Interface procedures for finite difference approximations of the advection-diffusion equation

Authors:
Jing Gong;Jan Nordström
Affiliations:
Department of Information Technology, Scientific Computing Division, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden;Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 25
Cited 2

The influence of open boundary conditions on the convergence to steady state for the Navier-Stokes equations

Journal of Computational Physics
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes

Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx

Journal of Computational Physics
Numerical studies of hyperbolic IBVP with high-order finite difference operators satisfying a summation by parts rule

Applied Numerical Mathematics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

SIAM Journal on Numerical Analysis
A stable and conservative interface treatment of arbitrary spatial accuracy

Journal of Computational Physics
Explicit Hybrid Time Domain Solver for the Maxwell Equations in 3D

Journal of Scientific Computing
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

Journal of Computational Physics
Boundary Procedures for Summation-by-Parts Operators

Journal of Scientific Computing
High Order Finite Difference Approximations of Electromagnetic Wave Propagation Close to Material Discontinuities

Journal of Scientific Computing
Finite volume methods, unstructured meshes and strict stability for hyperbolic problems

Applied Numerical Mathematics
Stable and Accurate Artificial Dissipation

Journal of Scientific Computing
High-order Compact Schemes with Filters on Multi-block Domains

Journal of Scientific Computing
Summation by parts operators for finite difference approximations of second derivatives

Journal of Computational Physics
Steady-State Computations Using Summation-by-Parts Operators

Journal of Scientific Computing
A stable hybrid method for hyperbolic problems

Journal of Computational Physics
On the order of accuracy for difference approximations of initial-boundary value problems

Journal of Computational Physics
A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions

Journal of Computational Physics
A stable and efficient hybrid scheme for viscous problems in complex geometries

Journal of Computational Physics
A stable high-order finite difference scheme for the compressible Navier-Stokes equations

Journal of Computational Physics
A massively parallel multi-block hybrid compact-WENO scheme for compressible flows

Journal of Computational Physics
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations

Journal of Computational Physics
A stable and high-order accurate conjugate heat transfer problem

Journal of Computational Physics
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators

Journal of Scientific Computing
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods

SIAM Journal on Scientific Computing

High-order accurate difference schemes for the Hodgkin-Huxley equations

Journal of Computational Physics
A generalized framework for nodal first derivative summation-by-parts operators

Journal of Computational Physics

Quantified Score

Hi-index	7.30

Visualization

Abstract

We investigate several existing interface procedures for finite difference methods applied to advection-diffusion problems. The accuracy, stiffness and reflecting properties of various interface procedures are investigated. The analysis and numerical experiments show that there are only minor differences between various methods once a proper parameter choice has been made.