One dimensional methods for the numerical solution of nonlinear hyperbolic systems

1971 ◽  
pp. 290-296 ◽  
Author(s):  
A. R. Gourlay ◽  
G. McGuire ◽  
J.Ll. Morris
Keyword(s):  
Numerical Solution ◽  
Hyperbolic Systems ◽  
One Dimensional ◽  
Nonlinear Hyperbolic Systems

scholarly journals Using the Sharp scheme of higher-order accuracy for solving some nonlinear hyperbolic systems of equations

2019 ◽  
pp. 45-53
Author(s):  
А.В. Соловьев ◽  
А.В. Данилин
Keyword(s):  
Difference Scheme ◽  
Hyperbolic Systems ◽  
Higher Order ◽  
Test Problems ◽  
Systems Of Equations ◽  
Order Accuracy ◽  
One Dimensional ◽  
Hyperbolic Systems Of Equations ◽  
Sharp Difference ◽  
Nonlinear Hyperbolic Systems

Разностная схема Диез повышенного порядка точности, ранее разработанная для решения скалярного одномерного уравнения переноса, с помощью балансно-характеристического подхода распространена на нелинейные системы уравнений мелкой воды и уравнений Эйлера. Для обеих систем уравнений решены тестовые задачи, иллюстрирующие особенности решений, полученных с помощью описываемой разностной схемы. The Sharp difference scheme of higher-order accuracy developed previously for solving the scalar one-dimensional transport equation is extended to the shallow water nonlinear systems and to the systems of Euler equations using the balance-characteristic approach. For these systems, a number of test problems are solved to illustrate the features of the solutions obtained by the described difference scheme.

scholarly journals Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems

2008 ◽  
Vol 47 (3) ◽  
pp. 1460-1498 ◽  
Author(s):  
Jean-Michel Coron ◽  
Georges Bastin ◽  
Brigitte d'Andréa-Novel
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Systems ◽  
One Dimensional ◽  
Dissipative Boundary ◽  
Nonlinear Hyperbolic Systems

ASYMPTOTIC METHOD FOR APPROXIMATION OF RESONANT INTERACTION OF NONLINEAR MULTIDIMENSIONAL HYPERBOLIC WAVES

2008 ◽  
Vol 13 (1) ◽  
pp. 47-54 ◽  
Author(s):  
A. Krylovas
Keyword(s):  
Asymptotic Method ◽  
Hyperbolic Systems ◽  
Resonant Interaction ◽  
Method Of Averaging ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Hyperbolic Waves ◽  
Wave Problems ◽  
Nonlinear Hyperbolic Systems

A method of averaging along characteristics of weakly nonlinear hyperbolic systems, which was presented in earlier works of the author for one dimensional waves, is generalized for some cases of multidimensional wave problems. In this work we consider such systems and discuss a way to use the internal averaging along characteristics for new problems of asymptotical integration.

On the Convergence Rate of Vanishing Viscosity Approximations for Nonlinear Hyperbolic Systems

2012 ◽  
Vol 44 (5) ◽  
pp. 3537-3563 ◽  
Author(s):  
Alberto Bressan ◽  
Feimin Huang ◽  
Yong Wang ◽  
Tong Yang
Keyword(s):  
Convergence Rate ◽  
Hyperbolic Systems ◽  
Vanishing Viscosity ◽  
Nonlinear Hyperbolic Systems
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