A new fifth order finite difference WENO scheme for Hamilton-Jacobi equations

2017 ◽  
Vol 33 (4) ◽  
pp. 1095-1113 ◽  
Author(s):  
Jun Zhu ◽  
Jianxian Qiu
Keyword(s):  
Finite Difference ◽  
Weno Scheme ◽  
Jacobi Equations ◽  
Fifth Order

A new type of finite difference WENO schemes for Hamilton–Jacobi equations

2019 ◽  
Vol 30 (02n03) ◽  
pp. 1950020 ◽  
Author(s):  
Xiaohan Cheng ◽  
Jianhu Feng ◽  
Supei Zheng ◽  
Xueli Song
Keyword(s):  
Finite Difference ◽  
Weno Schemes ◽  
Numerical Examples ◽  
Weighted Essentially Nonoscillatory ◽  
New Type ◽  
Spurious Oscillations ◽  
Symmetry Requirement ◽  
Finite Difference Weno Schemes ◽  
Jacobi Equations ◽  
Fifth Order

In this paper, we propose a new type of finite difference weighted essentially nonoscillatory (WENO) schemes to approximate the viscosity solutions of the Hamilton–Jacobi equations. The new scheme has three properties: (1) the scheme is fifth-order accurate in smooth regions while keep sharp discontinuous transitions with no spurious oscillations near discontinuities; (2) the linear weights can be any positive numbers with the symmetry requirement and that their sum equals one; (3) the scheme can avoid the clipping of extrema. Extensive numerical examples are provided to demonstrate the accuracy and the robustness of the proposed scheme.

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.

An efficient fifth-order finite difference multi-resolution WENO scheme for inviscid and viscous flow problems

2021 ◽  
Vol 230 ◽  
pp. 105138
Author(s):  
Zhenming Wang ◽  
Jun Zhu ◽  
Linlin Tian ◽  
Yuchen Yang ◽  
Ning Zhao
Keyword(s):  
Finite Difference ◽  
Viscous Flow ◽  
Weno Scheme ◽  
Flow Problems ◽  
Fifth Order
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