On the conservation of finite difference WENO schemes in non-rectangular domains using the inverse Lax-Wendroff boundary treatments

2020 ◽  
Vol 415 ◽  
pp. 109516
Author(s):  
Shengrong Ding ◽  
Chi-Wang Shu ◽  
Mengping Zhang
Keyword(s):  
Finite Difference ◽  
Weno Schemes ◽  
Finite Difference Weno Schemes ◽  
Boundary Treatments

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.

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