Trajectory integration in vortical flows

Abstract-Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators-integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated, which is not available at the interelement level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by interelement discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-increasing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through a numerical example the computational trade-offs exhibited when one applies such a strategy.

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“…as shown in [36] and [50]. We note that this makes the sum of the coefficients for a particular kernel equal to one:…”

Section: Theoretical Discussion Of Smoothness-increasing Accuracy-conmentioning

confidence: 95%

Investigation of Smoothness-Increasing Accuracy-Conserving Filters for Improving Streamline Integration through Discontinuous Fields

Steffen

Curtis

Kirby

et al. 2008

IEEE Trans. Visual. Comput. Graphics

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“…In the formula, P k represents the error covariance matrix of the estimated motion trajectory of the badminton player at the time of k, and I represent the identity matrix [7].…”

Section: Tracking Principle Of Badminton Player's Arm Shot Imagementioning

confidence: 99%

Badminton players’ trajectory under numerical calculation method

Chi

Alahmadi

2021

Applied Mathematics and Nonlinear Sciences

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The trajectory tracking of badminton players’ arm shots can be used effectively to enhance the player’s shot quality. To track the image trajectory of the batting arm, it is necessary to calculate the body posture ratio and tightness of the target area of the batting arm, to filter the background interference of the image segment of the batting and to complete the efficient tracking of the trajectory of the arm batting image. The traditional method combines the adaptive threshold segmentation method to extract the hitting arm target from the background, but ignores filtering out the background interference of the hitting image fragment. This paper proposes a trajectory tracking method based on the morphological operator of the batter image of the arm stroke. The method consists of (1) differentially calculating the image sequence of the hitting arm during two consecutive shots, (2) estimating the Gaussian model parameters of the differential image of the hitting arm during the hitting process, (3) extracting the outline of the moving target of the hitting arm during the hitting process and then calculating the body posture ratio of the hitting target area and compactness, (4) filtering the background interference of the shot image fragment, (6) constructing a global matching approximation function of the moving target and (7) finally determining the motion trajectory of the badminton arm of the batter. Simulation results show that the proposed method can effectively track the target of the hitting arm during the hitting process and generate a continuous trajectory of the hitting arm.

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“…To the best of our knowledge there is no paper presenting an error analysis of streaklines as curves. For some discussions on a trajectory of a particle we refer to [9] and [10]. The outline of the remainder of this paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

An error analysis of streaklines as curves

Itakura

Tabata

1999

Japan J. Indust. Appl. Math.

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A streakline is a visible curve consisting of fluid particles which emerged continuously from a fixed point in a given flow field. In many cases we do not know the exact velocity field but can get an approximate velocity field. The computation of streaklines includes the discretization error as well as the error caused by the approximate velocity field. We give an error analysis of streaklines as curves in terms of r and h, discretization parameters of the streakline and of the velocity field. We show that, when the velocity field is approximated piecewise linearly, a computation scheme based on the Heun method is the best choice to approximate streaklines from the viewpoint of accuracy and efficiency. We present simulation results of streaklines emerging from the surface of a circular cylinder at Reynolds numbers 100 and 10000.

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Trajectory integration in vortical flows

Cited by 21 publications

References 5 publications

Investigation of Smoothness-Increasing Accuracy-Conserving Filters for Improving Streamline Integration through Discontinuous Fields

Investigation of Smoothness-Increasing Accuracy-Conserving Filters for Improving Streamline Integration through Discontinuous Fields

Badminton players’ trajectory under numerical calculation method

An error analysis of streaklines as curves

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