High Resolution and High Order Schemes for Two-Fluid Plasma Equation

2005 ◽  
Author(s):  
A. Hakim ◽  
U. Shumlak
Keyword(s):  
High Resolution ◽  
High Order ◽  
High Order Schemes ◽  
Plasma Equation ◽  
Two Fluid ◽  
Two Fluid Plasma

Assessment of Time and Space High-Order Schemes for Two-Fluid Seven-Equation Two-Pressure Model Using the Reversed Water Faucet Problem

2018 ◽  
Author(s):  
Fei Chao ◽  
Jianqiang Shan ◽  
Junli Gou ◽  
Pan Wu ◽  
Li Ge
Keyword(s):  
Volume Fraction ◽  
High Order ◽  
High Order Accuracy ◽  
High Order Scheme ◽  
High Order Schemes ◽  
Order Scheme ◽  
Gravity Driven ◽  
Gas Volume Fraction ◽  
Gas Volume ◽  
Two Fluid

The Ransom water faucet problem has become one of the most important benchmark tests to study two-fluid/phase flow because it exists an analytical discontinuous solution. The water faucet problem is a gravity-driven wave problem and its analytical solution is derived from the liquid free fall motion. In this paper, the opposite gravity-driven wave problem named the reversed water faucet problem where the liquid admits a rising motion with reduced speed driven by gravity is studied. With assumptions of decoupled phasic pressures, approximate incompressible flow, no liquid pressure gradient, no phase change, no wall and interfacial drag, the analytical solutions of the gas volume fraction and liquid velocity distribution are derived. From the gas volume fraction analytical solution, there is a moving discontinuity which is a very important point for testing accuracy of the numerical scheme and its stability near discontinuities. Two-fluid seven-equation two-pressure model is of particular interest due to the nature of inherent well-posed advantage in all situations. What’s more, high-order accuracy schemes have attracted great increasing attention to overcome the challenge of serious numerical diffusion from 1st-order scheme for accurately simulating many nuclear thermal-hydraulics applications such as long term transient natural circulation problems. In this paper, the solution algorithms with high-order accuracy in space and time are developed for this well-posed two-fluid model and its robustness and accuracy are verified and assessed against the derived analytical solutions. The numerical results show that high-order schemes could prevent excessive numerical diffusion and are more accurate than first-order time and space schemes; the space high-order scheme could give more accurate numerical results than the time high-order scheme for discontinuous solutions.

Development of a two-fluid based thermal-hydraulic subchannel analysis code with high-resolution numerical method

2021 ◽  
Vol 134 ◽  
pp. 103671
Author(s):  
Minyang Gui ◽  
Wenxi Tian ◽  
Di Wu ◽  
Ronghua Chen ◽  
Mingjun Wang ◽  
...  
Keyword(s):  
High Resolution ◽  
Numerical Method ◽  
Two Fluid ◽  
Subchannel Analysis

scholarly journals Positivity preserving high order schemes for angiogenesis models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Carpio ◽  
E. Cebrian
Keyword(s):  
Kinetic Equation ◽  
Time Discretization ◽  
Strong Stability ◽  
High Order ◽  
Angiogenic Factor ◽  
Strong Stability Preserving ◽  
Positivity Preserving ◽  
Blood Vessel Formation ◽  
High Order Schemes ◽  
Asymptotic Reduction

Abstract Hypoxy induced angiogenesis processes can be described by coupling an integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the angiogenic factor. We propose high order positivity preserving schemes to approximate the marginal tip density by combining an asymptotic reduction with weighted essentially non oscillatory and strong stability preserving time discretization. We capture soliton-like solutions representing blood vessel formation and spread towards hypoxic regions.

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