Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I

1997 ◽  
Vol 18 (2) ◽  
pp. 315-354 ◽  
Author(s):  
Barna L. Bihari ◽  
Ami Harten
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Multiresolution Schemes

scholarly journals On New Means with Interesting Practical Applications: Generalized Power Means

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 925
Author(s):  
Sergio Amat ◽  
Alberto Magreñan ◽  
Juan Ruiz ◽  
Juan Carlos Trillo ◽  
Dionisio F. Yañez
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Arithmetic Mean ◽  
Practical Applications ◽  
Power Means ◽  
Multiresolution Schemes

Means of positive numbers appear in many applications and have been a traditional matter of study. In this work, we focus on defining a new mean of two positive values with some properties which are essential in applications, ranging from subdivision and multiresolution schemes to the numerical solution of conservation laws. In particular, three main properties are crucial—in essence, the ideas of these properties are roughly the following: to stay close to the minimum of the two values when the two arguments are far away from each other, to be quite similar to the arithmetic mean of the two values when they are similar and to satisfy a Lipchitz condition. We present new means with these properties and improve upon the results obtained with other means, in the sense that they give sharper theoretical constants that are closer to the results obtained in practical examples. This has an immediate correspondence in several applications, as can be observed in the section devoted to a particular example.

scholarly journals Numerical Solution of Scalar Conservation Laws with Random Flux Functions

2016 ◽  
Vol 4 (1) ◽  
pp. 552-591 ◽  
Author(s):  
Siddhartha Mishra ◽  
Nils Henrik Risebro ◽  
Christoph Schwab ◽  
Svetlana Tokareva
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Scalar Conservation Laws ◽  
Scalar Conservation

THE METHOD OF SPACE-TIME CONSERVATION ELEMENT AND SOLUTION ELEMENT — A NEW PARADIGM FOR NUMERICAL SOLUTION OF CONSERVATION LAWS

1998 ◽  
pp. 206-240 ◽  
Author(s):  
Sin-Chung CHANG ◽  
Sheng-Tao YU ◽  
Ananda HIMANSU ◽  
Xiao-Yen WANG ◽  
Chuen-Yen CHOW ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Space Time ◽  
New Paradigm ◽  
Solution Element

Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

2011 ◽  
Vol 3 (5) ◽  
pp. 519-561 ◽  
Author(s):  
Christophe Besse ◽  
Saja Borghol ◽  
Thierry Goudon ◽  
Ingrid Lacroix-Violet ◽  
Jean-Paul Dudon
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Conservation Laws ◽  
Numerical Solution ◽  
Boundary Layers ◽  
Mean Free Path ◽  
Euler System ◽  
Knudsen Layer ◽  
Microscopic Modeling ◽  
Definition Of

AbstractWe propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

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