| 1. |
- Efraimsson, Gunilla, et al.
(författare)
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A note on the effect of artificial viscosity on solutions of conservation laws
- 1996
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Ingår i: Applied Numerical Mathematics. - : Elsevier. - 0168-9274 .- 1873-5460. ; 21, s. 155-173
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Tidskriftsartikel (refereegranskat)abstract
- We consider central difference schemes with artificial viscosity terms for nonlinear hyperbolic systems. We analyze the influence of artificial viscosity on solutions with shocks of nonlinear hyperbolic problems in one dimension. Both stationary and moving shocks are considered. The analysis shows that for the Euler equations one can obtain well behaved (sharp) shock layers when a scalar viscosity coefficient is used. This is not true for a general system. Numerical computations of Burgers' equation and the Euler equations are presented. They support the results from the linear theory.
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| 2. |
- Efraimsson, Gunilla, et al.
(författare)
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Analysis of Stretched Grids as Buffer Zones in Aero-Acoustic Simulations
- 2009
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Ingår i: 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference). - Reston, Virigina : American Institute of Aeronautics and Astronautics.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- A zone of increasingly stretched grid is a robust and easy-to-use way to avoid unwanted reections at artificial boundaries in aero-acoustic simulations. There are two main damping mechanisms, dissipation and under-resolution a traveling wave, respectively. In this paper the behavior of acoustic waves and wave packages, respectively, are studied via analysis of solutions to a semi-discrete linear boundary value problem. The solutions of the linear problem is compared to solutions of the full non-linear Euler equations.
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| 3. |
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| 4. |
- Kreiss, Gunilla, et al.
(författare)
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Analysis of stretched grids as buffer zones in simulations of wave propagation
- 2016
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Ingår i: Applied Numerical Mathematics. - : Elsevier BV. - 0168-9274 .- 1873-5460. ; 107, s. 1-17
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Tidskriftsartikel (refereegranskat)abstract
- A zone of increasingly stretched grid is a robust and easy-to-use way to avoid unwanted reflections at artificial boundaries in wave propagating simulations. In such a buffer zone there are two main damping mechanisms, dissipation and under-resolution that turns a traveling wave into an evanescent wave. We present analysis in one and two space dimensions showing that evanescent decay through under-resolution is a very efficient way to damp waves. The analysis is supported by numerical computations.
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| 5. |
- Kreiss, Gunilla, et al.
(författare)
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Approximate solutions to slightly viscous conservation laws
- 2004
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Ingår i: Quarterly of Applied Mathematics. - : American Mathematical Society (AMS). - 0033-569X .- 1552-4485. ; 62:1, s. 117-133
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Tidskriftsartikel (refereegranskat)abstract
- We study an approximate solution of a slightly viscous conservation law in one dimension, constructed by two asymptotic expansions that are cut off after the third order terms. In the shock layer, an inner solution is valid and an outer solution is valid elsewhere. Based on the stability results in [10], we show that for a given time interval the difference between the approximate solution and the true solution is not larger than o(epsilon), where epsilon is the viscosity coefficient. The result holds for shocks of any strength.
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| 6. |
- Kreiss, Gunilla, et al.
(författare)
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Elimination of first order errors in shock calculations
- 2001
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Ingår i: SIAM Journal on Numerical Analysis. - : SIAM PUBLICATIONS. - 0036-1429 .- 1095-7170. ; 38:6, s. 1986-1998
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Tidskriftsartikel (refereegranskat)abstract
- First order errors downstream of shocks have been detected in computations with higher order shock capturing schemes in one and two dimensions. Based on a matched asymptotic expansion analysis we show how to modify the artificial viscosity and raise the order of accuracy.
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| 7. |
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| 8. |
- 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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| 9. |
- Appelö, Daniel, et al.
(författare)
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A New Absorbing Layer for Elastic Waves
- 2006
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 215:2, s. 642-660
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Tidskriftsartikel (refereegranskat)abstract
- A new perfectly matched layer (PML) for the simulation of elastic waves in anisotropic media on an unbounded domain is constructed. Theoretical and numerical results, showing that the stability properties of the present layer are better than previously suggested layers, are presented. In addition, the layer can be formulated with fewer auxiliary variables than the split-field PML.
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| 10. |
- Appelö, Daniel, 1977-
(författare)
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Absorbing Layers and Non-Reflecting Boundary Conditions for Wave Propagation Problems
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The presence of wave motion is the defining feature in many fields of application,such as electro-magnetics, seismics, acoustics, aerodynamics,oceanography and optics. In these fields, accurate numerical simulation of wave phenomena is important for the enhanced understanding of basic phenomenon, but also in design and development of various engineering applications. In general, numerical simulations must be confined to truncated domains, much smaller than the physical space were the wave phenomena takes place. To truncate the physical space, artificial boundaries, and corresponding boundary conditions, are introduced. There are four main classes of methods that can be used to truncate problems on unbounded or large domains: boundary integral methods, infinite element methods, non-reflecting boundary condition methods and absorbing layer methods. In this thesis, we consider different aspects of non-reflecting boundary conditions and absorbing layers. In paper I, we construct discretely non-reflecting boundary conditions for a high order centered finite difference scheme. This is done by separating the numerical solution into spurious and physical waves, using the discrete dispersion relation. In paper II-IV, we focus on the perfectly matched layer method, which is a particular absorbing layer method. An open issue is whether stable perfectly matched layers can be constructed for a general hyperbolic system. In paper II, we present a stable perfectly matched layer formulation for 2 x 2 symmetric hyperbolic systems in (2 + 1) dimensions. We also show how to choose the layer parameters as functions of the coefficient matrices to guarantee stability. In paper III, we construct a new perfectly matched layer for the simulation of elastic waves in an anisotropic media. We present theoretical and numerical results, showing that the stability properties of the present layer are better than previously suggested layers. In paper IV, we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters which is applicable to all hyperbolic systems, and which we prove is well-posed and perfectly matched. We also use an automatic method, derived in paper V, for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell s equations, the linearized Euler equations, as well as arbitrary 2 x 2 systems in (2 + 1) dimensions. In paper V, we use the method of Sturm sequences for bounding the real parts of roots of polynomials, to construct an automatic method for checking Petrowsky well-posedness of a general Cauchy problem. We prove that this method can be adapted to automatically symmetrize any well-posed problem, producing an energy estimate involving only local quantities.
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