On Approximations for Overdetermined Hyperbolic Equations

Годунов, С. К.

doi:10.1007/978-3-540-75712-2_2

Cited by 4 publications

(2 citation statements)

References 7 publications

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“…According to (4) and ( 5), we draw the conclusion of the equations of α = A + e x and β = A + e y . Under the condition of over-determination, we gained that A + = (A A) −1 A , thereby calculating the values of α and β [25], [26], and completing the fitting of the error curved surface.…”

Section: B Error Curved Surface Interpolation Methodsmentioning

confidence: 99%

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

et al. 2019

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Photoelectric non-contact measurement methods have been widely implemented in space target location, micro-displacement measurement and space optical communication. In term of the reliability and precision of measurement systems, it is a great significance to obtain the laser center location accurately. Since the two-dimensional position sensitive detector (2-D PSD) can continuously detects the gravity center position of the laser spot on its photosensitive surface, this paper provides a flexible method with high precision for the nonlinear correction of PSD as well as a new idea for PSD-based moving laser center positioning. Above all, a laser device system that rotating around a fixed-axis is designed, and the rotation angle can be controlled with the rotation accuracy of 0.5 • . The trace of the gravity center of the rotating spot generated by the device on the PSD surface is detected, and then the laser center location is obtained after further processing of data. In order to improve the detection accuracy of PSD, this research mainly focuses on the nonlinear correction method of the detector and the fitting method of the gravity center trace of the laser spot. Moreover, the effects of different sizes of light spots projected onto the 2-D PSD on the collected photocurrent and estimated coordinates were analyzed by experiments. From the experimental results, the non-linear error of PSD is corrected by the error curved surface interpolation method, the overall error is reduced by more than 32%, and the linearity of the positioning of the laser moving along the diagonal of PSD is 0.2%.

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Section: B Error Curved Surface Interpolation Methodsmentioning

confidence: 99%

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

et al. 2019

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“…The solution aspects of the overdetermined hyperbolic systems have been considered earlier (see e.g. [31]).…”

Section: Mathematical Modelmentioning

confidence: 99%

Passage of a shock wave through inhomogeneous media and its impact on gas-bubble deformation

2015

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The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using a Eulerian type mathematical model for compressible multicomponent flow problems. The model, which accounts for pressure nonequilibrium and applies different equations of state for individual flow components, shows excellent capabilities for the resolution of interfaces separating compressible fluids as well as for capturing the baroclinic source of vorticity generation. The developed finite volume Godunov type computational approach is equipped with an approximate Riemann solver for calculating fluxes and handles numerically diffused zones at flow component interfaces. The computations are performed for various initial conditions and are compared with available experimental data. The initial conditions promoting a shock-bubble interaction process include weak to high planar shock waves with a Mach number ranging from 1.2 to 3 and isolated cylindrical bubble inhomogeneities of helium, argon, nitrogen, krypton, and sulphur hexafluoride. The numerical results reveal the characteristic features of the evolving flow topology. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock, the compression, and acceleration as well as the vorticity generation within the medium. The study is further extended to investigate the influence of the ratio of the heat capacities on the interface deformation.

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Over-Determined and Under-Determined Systems of Time-Varying Linear Equations

Zhang

Guo

2015

Zhang Functions and Various Models

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On Approximations for Overdetermined Hyperbolic Equations

Cited by 4 publications

References 7 publications

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

Passage of a shock wave through inhomogeneous media and its impact on gas-bubble deformation

Over-Determined and Under-Determined Systems of Time-Varying Linear Equations

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