Discrete Methods and their Applications

1993 ◽  
Author(s):  
Peter L. Hammer ◽  
Fred S. Roberts ◽  
Gunzburger
Keyword(s):  
Discrete Methods

Discrete Methods for Elliptic Problems

2006 ◽  
pp. 445-470
Author(s):  
Victor S. Ryaben’kii ◽  
Semyon V. Tsynkov
Keyword(s):  
Elliptic Problems ◽  
Discrete Methods

scholarly journals Numerical Approximation for Fractional Neutron Transport Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhengang Zhao ◽  
Yunying Zheng
Keyword(s):  
Transport Equation ◽  
Nuclear Reactor ◽  
Neutron Transport ◽  
Transport Processes ◽  
Neutron Transport Equation ◽  
Spatial Direction ◽  
Fully Discrete ◽  
Discrete Methods ◽  
Fifth Order ◽  
Different Order

Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.

scholarly journals A Novel Approach to Discrete Representative Volume Element Automation and Generation-DRAGen

Materials ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1887 ◽  
Author(s):  
Manuel Henrich ◽  
Felix Pütz ◽  
Sebastian Münstermann
Keyword(s):  
Input Data ◽  
Volume Element ◽  
Data Sets ◽  
Rsa Algorithm ◽  
Representative Volume ◽  
Novel Approach ◽  
Random Sequential Addition ◽  
Sequential Addition ◽  
Discrete Methods ◽  
Synthetic Microstructures

In this study, a novel approach for generating Representative Volume Elements (RVEs) is introduced. In contrast to common generators, the new RVE generator is based on discrete methods to reconstruct synthetic microstructures, using simple methods and a modular structure. The plain and uncomplicated structure of the generator makes the extension with new features quite simple. It is discussed why certain features are essential for microstructural simulations. The discrete methods are implemented into a python tool. A Random Sequential Addition (RSA)-Algorithm for discrete volumes is developed and the tessellation is realized with a discrete tessellation function. The results show that the generator can successfully reconstruct realistic microstructures with elongated grains and martensite bands from given input data sets.

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