On the Finite Difference Schemes for Burgers Equation Solution

2021 ◽  
pp. 151-167
Author(s):  
Ilya V. Basharov ◽  
Aleksey I. Lobanov
Keyword(s):  
Finite Difference ◽  
Burgers Equation ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Equation Solution

Comparison of Two Sixth-Order Compact Finite Difference Schemes for Burgers' Equation

2013 ◽  
Vol 444-445 ◽  
pp. 681-686
Author(s):  
Xiao Gang He ◽  
Ying Yang ◽  
Ping Zhang ◽  
Xiao Hua Zhang
Keyword(s):  
Finite Difference ◽  
Burgers Equation ◽  
Difference Schemes ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Compact Finite Difference ◽  
Small Viscosity ◽  
Compact Finite Difference Schemes

In this study, two sixth-order compact finite difference schemes have been considered for solving the Burgers equation. The main difference of these schemes lies in the calculation of second-order derivative terms, which is obtained by applying the first-order operator twice and the method of undetermined coefficients. The aim is to comparison these schemes in terms of computational accuracy for solving the Burgers equation with difference viscosity values, especially for very small viscosity values. The results show that both schemes achieve almost the same accuracy for large viscosity values and second method is more accurate for moderate viscosity values, but both schemes are failed for very small viscosity values. However, when both schemes coupled low-pass filter for very small viscosity values, both schemes can well inhibit the problem.

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