A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

2021 ◽  
Author(s):  
Xucheng Meng ◽  
Yaguang Gu ◽  
Guanghui Hu
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Fourth Order ◽  
Weno Scheme

scholarly journals Fourth-order accurate finite-volume CWENO scheme for astrophysical MHD problems

2018 ◽  
Vol 482 (1) ◽  
pp. 416-437 ◽  
Author(s):  
Prabal Singh Verma ◽  
Jean-Mathieu Teissier ◽  
Oliver Henze ◽  
Wolf-Christian Müller
Keyword(s):  
Finite Volume ◽  
Fourth Order

scholarly journals The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 211 ◽  
Author(s):  
Haoyu Dong ◽  
Changna Lu ◽  
Hongwei Yang
Keyword(s):  
Finite Volume ◽  
Time Discretization ◽  
Euler System ◽  
Weno Scheme ◽  
Local Characteristic ◽  
Finite Volume Scheme ◽  
Mesh Structure ◽  
Hyperbolic Conservation Law ◽  
Higher Derivative ◽  
Accuracy Order

We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.

scholarly journals Arbitrary Order Finite Volume Well-Balanced Schemes for the Euler Equations with Gravity

2019 ◽  
Vol 41 (2) ◽  
pp. A695-A721 ◽  
Author(s):  
C. Klingenberg ◽  
G. Puppo ◽  
M. Semplice
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Arbitrary Order
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