scholarly journals A New Flux Splitting Scheme Based on Toro-Vazquez and HLL Schemes for the Euler Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Pascalin Tiam Kapen ◽  
Tchuen Ghislain
Keyword(s):  
Euler Equations ◽  
Compressible Flows ◽  
Arithmetic Mean ◽  
Shock Propagation ◽  
Test Cases ◽  
Splitting Scheme ◽  
Pressure System ◽  
Wave Speeds ◽  
Flux Splitting ◽  
Contact Discontinuities

This paper presents a new flux splitting scheme for the Euler equations. The proposed scheme termed TV-HLL is obtained by following the Toro-Vazquez splitting (Toro and Vázquez-Cendón, 2012) and using the HLL algorithm with modified wave speeds for the pressure system. Here, the intercell velocity for the advection system is taken as the arithmetic mean. The resulting scheme is more accurate when compared to the Toro-Vazquez schemes and also enjoys the property of recognition of contact discontinuities and shear waves. Accuracy, efficiency, and other essential features of the proposed scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. The accuracy of the scheme is shown in 1D test cases designed by Toro.

A new flux splitting scheme for the Euler equations

2014 ◽  
Vol 102 ◽  
pp. 203-214 ◽  
Author(s):  
Feng Qu ◽  
Chao Yan ◽  
Jian Yu ◽  
Di Sun
Keyword(s):  
Euler Equations ◽  
Splitting Scheme ◽  
Flux Splitting

TWO-DIMENSIONAL VORTEX SHEETS FOR THE NONISENTROPIC EULER EQUATIONS: LINEAR STABILITY

2008 ◽  
Vol 05 (03) ◽  
pp. 487-518 ◽  
Author(s):  
ALESSANDRO MORANDO ◽  
PAOLA TREBESCHI
Keyword(s):  
Linear Stability ◽  
Euler Equations ◽  
Compressible Flows ◽  
Tangential Velocity ◽  
Vortex Sheets ◽  
Isentropic Euler Equations ◽  
Contact Discontinuities ◽  
Two Space Dimensions ◽  
Loss Of Regularity ◽  
Additional Loss

We study the linear stability of contact discontinuities for the nonisentropic compressible Euler equations in two space dimensions. Assuming the jump of the tangential velocity across the discontinuity surface is sufficiently large, we derive a suitable energy estimate for the linearized boundary value problem. The found estimate extends to nonisentropic compressible flows the main result of Coulombel–Secchi for the isentropic Euler equations. Compared with this latter case, when the jump of the tangential velocity of the unperturbed flow attains a certain critical value in the region of weak stability, here an additional loss of regularity appears; this is related to the presence of a double root of the Lopatinskii determinant associated to the problem.

An Improved Hybrid Alternative WENO Scheme for High Mach Number Flows

2021 ◽  
Author(s):  
Uttam Singh Rajput ◽  
Krishna Mohan Singh
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Weno Scheme ◽  
Test Cases ◽  
Present Scheme ◽  
Low Dissipation ◽  
Scale Structures ◽  
High Mach ◽  
Fifth Order ◽  
High Resolution Method

Abstract This study presents the development of a fifth-order hybrid alternative mapped weighted essentially non-oscillatory scheme (HAW-M) for high-speed compressible flows. A new, improved smoothness indicator has been developed to design the HAW-M scheme. The performance of the present scheme has been evaluated through different one and two-dimensional test cases. The developed scheme shows higher accuracy and low dissipation. Further, it captures the fine-scale structures smoothly than the existing high-resolution method.

A low diffusion flux splitting method for inviscid compressible flows

2015 ◽  
Vol 112 ◽  
pp. 83-93 ◽  
Author(s):  
Wenjia Xie ◽  
Hua Li ◽  
Zhengyu Tian ◽  
Sha Pan
Keyword(s):  
Compressible Flows ◽  
Diffusion Flux ◽  
Splitting Method ◽  
Flux Splitting ◽  
Inviscid Compressible Flows
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