Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model

2019 ◽  
Vol 20 (3-4) ◽  
pp. 287-292
Author(s):  
Sidrah Ahmed
Keyword(s):  
Numerical Study ◽  
Splitting Method ◽  
Accurate Solution ◽  
Dimensional System ◽  
Two Dimensional ◽  
Flux Vector ◽  
Rarefaction Waves ◽  
Time Stepping ◽  
Flux Vector Splitting ◽  
Horizontal Temperature Gradients

AbstractThe kinetic flux vector splitting method has been introduced for two-dimensional system of shallow water equations with horizontal temperature gradients. The scheme preserves positivity conditions and resolves different regions of shock waves, rarefaction waves and contact discontinuity with negligible oscillations. The scheme is based on splitting of flux functions of the Ripa model. Moreover Runge-Kutta time stepping technique with MUSCL-type initial reconstruction is used to guarantee higher order accurate solution. The numerical example is taken from already published article. The obtained results reveal the accuracy and robustness of the proposed method.

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.

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.

Effects of various implicit operators on a flux vector splitting method

AIAA Journal ◽  
1987 ◽  
Vol 25 (9) ◽  
pp. 1162-1163
Author(s):  
E. Von Lavante ◽  
W. K. Anderson ◽  
D. Claes
Keyword(s):  
Splitting Method ◽  
Flux Vector ◽  
Flux Vector Splitting

Numerical Solution of Transient Flow in Wind Tunnels

Volume 1 ◽  
2004 ◽  
Author(s):  
A. Nouri-Borujerdi ◽  
M. Ziaei-Rad
Keyword(s):  
Atmospheric Pressure ◽  
Transient Flow ◽  
Splitting Method ◽  
Wind Tunnels ◽  
Flux Vector ◽  
Governing Equations ◽  
One Dimensional ◽  
Flux Vector Splitting ◽  
Pass Through ◽  
Good Agreement

This paper deals with design and analysis of intermittent supersonic wind tunnels. System can be constructed by allowing air at atmospheric pressure to pass through a converging-diverging nozzle, a test section and a diffuser into a vacuum tank. The governing equations of compressible fluid flow have been solved numerically using flux vector splitting method to obtain running time under which it works at the design Mach number. The formulation has been tested on the theory of quasi one-dimensional compressible flow. The numerical results are in good agreement with the results of the theory.

Sign in / Sign up

Export Citation Format

Share Document