Third-order WENO scheme with a new smoothness indicator

2017 ◽  
Vol 85 (2) ◽  
pp. 90-112 ◽  
Author(s):  
Naga Raju Gande ◽  
Yogita Rathod ◽  
Samala Rathan
Keyword(s):  
Weno Scheme ◽  
Third Order ◽  
Smoothness Indicator

Construction of an Improved Third-Order WENO Scheme with a New Smoothness Indicator

2020 ◽  
Vol 82 (3) ◽  
Author(s):  
Youngsoo Ha ◽  
Chang Ho Kim ◽  
Hyoseon Yang ◽  
Jungho Yoon
Keyword(s):  
Weno Scheme ◽  
Third Order ◽  
Smoothness Indicator

A new smoothness indicator for third-order WENO scheme

2015 ◽  
Vol 81 (7) ◽  
pp. 451-459 ◽  
Author(s):  
Xiaoshuai Wu ◽  
Jianhan Liang ◽  
Yuxin Zhao
Keyword(s):  
Weno Scheme ◽  
Third Order ◽  
Smoothness Indicator

scholarly journals A New Smoothness Indicator of Adaptive Order Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 69
Author(s):  
Omer Musa ◽  
Guoping Huang ◽  
Mingsheng Wang
Keyword(s):  
Hyperbolic Conservation Laws ◽  
Convex Combination ◽  
Computational Cost ◽  
Weno Scheme ◽  
Third Order ◽  
Simple Formulation ◽  
Order Linear ◽  
Linear Reconstruction ◽  
Smoothness Indicator ◽  
Fifth Order

Adaptive order weighted essentially non-oscillatory scheme (WENO-AO(5,3)) has increased the computational cost and complexity of the classic fifth-order WENO scheme by introducing a complicated smoothness indicator for fifth-order linear reconstruction. This smoothness indicator is based on convex combination of three third-order linear reconstructions and fifth-order linear reconstruction. Therefore, this paper proposes a new simple smoothness indicator for fifth-order linear reconstruction. The devised smoothness indicator linearly combines the existing smoothness indicators of third-order linear reconstructions, which reduces the complexity of that of WENO-AO(5,3) scheme. Then WENO-AO(5,3) scheme is modified to WENO-O scheme with new and simple formulation. Numerical experiments in 1-D and 2-D were run to demonstrate the accuracy and efficacy of the proposed scheme in which WENO-O scheme was compared with original WENO-AO(5,3) scheme along with WENO-AO-N, WENO-Z, and WENO-JS schemes. The results reveal that the proposed WENO-O scheme is not only comparable to the original scheme in terms of accuracy and efficacy but also decreases its computational cost and complexity.

Novel local smoothness indicators for improving the third-order WENO scheme

2017 ◽  
Vol 87 (2) ◽  
pp. 51-69 ◽  
Author(s):  
Shengping Liu ◽  
Yiqing Shen ◽  
Bei Chen ◽  
Fangjun Zeng
Keyword(s):  
Weno Scheme ◽  
Third Order ◽  
The Third ◽  
Local Smoothness ◽  
Smoothness Indicators

scholarly journals The accuracy of finite-difference schemes calculating the interaction of shock waves

2019 ◽  
Vol 485 (6) ◽  
pp. 691-696 ◽  
Author(s):  
V. V. Ostapenko ◽  
N. A. Khandeeva
Keyword(s):  
Finite Difference ◽  
Shock Waves ◽  
Difference Schemes ◽  
Weno Scheme ◽  
Shock Capturing ◽  
Finite Difference Schemes ◽  
Third Order ◽  
Interaction Of Shock Waves ◽  
Fifth Order

The accuracy with which the shock-capturing finite-difference schemes calculate the flows with interaction of shock waves is studied. It is shown that, in the domains between the shock waves after their incidence, the calculation accuracy of invariants of the combined schemes is several orders of magnitude higher than the accuracy of the WENO-scheme, which is fifth-order in space and third-order in time.

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