An interpolation method for the optimal control problem governed by the elliptic convection–diffusion equation

2020 ◽  
Author(s):  
Majid Darehmiraki ◽  
Arezou Rezazadeh ◽  
Ali Ahmadian ◽  
Soheil Salahshour
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Diffusion Equation ◽  
Control Problem ◽  
Interpolation Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

scholarly journals Lattice-Boltzmann Simulations of the Convection-Diffusion Equation with Different Reactive Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 13
Author(s):  
Rui Du ◽  
Jincheng Wang ◽  
Dongke Sun
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Lattice Boltzmann ◽  
Mixed Boundary ◽  
Interpolation Method ◽  
Mixed Boundary Conditions ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Lattice Boltzmann Simulations ◽  
Accuracy And Stability

We have tested the accuracy and stability of lattice-Boltzmann (LB) simulations of the convection-diffusion equation in a two-dimensional channel flow with reactive-flux boundary conditions. We compared several different implementations of a zero-concentration boundary condition using the Two-Relaxation-Time (TRT) LB model. We found that simulations using an interpolation of the equilibrium distribution were more stable than those based on Multi-Reflection (MR) boundary conditions. We have extended the interpolation method to include mixed boundary conditions, and tested the accuracy and stability of the simulations over a range of Damköhler and Péclet numbers.

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