| 1. |
- Engquist, Björn, et al.
(författare)
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Projection shock capturing algorithms
- 1990
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Ingår i: Twelfth International Conference on Numerical Methods in Fluid Dynamics. - Berlin : Springer-Verlag. ; , s. 335-336
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Konferensbidrag (refereegranskat)
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| 2. |
- Häggblad, Jon, 1981-
(författare)
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Modified Stencils for Boundaries and Subgrid Scales in the Finite-Difference Time-Domain Method
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis centers on modified stencils for the Finite-Difference Time-Domain method (FDTD), or Yee scheme, when modelling curved boundaries, obstacles and holes smaller than the discretization length. The goal is to increase the accuracy while keeping the structure of the standard method, enabling improvements to existing implementations with minimal effort.We present an extension of a previously developed technique for consistent boundary approximation in the Yee scheme. We consider both Maxwell's equations and the acoustic equations in three dimensions, which require separate treatment, unlike in two dimensions.The stability properties of coefficient modifications are essential for practical usability. We present an analysis of the requirements for time-stable modifications, which we use to construct a simple and effective method for boundary approximations. The method starts from a predetermined staircase discretization of the boundary, requiring no further data on the underlying geometry that is being approximated.Not only is the standard staircasing of curved boundaries a poor approximation, it is inconsistent, giving rise to errors that do not disappear in the limit of small grid lengths. We analyze the standard staircase approximation by deriving exact solutions of the difference equations, including the staircase boundary. This facilitates a detailed error analysis, showing how staircasing affects amplitude, phase, frequency and attenuation of waves.To model obstacles and holes of smaller size than the grid length, we develop a numerical subgrid method based on locally modified stencils, where a highly resolved micro problem is used to generate effective coefficients for the Yee scheme at the macro scale.The implementations and analysis of the developed methods are validated through systematic numerical tests.
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| 3. |
- Einfeldt, Bernd, et al.
(författare)
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On Godunov-type methods near low densities
- 1991
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 92, s. 273-295
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Tidskriftsartikel (refereegranskat)
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| 4. |
- Engquist, Björn, et al.
(författare)
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High Order shock capturing methods
- 1995
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Ingår i: Computational Fluid Dynamics Review. - New York : John Wiley & Sons. - 0471955892 ; , s. 210-233
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Bokkapitel (refereegranskat)
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| 5. |
- Engquist, Björn, et al.
(författare)
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Nonlinear filters for efficient shock computation
- 1989
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Ingår i: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 52:186, s. 509-537
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Tidskriftsartikel (refereegranskat)abstract
- A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.
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| 6. |
- Engquist, Björn, et al.
(författare)
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The convergence rate of finite difference schemes in the presence of shocks
- 1998
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Ingår i: SIAM Journal on Numerical Analysis. - 0036-1429 .- 1095-7170. ; 35:6, s. 2464-2485
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Tidskriftsartikel (refereegranskat)abstract
- : Finite difference approximations generically have O(1) pointwise errors close to a shock. We show that this local error may effect the smooth part of the solution such that only first order is achieved even for formally higher-order methods. Analytic and numerical examples of this form of accuracy are given. We also show that a converging method will have the formal order of accuracy in domains where no characteristics have passed through a shock.
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| 7. |
- Ghasemi, J., et al.
(författare)
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A new algorithm for the determination of protolytic constants from spectrophotometric data in multiwavelength mode : Calculations of acidity constants of 4-(2-pyridylazo)resorcinol (PAR) in mixed nonaqueous-water solvents
- 2006
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Ingår i: Talanta. - : Elsevier BV. - 0039-9140 .- 1873-3573. ; 68:4, s. 1201-1214
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Tidskriftsartikel (refereegranskat)abstract
- A new efficient, simple and versatile algorithm is presented for determination of the protolytic constants from spectrophotmetric data in multiwavelength mode based on the combining of hard and soft modeling. The algorithm was checked by determining the acidity constants of a triprotic acid from theoretical and real absorption-pH data. The real spectral data are obtained from photometric titration of different solutions of 4-(2-pyridylazo)resorcinol (PAR) by a standard base solution under an inert atmosphere. The algorithm starts the minimization process using an user supplied number of components and initial guesses of the unknown parameters and refined in a least squares manner. New algorithm is implemented in the new version of DATAN package (version 3.1). The validity of the obtained results was checked by some well known programs such as DATAN 2.1, SPECFIT/32, SQUAD, a modified version of difference spectra and a A-pH curve method. The comparison of the outputs of the DATAN 3.1 with the other programs reveals that there is a very good agreement between the obtained results and mentioned programs.
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| 8. |
- Gudmundsson, Reynir Levi, 1972-
(författare)
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A numerical study of two-fluid models for dispersed two-phase flow
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis the two-fluid (Eulerian/Eulerian) formulation for dispersed two-phase flow is considered. Closure laws are needed for this type of models. We investigate both empirically based relations, which we refer to as a nongranular model, and relations obtained from kinetic theory of dense gases, which we refer to as a granular model. For the granular model, a granular temperature is introduced, similar to thermodynamic temperature. It is often assumed that the granular energy is in a steady state, such that an algebraic granular model is obtained. The inviscid non-granular model in one space dimension is known to be conditionally well-posed. On the other hand, the viscous formulation is locally in time well-posed for smooth initial data, but with a medium to high wave number instability. Linearizing the algebraic granular model around constant data gives similar results. In this study we consider a couple of issues. First, we study the long time behavior of the viscous model in one space dimension, where we rely on numerical experiments, both for the non-granular and the algebraic granular model. We try to regularize the problem by adding second order artificial dissipation to the problem. The simulations suggest that it is not possible to obtain point-wise convergence using this regularization. Introducing a new measure, a concept of 1-D bubbles, gives hope for other convergence than point-wise. Secondly, we analyse the non-granular formulation in two space dimensions. Similar results concerning well-posedness and instability is obtained as for the non-granular formulation in one space dimension. Investigation of the time scales of the formulation in two space dimension suggests a sever restriction on the time step, such that explicit schemes are impractical. Finally, our simulation in one space dimension show that peaks or spikes form in finite time and that the solution is highly oscillatory. We introduce a model problem to study the formation and smoothness of these peaks.
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