High‐order non‐linear split paths construction algorithm for clustered axisymmetric agriculture products

2021 ◽  
Author(s):  
Zihao Liu
Keyword(s):  
High Order ◽  
Construction Algorithm ◽  
Non Linear ◽  
Agriculture Products

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.

High-Order Non-Linear Optical Effects in Organic Luminogens with Aggregation-Induced Emission

2015 ◽  
Vol 27 (14) ◽  
pp. 2332-2339 ◽  
Author(s):  
Jun Qian ◽  
Zhenfeng Zhu ◽  
Anjun Qin ◽  
Wei Qin ◽  
Liliang Chu ◽  
...  
Keyword(s):  
High Order ◽  
Aggregation Induced Emission ◽  
Optical Effects ◽  
Non Linear ◽  
Linear Optical
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