Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Boundary Procedures for Summation-by-Parts Operators
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
Well-Posed Boundary Conditions for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Journal of Computational Physics
A stable high-order finite difference scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
A composite grid solver for conjugate heat transfer in fluid-structure systems
Journal of Computational Physics
Analysis of the order of accuracy for node-centered finite volume schemes
Applied Numerical Mathematics
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
On the impact of boundary conditions on dual consistent finite difference discretizations
Journal of Computational Physics
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In this paper we study the heat and advection equation in single and multiple domains. The equations are discretized using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices. It is shown how the spectrum of the single domain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. The interface treatments are posed as a function of one parameter, and the impact on the spectrum and discretization error is investigated as a function of this parameter. Finally we briefly discuss the generalization to higher order accurate schemes.