Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws

2008 ◽  
Vol 46 (2) ◽  
pp. 1012-1039 ◽  
Author(s):  
Manuel Castro ◽  
José M. Gallardo ◽  
Juan A. López-GarcÍa ◽  
Carlos Parés
Keyword(s):  
High Order ◽  
Balance Laws ◽  
Godunov’S Method ◽  
Godunov′S Method

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

AZTEC: A front tracking code based on Godunov's method

1986 ◽  
Vol 2 (3-5) ◽  
pp. 385-397 ◽  
Author(s):  
Blair K. Swartz ◽  
Burton Wendroff
Keyword(s):  
Front Tracking ◽  
Godunov’S Method ◽  
Godunov′S Method

High-order well-balanced methods for systems of balance laws: a control-based approach

2021 ◽  
Vol 394 ◽  
pp. 125820
Author(s):  
Irene Gómez-Bueno ◽  
Manuel J. Castro ◽  
Carlos Parés
Keyword(s):  
High Order ◽  
Balance Laws ◽  
Systems Of Balance Laws

Godunov's method for supersonic tactical missile computations

1985 ◽  
Author(s):  
A. WARDLAW, JR. ◽  
F. BALTAKIS ◽  
F. MARTIN ◽  
F. PRIOLO ◽  
R. JETTMAR
Keyword(s):  
Godunov’S Method ◽  
Godunov′S Method

Study of Entropy Properties of a Linearized Version of Godunov’s Method

2020 ◽  
Vol 60 (4) ◽  
pp. 628-640 ◽  
Author(s):  
S. K. Godunov ◽  
V. V. Denisenko ◽  
D. V. Klyuchinskii ◽  
S. V. Fortova ◽  
V. V. Shepelev
Keyword(s):  
Godunov’S Method ◽  
Godunov′S Method
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