| 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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| 9. |
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| 10. |
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| 11. |
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| 12. |
- Noreland, Daniel, 1972-
(författare)
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Numerical Techniques for Acoustic Modelling and Design of Brass Wind Instruments
- 2003
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Acoustic horns are used in musical instruments and loudspeakers in order to provide an impedance match between an acoustic source and the surrounding air. The aim of this study is to develop numerical tools for the analysis and optimisation of such horns, with respect to their input impedance spectra. Important effects such as visco-thermal damping and modal conversion are shown to be localised to different parts of a typical brass instrument. This makes it possible to construct hybrid methods that apply different numerical techniques in different parts of the instrument. Narrow and slowly flaring parts are modelled using a one-dimensional transmission line analogy, and the rapidly flaring bell is modelled using a two-dimensional finite-difference method. The connection between the different regions is done by the aid of impedance boundary conditions. The use of such boundary conditions is investigated with respect to the required number of degrees of freedom. Numerical shape optimisation is employed in order to design horns with desired impedance characteristics throughout a design frequency band. A loudspeaker horn is optimised with respect to its sound power output, and a brass instrument is optimised with respect to its intonation. The horns are modelled using the finite-element method and a transmission line analogy. In order to achieve rapid convergence of the optimisation, gradient based minimisation algorithms are used. A prerequisite for success is the ability to accurately and inexpensively compute the gradient of the objective function. The gradient for the finite-element method is computed by an adjoint equation technique, whereas for the transmission line analogy, it is derived by formal differentiation of the model. In order to find smooth solutions, a smoothing technique is used, where optimisation is done with respect to the right hand side of a Poisson type equation.
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| 13. |
- Petersson, N. Anders, et al.
(författare)
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Discretizing singular point sources in hyperbolic wave propagation problems
- 2016
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 321, s. 532-555
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Tidskriftsartikel (refereegranskat)abstract
- We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.
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| 14. |
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| 15. |
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| 16. |
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| 17. |
- Sjögreen, Björn, et al.
(författare)
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A model for peak formation in the two-phase equations
- 2007
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Ingår i: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 76:260, s. 1925-1940
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Tidskriftsartikel (refereegranskat)abstract
- We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.
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| 18. |
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| 19. |
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| 20. |
- Sjögreen, Björn, et al.
(författare)
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Multiresolution wavelet based adaptive numerical dissipation control for high order methods
- 2004
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Ingår i: Journal of Scientific Computing. - 0885-7474 .- 1573-7691. ; 20:2, s. 211-255
-
Tidskriftsartikel (refereegranskat)abstract
- The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham, and Djomehri [25] aimed at minimizing numerical dissipations for high speed compressible viscous flows containing shocks, shears and turbulence. To detect non-smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artificial compression method (ACM) of Harten [4] but utilize it in an entirely different context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem dependence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch off the extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet ( Mallat and Zhong [14]) used by Gerritsen and Olsson [3] in an adaptive mesh refinement method, to determine regions where refinement should be done. The other is the modification of the multiresolution method of Harten [ 5] by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen physical quantity ( or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these sensors are scheme independent and can be stand-alone options for numerical algorithms other than the Yee et al. scheme.
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| 21. |
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| 22. |
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| 23. |
- Sjögreen, Björn, et al.
(författare)
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Perfectly matched layers for Maxwell's equations in second order formulation
- 2005
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 209:1, s. 19-46
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Tidskriftsartikel (refereegranskat)abstract
- We consider the two-dimensional Maxwell's equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary condition are discretized to second order accuracy employing an embedded technique which does not suffer from a "small-cell" time-step restriction in the explicit time-integration method. The computational domain is truncated by a perfectly matched layer (PML). We derive estimates for both the error due to reflections at the outer boundary of the PML, and due to discretizing the continuous PML equations. Using these estimates, we show how the parameters of the PML can be chosen to make the discrete solution of the PML equations converge to the solution of Maxwell's equations on the unbounded domain, as the grid size goes to zero. Several numerical examples are given.
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| 24. |
- Sjögreen, Björn, et al.
(författare)
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Performance of High Order Filter Methods for a Richtmyer-Meshkov Instability
- 2009
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Ingår i: Computational Fluid Dynamics 2006 - Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD 2006. - Berlin, Heidelberg : Springer Berlin/Heidelberg. ; , s. 771-776
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Konferensbidrag (refereegranskat)abstract
- Sixth-order compact and non-compact filter schemes that were designed for multiscale Navier-Stokes, and ideal and non-ideal magnetohydrodynam-ics (MHD) systems are employed to simulate a 2-D Rightmyer-Meshkov instability (RMI). The suppression of this RMI in the presence of a magnetic field was investigated by Samtaney (2003) and Wheatley et al. (2005). Numerical results illustrated here exhibit behavior similar to the work of Samtaney. Due to the different amounts and different types of numerical dissipations contained in each scheme, the structures and the growth of eddies for this chaotic-like inviscid gas dynamics RMI case are highly grid size and scheme dependent, even with many levels of refinement.
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| 25. |
- Ståhlberg, Anders, 1975, et al.
(författare)
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Multiway real-time PCR gene expression profiling in yeast Saccharomyces cerevisiae reveals altered transcriptional response of ADH-genes to glucose stimuli.
- 2008
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Ingår i: BMC genomics. - : Springer Science and Business Media LLC. - 1471-2164. ; 9
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: The large sensitivity, high reproducibility and essentially unlimited dynamic range of real-time PCR to measure gene expression in complex samples provides the opportunity for powerful multivariate and multiway studies of biological phenomena. In multiway studies samples are characterized by their expression profiles to monitor changes over time, effect of treatment, drug dosage etc. Here we perform a multiway study of the temporal response of four yeast Saccharomyces cerevisiae strains with different glucose uptake rates upon altered metabolic conditions. RESULTS: We measured the expression of 18 genes as function of time after addition of glucose to four strains of yeast grown in ethanol. The data are analyzed by matrix-augmented PCA, which is a generalization of PCA for 3-way data, and the results are confirmed by hierarchical clustering and clustering by Kohonen self-organizing map. Our approach identifies gene groups that respond similarly to the change of nutrient, and genes that behave differently in mutant strains. Of particular interest is our finding that ADH4 and ADH6 show a behavior typical of glucose-induced genes, while ADH3 and ADH5 are repressed after glucose addition. CONCLUSION: Multiway real-time PCR gene expression profiling is a powerful technique which can be utilized to characterize functions of new genes by, for example, comparing their temporal response after perturbation in different genetic variants of the studied subject. The technique also identifies genes that show perturbed expression in specific strains.
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| 26. |
- Yee, H. C., et al.
(författare)
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Adaptive filtering and limiting in compact high order methods for multiscale gas dynamics and MHD systems
- 2008
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Ingår i: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 37:5, s. 593-619
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Tidskriftsartikel (refereegranskat)abstract
- The adaptive multistep linear and nonlinear filters for multiscale shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows of the authors are extended to include compact high order central differencing as the spatial base scheme. The adaptive mechanism makes used of multiresolution wavelet decomposition of the computed flow data as sensors for numerical dissipative control. The objective is to expand the work initiated in [Yee HC, Sjogreen B. Nonlinear filtering in compact high order schemes. In: Proceedings of the 19th ICNSP and 7th APPTC conference; 2005; J Plasma Phys 2006;72:833-36] and compare the performance of adaptive multistep filtering in compact high order schemes with adaptive filtering in standard central (non-compact) schemes for multiscale problems containing shock waves.
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| 27. |
- Yee, H. C., et al.
(författare)
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Designing adaptive low-dissipative high order schemes for long-time integrations
- 2004
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Ingår i: Turbulent flow computation. - Dordrecht : Kluwer Academic Publishers. - 1402005237 - 9781402005237 ; , s. 141-198
-
Bokkapitel (refereegranskat)abstract
- A general framework for the design of adaptive low-dissipative high order schmes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible. (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred. (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used. (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought [79, 17]. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.
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| 28. |
- Yee, H. C., et al.
(författare)
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Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
- 2006
-
Ingår i: Numerical Modeling of Space Plasma Flows. - SAN FRANCISCO : ASTRONOMICAL SOC PACIFIC. - 9781583812273 ; , s. 47-61
-
Konferensbidrag (refereegranskat)abstract
- Recent progress in the development of a class of low dissipative high order filter schemes for multiscale Navier-Stokes, and ideal and non-ideal magnetohydrodynamics (MHD) systems is described. The four main features of this schemes are: (a) multiresolution wavelet decomposition of the computed flow data as sensors for adaptive numerical dissipative control, (b) multistep filter to accommodate efficient application of different numerical dissipation models and different spatial high order base schemes, (c) solving the ideal conservative MHD system without having to deal with an incomplete eigensystern set while at the same time ensuring that correct shock speeds and locations are computed, and (d) minimization of the divergence of the magnetic field (del(.) B) numerical error. By design, the flow sensors, different choice of high order base schemes and numerical dissipation models are stand-alone modules. A whole class of low dissipative high order schemes can be derived at ease, making the resulting computer software very flexible with widely applicable.
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| 29. |
- Yee, H. C., et al.
(författare)
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Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
- 2007
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 225:1, s. 910-934
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Tidskriftsartikel (refereegranskat)abstract
- Recent progress in the development of a class of low dissipative high order (fourth-order or higher) filter schemes for multiscale Navier-Stokes, and ideal and non-ideal magnetohydrodynamics (MHD) systems is described. The four main features of this class of schemes are: (a) multiresolution wavelet decomposition of the computed flow data as sensors for adaptive numerical dissipative control, (b) multistep filter to accommodate efficient application of different numerical dissipation models and different spatial high order base schemes, (c) a unique idea in solving the ideal conservative MHD system (a non-strictly hyperbolic conservation law) without having to deal with an incomplete eigensystem set while at the same time ensuring that correct shock speeds and locations are computed, and (d) minimization of the divergence of the magnetic field (del center dot B) numerical error. By design, the flow sensors, different choice of high order base schemes and numerical dissipation models are stand-alone modules. A whole class of low dissipative high order schemes can be derived at ease, making the resulting computer software very flexible with widely applicable. Performance of multiscale and multiphysics test cases are illustrated with many levels of grid refinement and comparison with commonly used schemes in the literature.
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| 30. |
- Yee, H. C., et al.
(författare)
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Efficient low dissipative high order schemes for multiscale MHD flows, II : Minimization of del center dot B numerical error
- 2006
-
Ingår i: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 29:1, s. 115-164
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Tidskriftsartikel (refereegranskat)abstract
- An adaptive numerical dissipation control in a class of high order filter methods for compressible MHD equations is systematically discussed. The filter schemes consist of a divergence-free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Some of these filter variants provide a natural and efficient way for the minimization of the divergence of the magnetic field (del center dot B) numerical error in the sense that commonly used divergence cleaning is not required. Numerical experiments presented emphasize the performance of the del center dot B numerical error. Many levels of grid refinement and detailed comparison of the filter methods with several commonly used compressible MHD shock-capturing schemes will be illustrated.
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| 31. |
- Yee, H C, et al.
(författare)
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Non-linear filtering and limiting in high order methods for ideal and non-ideal MHD
- 2006
-
Ingår i: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 27:1-3, s. 507-521
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Tidskriftsartikel (refereegranskat)abstract
- The adaptive nonlinear filtering and limiting in spatially high order schemes (Yee et al. J. Comput. Phys. 150, 199 - 238, ( 1999), Sjogreen and Yee, J. Scient. Comput. 20, 211 - 255, ( 2004)) for the compressible Euler and Navier - Stokes equations have been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations, (Sjogreen and Yee, ( 2003), Proceedings of the 16th AIAA/CFD conference, June 23 - 26, Orlando F1; Yee and Sjogreen ( 2003), Proceedings of the International Conference on High Performance Scientific Computing, March, 10 - 14, Honai, Vietnam; Yee and Sjogreen ( 2003), RIACS Technical Report TR03. 10, July, NASA Ames Research Center; Yee and Sjogreen ( 2004), Proceedings of the ICCF03, July 12 - 16, Toronto, Canada). The numerical dissipation control in these adaptive filter schemes consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of discontinuity capturing nonlinear numerical dissipation for both the ideal and non-ideal MHD.
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| 32. |
- Yee, H. C., et al.
(författare)
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Nonlinear filtering in compact high-order schemes
- 2006
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 72, s. 833-836
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Tidskriftsartikel (refereegranskat)abstract
- The adaptive nonlinear filtering approach for shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows adopted in our previous world is employed in conjunction with compact high-order methods as the spatial base scheme. The objective is to compare the performance of nonlinear filtering in compact high-order schemes with nonlinear filtering in standard central (non-compact) schemes for multiseale problems containing shock waves.
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| 33. |
- Yee, H. C., et al.
(författare)
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Simulation of Richtmyer-Meshkov instability by sixth-order filter methods
- 2007
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Ingår i: Shock Waves. - : Springer Science and Business Media LLC. - 0938-1287 .- 1432-2153. ; 17:3, s. 185-193
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Tidskriftsartikel (refereegranskat)abstract
- Simulation of a 2-D Richtmyer-Meshkov instability (RMI), including inviscid, viscous and magnetic field effects was conducted comparing recently developed sixth-order filter schemes with various standard shock-capturing methods. The suppression of the inviscid gas dynamics RMI in the presence of a magnetic field was investigated by Samtaney and Wheatley et al. Numerical results illustrated here exhibit behavior similar to the work of Samtaney. Due to the different amounts and different types of numerical dissipation contained in each scheme, the structures and the growth of eddies for the chaotic-like inviscid gas dynamics RMI case are highly grid size and scheme dependent, even with many levels of refinement. The failure of grid refinement for all studied numerical methods extends to the viscous gas dynamics case for high Reynolds number. For lower Reynolds number, grid convergence has been achieved by all studied methods. To achieve similar resolution, standard shock-capturing methods require more grid points than filter schemes and yet the CPU times using the same grid for all studied methods are comparable.
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