.png){kind=icon}
.png){kind=icon}
Return
An Upwind-Type Rotated Characteristic Decomposition Method for Steady-State Simulations of the Euler Equations
.png){kind=icon}
PRE
AI
Y
Y
H
R
H
C
DOI：10.1016/j.jcp.2026.115025.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
A widely used high-order method for solving the Euler equations is the WENO (Weighted Essentially Non-Oscillatory) scheme, which typically demonstrates excellent shock-capturing capabilities. However, it encounters significant convergence challenges when applied to steady shock simulations of the Euler equations. In this paper, we propose an upwind-type rotated characteristic decomposition method for steady-state simulations of the Euler equations. We retain the advantage of upwind-biased interpolation in suppressing slight post-shock oscillations, while incorporating the rotated characteristic decomposition technique to compute multidimensional steady shocks. Specifically, instead of performing characteristic projections along the coordinate axes, we align them with the gradient direction of the physical quantities. This new characteristic decomposition method significantly improves the convergence of steady-state simulations of Euler equations, reducing the average residual to a tiny value, with many test cases converging to machine precision. Moreover, the new method effectively suppresses spurious oscillations caused by shock waves. The results of two-dimensional numerical cases validate the superior convergence properties of the new method and its ability to achieve better essentially non-oscillatory characteristics compared to traditional characteristic decomposition methods.
Keywords:
WENO scheme
Euler equations
steady-state simulations
rotated characteristic decomposition
shock-capturing
Journal
IF:
3.8
Papers:
1.5W
Citations:
7.4W
Organization
Cited Papers