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.

FACTORIZATION OF THE CONVECTION-DIFFUSION OPERATOR AND THE SCHWARZ ALGORITHM

1995 ◽  
Vol 05 (01) ◽  
pp. 67-93 ◽  
Author(s):  
F. NATAF ◽  
F. ROGIER
Keyword(s):  
Boundary Conditions ◽  
Rate Of Convergence ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Interface Conditions ◽  
Diffusion Operator ◽  
Convection Diffusion ◽  
Numerical Tests ◽  
Schwarz Algorithm ◽  
Theoretical Results

In the original Schwarz algorithm, Dirichlet boundary conditions are used as interface conditions. We consider the use of the operators arising from the factorization of the convection-diffusion operator as transmission conditions. The rate of convergence is then significantly higher. Theoretical results are proven and numerical tests are shown.

scholarly journals Sweeping preconditioners for stratified media in the presence of reflections

2020 ◽  
Vol 1 (4) ◽  
Author(s):  
Janosch Preuß ◽  
Thorsten Hohage ◽  
Christoph Lehrenfeld
Keyword(s):  
Boundary Conditions ◽  
Harmonic Wave ◽  
Absorbing Boundary Conditions ◽  
Stratified Medium ◽  
Stratified Media ◽  
Absorbing Boundary ◽  
Small Perturbations ◽  
Numerical Tests ◽  
Time Harmonic ◽  
Dirichlet To Neumann Operator

Abstract In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sweeping preconditioners Dirichlet-to-Neumann operators for half-space problems are approximated through absorbing boundary conditions. In the presence of reflections absorbing boundary conditions are not accurate resulting in an unsatisfactory performance of these sweeping preconditioners. We explore the potential of using more accurate Dirichlet-to-Neumann operators within the sweep. To this end, we make use of the separability of the equation for the background model. While this improves the accuracy of the Dirichlet-to-Neumann operator, we find both from numerical tests and analytical arguments that it is very sensitive to perturbations in the presence of reflections. This implies that even if accurate approximations to Dirichlet-to-Neumann operators can be devised for a stratified medium, sweeping preconditioners are limited to very small perturbations.

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.

Improvement of Absorbing Boundary Conditions for Non-Hydrostatic Wave-Flow Model SWASH

2013 ◽  
Vol 353-356 ◽  
pp. 2676-2682 ◽  
Author(s):  
Guo Liang Zou ◽  
Qing He Zhang
Keyword(s):  
Boundary Conditions ◽  
Flow Model ◽  
Absorbing Boundary Conditions ◽  
Wave Flow ◽  
Decay Function ◽  
Absorbing Boundary ◽  
Numerical Tests ◽  
Multiple Processors ◽  
Layer Region ◽  
Sponge Layer

The performance of absorbing boundary conditions in SWASH is examined. The method to determine the sponge layer region in each processor when calculating with multiple processors is improved. An exponential decay function is employed to the momentum equations in the sponge layer region. The numerical tests show that the proposed damping coefficients work efficiently on reducing the wave energy of reflective waves in the sponge layer.

Sign in / Sign up

Export Citation Format

Share Document