Very efficient high-order hyperbolic schemes for time-dependent advection–diffusion problems: Third-, fourth-, and sixth-order

2014 ◽  
Vol 102 ◽  
pp. 131-147 ◽  
Author(s):  
Alireza Mazaheri ◽  
Hiroaki Nishikawa
Keyword(s):  
High Order ◽  
Sixth Order ◽  
Time Dependent ◽  
Advection Diffusion ◽  
Diffusion Problems

scholarly journals Solution of Time-dependent Advection-Diffusion Problems with the Sparse-grid Combination Technique and a Rosenbrock Solver

2001 ◽  
Vol 1 (1) ◽  
pp. 86-98 ◽  
Author(s):  
Boris Lastdrager ◽  
Barry Koren ◽  
Jan Verwer
Keyword(s):  
Time Integration ◽  
Size Control ◽  
Sparse Grid ◽  
Time Dependent ◽  
Step Size ◽  
Combination Technique ◽  
Burgers Equations ◽  
Advection Diffusion ◽  
Grid Approach ◽  
Diffusion Problems

Abstract In the current paper the efficiency of the sparse-grid combination tech- nique applied to time-dependent advection-diffusion problems is investigated. For the time-integration we employ a third-order Rosenbrock scheme implemented with adap- tive step-size control and approximate matrix factorization. Two model problems are considered, a scalar 2D linear, constant-coe±cient problem and a system of 2D non- linear Burgers' equations. In short, the combination technique proved more efficient than a single grid approach for the simpler linear problem. For the Burgers' equations this gain in efficiency was only observed if one of the two solution components was set to zero, which makes the problem more grid-aligned.

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