scholarly journals Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences

2012 ◽  
Author(s):  
Jan Hesthaven
Keyword(s):  
Hyperbolic Equations ◽  
High Order ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
Non Linear ◽  
Linear Hyperbolic Equations

Fast high order ADER schemes for linear hyperbolic equations

2004 ◽  
Vol 197 (2) ◽  
pp. 532-539 ◽  
Author(s):  
Thomas Schwartzkopff ◽  
Michael Dumbser ◽  
Claus-Dieter Munz
Keyword(s):  
Hyperbolic Equations ◽  
High Order ◽  
Linear Hyperbolic Equations

scholarly journals High-Order Hybrid WCNS-CPR Scheme for Shock Capturing of Conservation Laws

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jia Guo ◽  
Huajun Zhu ◽  
Zhen-Guo Yan ◽  
Lingyan Tang ◽  
Songhe Song
Keyword(s):  
Computational Cost ◽  
High Order ◽  
Shock Capturing ◽  
High Order Accuracy ◽  
Hybrid Technique ◽  
Hybrid Scheme ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Reconstruction Scheme ◽  
High Gradients

By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.

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