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.

COMPARISON BETWEEN GLOBAL, CLASSICAL DOMAIN DECOMPOSITION AND LOCAL, SINGLE AND DOUBLE COLLOCATION METHODS BASED ON RBF INTERPOLATION FOR SOLVING CONVECTION-DIFFUSION EQUATION

2008 ◽  
Vol 19 (11) ◽  
pp. 1737-1751 ◽  
Author(s):  
GAIL GUTIERREZ ◽  
WHADY FLOREZ
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Mixed Boundary ◽  
Domain Decomposition Method ◽  
Collocation Methods ◽  
Special Treatment ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Full Domain ◽  
Diffusion Problems

This work presents a performance comparison of several meshless RBF formulations for convection-diffusion equation with moderate-to-high Peclet number regimes. For the solution of convection-diffusion problems, several comparisons between global (full-domain) meshless RBF methods and mesh-based methods have been presented in the literature. However, in depth studies between new local RBF collocation methods and full-domain symmetric RBF collocation methods are not reported yet. The RBF formulations included: global symmetric method, symmetric double boundary collocation method, additive Schwarz domain decomposition method (DDM) when it is incorporated into two anterior approaches, and local single and double collocation methods. It can be found that the accuracy of solutions deteriorates as Pe increases, if no special treatment is used. From the numerical tests, it seems that the local methods, especially the derived double collocation technique incorporating PDE operator, are more effective than full domain approaches even with iterative DDM in solving moderate-to-high Pe convection-diffusion problems subject to mixed boundary conditions.

A VISCOUS-INVISCID COUPLING UNDER MIXED BOUNDARY CONDITIONS

1992 ◽  
Vol 02 (04) ◽  
pp. 461-482 ◽  
Author(s):  
C. CANUTO ◽  
A. RUSSO
Keyword(s):  
Boundary Conditions ◽  
Original Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Diffusion Problem ◽  
Convection Diffusion ◽  
Convection Equation ◽  
Convection Dominated

In this paper we consider a nonlinear modification of a linear convection-diffusion problem in order to get a pure convection equation where the original problem is convection dominated. We extend the results of previous papers by considering mixed Dirichlet/Oblique derivative boundary conditions.

ABSORBING BOUNDARY CONDITIONS IN BLOCK GAUSS–SEIDEL METHODS FOR CONVECTION PROBLEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 481-502 ◽  
Author(s):  
FREDERIC NATAF
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Convection Diffusion ◽  
Radiation Boundary Conditions ◽  
Convection Diffusion Equation ◽  
Numerical Tests ◽  
Radiation Boundary ◽  
Theoretical Results

In the context of convection-diffusion equation, the use of absorbing boundary conditions (also called radiation boundary conditions) is considered in block Gauss–Seidel algorithms. Theoretical results and numerical tests show that the convergence is thus accelerated.

The Inverse Least-Squares Finite Element Method Applied to the Convection-Diffusion Equation

2009 ◽  
Author(s):  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Least Squares ◽  
Heat Fluxes ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Current Formulation ◽  
Element Method

A Least Squares Finite Element Method (LSFEM) formulation for the detection of unknown boundary conditions in problems governed by the steady convection-diffusion equation will be presented. The method is capable of determining temperatures, and heat fluxes in location where such quantities are unknown provided such quantities are sufficiently over-specified in other locations. For the current formulation it is assumed the velocity field is known. The current formulation is unique in that it results in a sparse square system of equations even for partial differential equations that are not self-adjoint. Since this formulation always results in a symmetric positive-definite matrix, the solution can be found with standard sparse matrix solvers such as preconditioned conjugate gradient method. In addition, the formulation allows for equal order approximation of temperature and heat fluxes as it is not subject to the inf-sup condition. The formulation allow for a treatment of over-specified boundary conditions. Also, various forms of regularization can be naturally introduced within the formulation. Details of the discretization and sample results will be presented.

Sign in / Sign up

Export Citation Format

Share Document