Boundary Procedures for Summation-by-Parts Operators

Authors:
Ken Mattsson
Affiliations:
Department of Scientific Computing, Information Technology, Uppsala University, P.O. Box 120, S-751 04 Uppsala, Sweden. ken@tdb.uu.se
Venue:
Journal of Scientific Computing
Year:
2003

Citing 6
Cited 14

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Summation by parts, projections, and stability. I

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A stable and conservative interface treatment of arbitrary spatial accuracy

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Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators

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Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods

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

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Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations

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Derivation of Strictly Stable High Order Difference Approximations for Variable-Coefficient PDE

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Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions

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Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations

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Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains

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A generalized framework for nodal first derivative summation-by-parts operators

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Abstract

Four different methods of imposing boundary conditions for the linear advection-diffusion equation and a linear hyperbolic system are considered. The methods are analyzed using the energy method and the Laplace transform technique. Numerical calculations are done, considering in particular the case when the initial data and boundary data are inconsistent.