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| 2. |
- Kreiss, Gunilla, et al.
(författare)
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Stability of viscous shocks on finite intervals
- 2008
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Ingår i: Archive for Rational Mechanics and Analysis. - : Springer Science and Business Media LLC. - 0003-9527 .- 1432-0673. ; 187:1, s. 157-183
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Tidskriftsartikel (refereegranskat)abstract
- Consider the Cauchy problem for a system of viscous conservation laws with a solution consisting of a thin, viscous shock layer connecting smooth regions. We expect the time-dependent behavior of such a solution to involve two processes. One process consists of the large-scale evolution of the solution. This process is well modeled by the corresponding inviscid equations. The other process is the adjustment in shape and position of the shock layer to the large-scale solution. The time scale of the second process is much faster than the first, 1/nu compared to 1. The second process can be divided into two parts, adjustment of the shape and of the position. During this adjustment the end states are essentially constant. In order to answer the question of stability we have developed a technique where the two processes can be separated. To isolate the fast process, we consider the region in the vicinity of the shock layer. The equations are augmented with special boundary conditions that reflect the slow change of the end states. We show that, for the isolated fast process, the perturbations decay exponentially in time.
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| 4. |
- Babiuc, M. C., et al.
(författare)
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Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
- 2007
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Ingår i: PHYSICAL REVIEW D. - 1550-7998. ; 75:4, s. 044002-
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Tidskriftsartikel (refereegranskat)abstract
- The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of the Sommerfeld-type for such systems has recently been proposed. We implement these boundary conditions in a nonlinear 3D evolution code and test their accuracy.
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| 5. |
- Babiuc, M. C., et al.
(författare)
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Testing the well-posedness of characteristic evolution of scalar waves
- 2014
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 31:2, s. 025022-
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Tidskriftsartikel (refereegranskat)abstract
- Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for scalar waves well posed even on a background spacetime with closed lightlike curves. These results provide new guidance for developing stable characteristic evolution algorithms. In this regard, we present here the finite difference version of these recent results and implement them in a stable evolution code. We describe test results which validate the code and exhibit some of the interesting features due to the lower order terms.
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| 6. |
- Browning, Gerald, et al.
(författare)
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Mesh refinement
- 1973
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Ingår i: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 27:121, s. 29-39
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Tidskriftsartikel (refereegranskat)
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