Sensitivity Parameter-Independent Characteristic-Wise Well-Balanced Finite Volume WENO Scheme for the Euler Equations Under Gravitational Fields

2021 ◽  
Vol 88 (2) ◽  
Author(s):  
Peng Li ◽  
Bao-Shan Wang ◽  
Wai-Sun Don
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Weno Scheme ◽  
Gravitational Fields ◽  
Sensitivity Parameter

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

Advances in the Numerical Integration of the Three-Dimensional Euler Equations in Vibrating Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 781-790 ◽  
Author(s):  
G. A. Gerolymos
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Euler Equations ◽  
Finite Volume ◽  
Three Dimensional ◽  
Computational Results ◽  
Grid Refinement ◽  
Mobile Grid ◽  
Transonic Compressor ◽  
Runge Kutta

In the present work an algorithm for the numerical integration of the three-dimensional unsteady Euler equations in vibrating transonic compressor cascades is described. The equations are discretized in finite-volume formulation in a mobile grid using isoparametric brick elements. They are integrated in time using Runge-Kutta schemes. A thorough discussion of the boundary conditions used and of their influence on results is undertaken. The influence of grid refinement on computational results is examined. Unsteady convergence of results is discussed.

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