Tailoring the longitudinal electric fields of high-order laser beams and their direct verification in three dimensions

Abstract In this work we investigate the Brinkman volume penalization technique in the context of a high-order Discontinous Galerkin method to model moving wall boundaries for compressible fluid flow simulations. High-order approximations are especially of interest as they require few degrees of freedom to represent smooth solutions accurately. This reduced memory consumption is attractive on modern computing systems where the memory bandwidth is a limiting factor. Due to their low dissipation and dispersion they are also of particular interest for aeroacoustic problems. However, a major problem for the high-order discretization is the appropriate representation of wall geometries. In this work we look at the Brinkman penalization technique, which addresses this problem and allows the representation of geometries without modifying the computational mesh. The geometry is modelled as an artificial porous medium and embedded in the equations. As the mesh is independent of the geometry with this method, it is not only well suited for highorder discretizations but also for problems where the obstacles are moving.We look into the deployment of this strategy by briefly discussing the Brinkman penalization technique and its application in our solver and investigate its behavior in fundamental one-dimensional setups, such as shock reflection at a moving wall and the formation of a shock in front of a piston. This is followed by the application to setups with two and three dimensions, illustrating the method in the presence of curved surfaces.

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A high order spectral algorithm for elastic obstacle scattering in three dimensions

Journal of Computational Physics ◽

10.1016/j.jcp.2014.08.047 ◽

2014 ◽

Vol 279 ◽

pp. 1-17 ◽

Cited By ~ 10

Author(s):

Frédérique Le Louër

Keyword(s):

High Order ◽

Three Dimensions ◽

Spectral Algorithm ◽

Obstacle Scattering

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High-Order Output-Based Adaptive Simulations of Turbulent Flow in Three Dimensions (Invited)

54th AIAA Aerospace Sciences Meeting ◽

10.2514/6.2016-0862 ◽

2016 ◽

Author(s):

Krzysztof Fidkowski ◽

Marco Ceze

Keyword(s):

Turbulent Flow ◽

High Order ◽

Three Dimensions ◽

Adaptive Simulations

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Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2009.0112 ◽

2009 ◽

Vol 465 (2109) ◽

pp. 2725-2749 ◽

Cited By ~ 4

Author(s):

M. J. Ablowitz ◽

T. S. Haut

Keyword(s):

Surface Tension ◽

Solitary Wave ◽

Solitary Waves ◽

Asymptotic Series ◽

High Order ◽

Three Dimensions ◽

Two Dimensional ◽

Small Surface ◽

Petviashvili Equation ◽

Dimensional Series

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech 2 solution of the Korteweg–de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev–Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes’ extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney–Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

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Development of the high-order decoupled direct method in three dimensions for particulate matter: enabling advanced sensitivity analysis in air quality models

Geoscientific Model Development ◽

10.5194/gmd-5-355-2012 ◽

2012 ◽

Vol 5 (2) ◽

pp. 355-368 ◽

Cited By ~ 30

Author(s):

W. Zhang ◽

S. L. Capps ◽

Y. Hu ◽

A. Nenes ◽

S. L. Napelenok ◽

...

Keyword(s):

Sensitivity Analysis ◽

Particulate Matter ◽

Air Quality ◽

Direct Method ◽

Statistical Significance ◽

Second Order ◽

High Order ◽

Three Dimensions ◽

So2 Emissions ◽

Aerosol Module

Abstract. The high-order decoupled direct method in three dimensions for particulate matter (HDDM-3D/PM) has been implemented in the Community Multiscale Air Quality (CMAQ) model to enable advanced sensitivity analysis. The major effort of this work is to develop high-order DDM sensitivity analysis of ISORROPIA, the inorganic aerosol module of CMAQ. A case-specific approach has been applied, and the sensitivities of activity coefficients and water content are explicitly computed. Stand-alone tests are performed for ISORROPIA by comparing the sensitivities (first- and second-order) computed by HDDM and the brute force (BF) approximations. Similar comparison has also been carried out for CMAQ sensitivities simulated using a week-long winter episode for a continental US domain. Second-order sensitivities of aerosol species (e.g., sulfate, nitrate, and ammonium) with respect to domain-wide SO2, NOx, and NH3 emissions show agreement with BF results, yet exhibit less noise in locations where BF results are demonstrably inaccurate. Second-order sensitivity analysis elucidates poorly understood nonlinear responses of secondary inorganic aerosols to their precursors and competing species. Adding second-order sensitivity terms to the Taylor series projection of the nitrate concentrations with a 50% reduction in domain-wide NOx or SO2 emissions rates improves the prediction with statistical significance.

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