbolic-elliptic system of conservation laws describing the dynamics of van der Waals fluids. The model is based on a constitutive equation of state containing two inflection points and incorporates nonlinear viscosity and capillarity terms. A global description of the traveling wave solutions is provided. We distinguish between classical and non-classical trajectories and, for the latter, the existence and properties of kinetic functions is investigated. An earlier work in this direction (cf. [4]) was restricted to dealing with one inflection point only. Specifically, given any left-hand state and any shock speed (within some admissible range), we prove the existence of a non-classical traveling wave for a sequence of parameter values representing the ratio of viscosity and capillarity. Our analysis exhibits a surprising lack of monotonicity of traveling waves. The behavior of these non-classical trajectories is also investigated numerically.

Shock waves by a kinetic model of van der Waals fluids

ARI ◽  
1999 ◽  
Vol 51 (3) ◽  
pp. 203-215 ◽  
Author(s):  
B. Kaźmierczak ◽  
K. Piechór
Keyword(s):  
Kinetic Model ◽  
Shock Waves ◽  
Van Der Waals ◽  
Van Der Waals Fluids
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