scholarly journals Geometrically exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods

2017 ◽  
Vol 112 (9) ◽  
pp. 1175-1193 ◽  
Author(s):  
L. Fedeli ◽  
A. Pandolfi ◽  
M. Ortiz
Keyword(s):  
Time Integration ◽  
Optimal Transportation ◽  
Particle Methods ◽  
Exact Time ◽  
Advection Diffusion ◽  
Mesh Free ◽  
Transportation Theory ◽  
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.

scholarly journals The Effect of Grid Skewness on Non-Unified Compact Residual Distribution Methods for Scalar Advection Diffusion Problems

CFD letters ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 58-65
Author(s):  
Hazim Fadli Aminnuddin ◽  
Farzad Ismail ◽  
Akmal Nizam Mohamed ◽  
Kamil Abdullah
Keyword(s):  
Residual Distribution ◽  
Advection Diffusion ◽  
Diffusion Problems

scholarly journals Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Heng Cheng ◽  
Guodong Zheng
Keyword(s):  
Penalty Method ◽  
Weak Form ◽  
Singular Matrix ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Advection Diffusion ◽  
Computational Speed ◽  
The Difference ◽  
Element Free ◽  
Diffusion Problems

In this paper, the improved element-free Galerkin (IEFG) method is used for solving 3D advection-diffusion problems. The improved moving least-squares (IMLS) approximation is used to form the trial function, the penalty method is applied to introduce the essential boundary conditions, the Galerkin weak form and the difference method are used to obtain the final discretized equations, and then the formulae of the IEFG method for 3D advection-diffusion problems are presented. The error and the convergence are analyzed by numerical examples, and the numerical results show that the IEFG method not only has a higher computational speed but also can avoid singular matrix of the element-free Galerkin (EFG) method.

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