scholarly journals Variational Multiscale error estimator for anisotropic adaptive fluid mechanic simulations: Application to convection–diffusion problems

2018 ◽  
Vol 331 ◽  
pp. 94-115 ◽  
Author(s):  
A. Bazile ◽  
E. Hachem ◽  
J.C. Larroya-Huguet ◽  
Y. Mesri
Keyword(s):  
Fluid Mechanic ◽  
Error Estimator ◽  
Convection Diffusion ◽  
Variational Multiscale ◽  
Diffusion Problems

A Hybrid Variational Multiscale Element-Free Galerkin Method for Convection-Diffusion Problems

2019 ◽  
Vol 11 (07) ◽  
pp. 1950063 ◽  
Author(s):  
Jufeng Wang ◽  
Fengxin Sun
Keyword(s):  
Splitting Method ◽  
Two Dimensional ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Variational Multiscale ◽  
Discrete Equations ◽  
Element Free Galerkin ◽  
Oscillating Solutions ◽  
Element Free ◽  
Diffusion Problems

By coupling the dimension splitting method (DSM) and the variational multiscale element-free Galerkin (VMEFG) method, a hybrid variational multiscale element-free Galerkin (HVMEFG) method is developed for the two-dimensional convection-diffusion problems. In the HVMEFG method, the two-dimensional problem is converted into a battery of one-dimensional problems by the DSM. Combining the non-singular improved interpolating moving least-squares (IIMLS) method, the VMEFG method is used to obtain the discrete equations of the one-dimensional problems on the splitting plane. Then, final discretized equations of the entire convection-diffusion problems are assembled by the IIMLS method. The HVMEFG method has high accuracy and efficiency. Numerical examples show that the HVMEFG method can obtain non-oscillating solutions and has higher efficiency and accuracy than the EFG and VMEFG methods for convection-diffusion problems.

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