Systems of balance laws in fluid dynamics problems

2015 ◽  
Author(s):  
Abel Alvarez Bustos
Keyword(s):  
Fluid Dynamics ◽  
Balance Laws ◽  
Systems Of Balance Laws ◽  
Dynamics Problems

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.

scholarly journals Application of a bounded upwinding scheme to complex fluid dynamics problems

2013 ◽  
Vol 57 (3-4) ◽  
pp. 435-459 ◽  
Author(s):  
V.G. Ferreira ◽  
M.K. Kaibara ◽  
G.A.B. Lima ◽  
J.M. Silva ◽  
M.H. Sabatini ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Complex Fluid ◽  
Dynamics Problems

Fluid Dynamics Problems in Uncertain Environment

2020 ◽  
pp. 125-144
Author(s):  
Perumandla Karunakar ◽  
Uddhaba Biswal ◽  
Snehashish Chakraverty
Keyword(s):  
Fluid Dynamics ◽  
Uncertain Environment ◽  
Dynamics Problems

scholarly journals Coordinate Free Programming of Computational Fluid Dynamics Problems

2000 ◽  
Vol 8 (4) ◽  
pp. 211-230 ◽  
Author(s):  
Philip W. Grant ◽  
Magne Haveraaen ◽  
Michael F. Webster
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Software Engineering ◽  
Software Development ◽  
Coordinate Systems ◽  
Scientific Applications ◽  
Software Modules ◽  
The Difference ◽  
Engineering Practices ◽  
Dynamics Problems

It has long been acknowledged that the development of scientific applications is in need of better software engineering practices. Here we contrast the difference between conventional software development of CFD codes with a method based on coordinate free mathematics. The former approach leads to programs where different aspects, such as the discretisation technique and the coordinate systems, can get entangled with the solver algorithm. The latter approach yields programs that segregate these concerns into fully independent software modules. Such considerations are important for the construction of numerical codes for practical problems. The two approaches are illustrated on the coating problem: the simulation of coating a wire with a polymer.

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