An Adaptive Artificial Viscosity Method for the Saint-Venant System

2013 ◽  
pp. 125-141 ◽  
Author(s):  
Yunlong Chen ◽  
Alexander Kurganov ◽  
Minlan Lei ◽  
Yu Liu
Keyword(s):  
Artificial Viscosity ◽  
Viscosity Method ◽  
Adaptive Artificial Viscosity

scholarly journals Modified Method of Adaptive Artificial Viscosity for Solution of Gas Dynamics Problems on Parallel Computer Systems

2018 ◽  
Vol 173 ◽  
pp. 03020 ◽  
Author(s):  
Igor Popov ◽  
Sergey Sukov
Keyword(s):  
Gas Dynamics ◽  
Unstructured Grids ◽  
Computer Experiments ◽  
Artificial Viscosity ◽  
Parallel Computer ◽  
Time Approximation ◽  
Adaptive Artificial Viscosity ◽  
Modified Method ◽  
Gas Dynamics Problems ◽  
Dynamics Problems

A modification of the adaptive artificial viscosity (AAV) method is considered. This modification is based on one stage time approximation and is adopted to calculation of gasdynamics problems on unstructured grids with an arbitrary type of grid elements. The proposed numerical method has simplified logic, better performance and parallel efficiency compared to the implementation of the original AAV method. Computer experiments evidence the robustness and convergence of the method to difference solution.

Convergence of the viscosity method for some nonlinear hyperbolic systems

1994 ◽  
Vol 124 (2) ◽  
pp. 341-352 ◽  
Author(s):  
Yunguang Lu
Keyword(s):  
Perturbation Theory ◽  
Hyperbolic Systems ◽  
Artificial Viscosity ◽  
Singular Perturbation Theory ◽  
Compensated Compactness ◽  
Cauchy Problems ◽  
Single Variable ◽  
Viscosity Method ◽  
Entropy Flux ◽  
Nonlinear Hyperbolic Systems

In this paper some special entropy–entropy flux pairs of Lax type are constructed for nonlinear hyperbolic systems of types (1.1) and (1.2), in which the progression terms are functions of a single variable. The necessary estimates for the major terms are obtained by the use of singular perturbation theory. The special entropies provide a convergence theorem in the strong topology for the artificial viscosity method when applied to the Cauchy problems (1.1), (1.3) and (1.2), (1.3) and used together with the theory of compensated compactness.

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