A High Order Finite Difference Weighted Essentially NonOscillatory Schemes with a Kernel-Based Constrained Transport Method for Ideal Magnetohydrodynamics

2021 ◽  
Vol 43 (3) ◽  
pp. B598-B622
Author(s):  
Firat Cakir ◽  
Andrew Christlieb ◽  
Yan Jiang
Keyword(s):  
Finite Difference ◽  
High Order ◽  
Weighted Essentially Nonoscillatory ◽  
Ideal Magnetohydrodynamics ◽  
High Order Finite Difference ◽  
Constrained Transport ◽  
Transport Method ◽  
Essentially Nonoscillatory

scholarly journals An adaptive finite‐difference method for traveltimes and amplitudes

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 167-176 ◽  
Author(s):  
Jianliang Qian ◽  
William W. Symes
Keyword(s):  
Finite Difference ◽  
Lower Cost ◽  
Finite Difference Methods ◽  
Grid Method ◽  
Posteriori Error ◽  
High Order ◽  
Weighted Essentially Nonoscillatory ◽  
Geometric Spreading ◽  
High Order Finite Difference ◽  
Upwind Finite Difference

The point‐source traveltime field has an upwind singularity at the source point. Consequently, all formally high‐order, finite‐difference eikonal solvers exhibit first‐order convergence and relatively large errors. Adaptive upwind finite‐difference methods based on high‐order Weighted Essentially NonOscillatory (WENO) Runge‐Kutta difference schemes for the paraxial eikonal equation overcome this difficulty. The method controls error by automatic grid refinement and coarsening based on a posteriori error estimation. It achieves prescribed accuracy at a far lower cost than does the fixed‐grid method. Moreover, the achieved high accuracy of traveltimes yields reliable estimates of auxiliary quantities such as take‐off angles and geometric spreading factors.

A discontinuous collocated-grid implementation for high-order finite-difference modeling

Geophysics ◽  
2015 ◽  
Vol 80 (4) ◽  
pp. T175-T181 ◽  
Author(s):  
Na Fan ◽  
Lian-Feng Zhao ◽  
Ying-Jie Gao ◽  
Zhen-Xing Yao
Keyword(s):  
Finite Difference ◽  
High Order ◽  
Collocated Grid ◽  
High Order Finite Difference
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