DEVELOPMENT AND ASSESSMENT OF SEVERAL HIGH-RESOLUTION SCHEMES FOR COMPRESSIBLE EULER EQUATIONS

2013 ◽  
Vol 11 (01) ◽  
pp. 1350049
Author(s):  
M. P. RAY ◽  
B. P. PURANIK ◽  
U. V. BHANDARKAR
Keyword(s):  
High Resolution ◽  
Temporal Integration ◽  
Splitting Scheme ◽  
Flux Vector ◽  
Riemann Solvers ◽  
Weighted Essentially Nonoscillatory ◽  
Time Stepping ◽  
Flux Vector Splitting ◽  
Piecewise Parabolic ◽  
Essentially Nonoscillatory

High-resolution extensions to six Riemann solvers and three flux vector splitting schemes are developed within the framework of a reconstruction-evolution approach. Third-order spatial accuracy is achieved using two different piecewise parabolic reconstructions and a weighted essentially nonoscillatory scheme. A three-stage TVD Runge–Kutta time stepping is employed for temporal integration. The modular development of solvers provides an ease in selecting a reconstruction scheme and/or a Riemann solver/flux vector splitting scheme. The performances of these high-resolution solvers are compared for several one- and two-dimensional test cases. Based on a comprehensive assessment of the solutions obtained with all solvers, it is found that the use of the weighted essentially nonoscillatory reconstruction with the van Leer flux vector splitting scheme provides solutions for a variety of problems with acceptable accuracy.

scholarly journals Application of Kinetic Flux Vector Splitting Scheme for Solving Viscous Quantum Hydrodynamical Model of Semiconductor Devices

2018 ◽  
Author(s):  
Ubaid Ahmed Nisar ◽  
Waqas Ashraf ◽  
Shamsul Qamar
Keyword(s):  
Semiconductor Device ◽  
Electron Flow ◽  
Semiconductor Devices ◽  
Hydrodynamical Model ◽  
Splitting Scheme ◽  
Flux Vector ◽  
Time Stepping ◽  
Flux Vector Splitting ◽  
Runge Kutta ◽  
Model Equations

In this article, one-dimensional viscous quantum hydrodynamical model of semiconductor devices is numerically investigated. The model treats the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. The nonlinear viscous quantum hydrodynamic models contain Euler-type equations for density and current, viscous and quantum correction terms, and a Poisson equation for electrostatic potential. Due to high nonlinearity of model equations, numerical solution techniques are applied to obtain their solutions.. The proposed numerical scheme is a splitting scheme based on the kinetic flux-vector splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct splitting of macroscopic flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the splitting scheme based on the NT central scheme. The effects of various parameters such as device length, viscosities, different doping and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations.

Hydrodynamic modeling of short-channel devices using an upwind flux vector splitting scheme

2002 ◽  
Vol 191 (47-48) ◽  
pp. 5427-5445 ◽  
Author(s):  
Wai-Kay Yip ◽  
Min Shen ◽  
Ming-C. Cheng ◽  
Robert Fithen ◽  
Goodarz Ahmadi
Keyword(s):  
Hydrodynamic Modeling ◽  
Splitting Scheme ◽  
Flux Vector ◽  
Short Channel ◽  
Flux Vector Splitting

A kinetic flux vector splitting scheme for shallow water flows

2003 ◽  
Vol 26 (6) ◽  
pp. 635-647 ◽  
Author(s):  
S.Q. Zhang ◽  
M.S. Ghidaoui ◽  
W.G. Gray ◽  
N.Z. Li
Keyword(s):  
Shallow Water ◽  
Splitting Scheme ◽  
Flux Vector ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Flux Vector Splitting

Propagation of diffusing pollutant by kinetic flux-vector splitting method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Saqib Zia ◽  
Omar Rabbani ◽  
Asad Rehman ◽  
Munshoor Ahmed
Keyword(s):  
Numerical Test ◽  
Splitting Method ◽  
Test Problems ◽  
Flux Vector ◽  
Order Accuracy ◽  
Time Stepping ◽  
Flux Vector Splitting ◽  
And Performance ◽  
The One ◽  
Central Scheme

Abstract In this article, the transport of a passive pollutant by a flow modeled by shallow water equations is numerically investigated. The kinetic flux-vector splitting (KFVS) scheme is extended to solve the one and two-dimensional equations. The first two equations of the considered model are mass and momentum equations and the third equation is the transport equation. The suggested scheme focuses on the direct splitting of the macroscopic flux functions at the cell interfaces. It achieves second-order accuracy by using MUSCL-type initial reconstruction and the Runge–Kutta time stepping technique. Several numerical test problems from literature are considered to check the efficiency and performance of the scheme. The results of the proposed scheme are compared to the central scheme for validation. It is found that the results of both the schemes are in close agreement with each other. However, our suggested KFVS scheme resolves the sharp discontinuous profiles precisely.

Kinetic flux vector splitting scheme for solving non-reactive multi-component flows

2019 ◽  
Vol 83 ◽  
pp. 107107
Author(s):  
Muhammad Saqib ◽  
Attia Rabbani ◽  
Ubaid Ahmed Nisar ◽  
Waqas Ashraf ◽  
Shamsul Qamar
Keyword(s):  
Splitting Scheme ◽  
Flux Vector ◽  
Flux Vector Splitting
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