| 1. |
- Abbas, Qaisar, et al.
(författare)
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A weak boundary procedure for high order finite difference approximations of hyperbolic problems
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We introduce a new weak boundary procedures for high order finite difference operators on summation-by-parts type applied to hyperbolic problems. The boundary procedure is applied in an extended domain where data is known. We show how to raise the order of accuracy for a diagonal norm based approximation and how to modify the spectrum of the resulting operator to get a faster convergence to steady-state. Furthermore, we also show how to construct better non-reflecting properties at the boundaries using the above procedure. Numerical results that corroborate the analysis are presented.
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| 2. |
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| 3. |
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| 4. |
- Carpenter, Mark H., et al.
(författare)
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Revisiting and extending interface penalties for multi-domain summation-by-parts operators
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A general interface procedure is presented for multi-domain collocation methods satisfying the summation-by-parts (SBP) spatial discretization convention. Unlike more traditional operators (e.g. FEM) applied to the advection-diffusion equation, the new procedure penalizes the solution and the first p derivatives across the interface. The combined interior/interface operators are proven to be pointwise stable, and conservative, although accuracy deteriorates for p>=2. Penalties between two different sets of variables are compared (motivated by FEM primal and flux formulations), and are shown to be equivalent for certain choices of penalty parameters. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.
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| 5. |
- Eriksson, Sofia, et al.
(författare)
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Exact non-reflecting boundary conditions revisited : well-posedness and stability
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Exact non-reflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that well-posedness is a fundamental property of the non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, energy stability follows automatically. The stability in combination with the high order accuracy results in a reliable, efficient and accurate method. The theory is supported by numerical simulations.
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| 6. |
- Eriksson, Sofia, et al.
(författare)
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Simulations of Ground Effects on Wake Vortices at Runways
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- n this paper the interaction between two counter-rotating vortices is examined, and the performance of a newly developed finite difference code is discussed. The Reynolds numbers considered are low to medium, and the flow is compressible. Most of the computations are performed in a two dimensional domain, with different grid sizes, Reynolds number and order of accuracy of the scheme. Finally, a three dimensional computation is made in order to examine the relevance of the two dimensional model.
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| 7. |
- Gong, Jing, et al.
(författare)
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A Hybrid Method for the Unsteady Compressible Navier-Stokes Equations
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A hybrid method composed of finite difference-finite difference and finite difference-finite volume schemes for the time-dependent Navier-Stokes equations has been developed. A detailed analysis of the stability of the proposed algorithms, paying special attention to the stability of the interfaces between the subdomains is performed. We prove that the interface coupling is stable and conservative. This techniques makes it possible to combine the efficiency of the finite difference method and the flexibility of the finite volume schemes. We exemplify the procedure by using finite difference methods. The computational results corroborate the theoretical analysis.
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| 8. |
- Gong, Jing, et al.
(författare)
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A Stable Hybrid Method for Hyperbolic Problems
- 2004
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A stable hybrid method that combines the unstructured finite volume method with high order finite difference methods have been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.
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| 9. |
- Gong, Jing, et al.
(författare)
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Stable, Accurate and Efficient Interface Procedures for Viscous Problems
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we investigate and study several different interface procedures for finite difference methods applied to viscous problems. The analysis show that stable, accurate and efficient interface procedures can be obtained. The analysis also show that only minor differences of the various methods exist.
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| 10. |
- Kozdon, Jeremy E., et al.
(författare)
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Interaction of waves with frictional interfaces using summation-by-parts difference operators I : Weak enforcement of nonlinear boundary conditions
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this work we develop a high-order method for problems in scalar elastodynamics with nonlinear boundary conditions in a form closely related to those seen in earthquake rupture modeling and other frictional sliding problems. By using summation-by-parts finite difference operators and weak enforcement of boundary conditions with the simultaneous approximation term method, a strictly stable method is developed that dissipates energy at a slightly faster rate than the continuous solution (with the difference in energy dissipation rates vanishing as the mesh is refined). Furthermore, it is shown that unless boundary conditions are formulated in terms of characteristic variables, as opposed to the physical variables in terms of which boundary conditions are more naturally stated, the semi-discretized system of equations can become extremely stiff, preventing efficient solution using explicit time integrators.These theoretical results are confirmed by several numerical tests demonstrating the high-order convergence rate of the method and the benefits of using strictly stable numerical methods for long time integration.
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