Canonical planetary perturbation equations for velocity-dependent forces, and the Lense-Thirring precession

1993 ◽  
Vol 57 (4) ◽  
pp. 537-585 ◽  
Author(s):  
Neil Ashby ◽  
Timothy Allison
Keyword(s):  
Planetary Perturbation ◽  
Perturbation Equations

scholarly journals Planetary perturbation equations based on relativistic Keplerian motion

1986 ◽  
Vol 114 ◽  
pp. 41-52
Author(s):  
Neil Ashby
Keyword(s):  
Test Particle ◽  
Particle Motion ◽  
Elliptic Functions ◽  
Orbital Elements ◽  
Keplerian Motion ◽  
Jacobian Elliptic Functions ◽  
Planetary Perturbation ◽  
Geodesic Equations ◽  
Bound Test ◽  
Perturbation Equations

Solutions of the geodesic equations for bound test particle motion in a Schwarzschild field are expressed using Jacobian elliptic functions. Keplerian orbital elements are identified and related to a set of canonical constants. Relativistic Lagrange planetary perturbation equations are derived.

A class of new perturbation equations for the Kerr geometry

1982 ◽  
Vol 89 (2) ◽  
pp. 68-70 ◽  
Author(s):  
Misao Sasaki ◽  
Takashi Nakamura
Keyword(s):  
Kerr Geometry ◽  
New Perturbation ◽  
Perturbation Equations

scholarly journals A Lagrangian Approach for Computational Acoustics with Meshfree Method

2017 ◽  
Author(s):  
Yong Ou Zhang ◽  
Stefan G. Llewellyn Smith ◽  
Tao Zhang ◽  
Tian Yun Li
Keyword(s):  
Sound Propagation ◽  
Fluid Dynamic ◽  
Taylor Series Expansion ◽  
Meshfree Method ◽  
Lagrangian Approach ◽  
Meshfree Methods ◽  
Combustion Noise ◽  
Smoothed Particle ◽  
The Time Domain ◽  
Perturbation Equations

Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

scholarly journals Prediction of flow-control devices' noise with modified acoustic perturbation equations

2020 ◽  
Vol 22 (3) ◽  
pp. 619-627
Author(s):  
Luca Fenini ◽  
Stefano Malavasi
Keyword(s):  
Flow Control ◽  
Fluid Dynamic ◽  
International Standards ◽  
The Other ◽  
Computational Time ◽  
Noise Prediction ◽  
Acoustic Perturbation ◽  
Flow Control Devices ◽  
Control Devices ◽  
Perturbation Equations

Abstract Fluid-dynamic noise emissions produced by flow-control devices inside ducts are a concerning issue for valve manufacturers and pipeline management. This work proposes a modified formulation of Acoustic Perturbation Equations (APE) that is applicable to industrial frameworks where the interest is addressed to noise prediction according to international standards. This formulation is derived from a literature APE system removing two terms allowing for a computational time reduction of about 20%. The physical contribution of the removed terms is discussed according to the literature. The modified APE are applied to the prediction of the noise emitted by an orifice. The reliability of the new APE system is evaluated by comparing the Sound Pressure Level (SPL) and the acoustic pressure with the ones returned by LES and literature APE. The new formulation agrees with the other methods far from the orifice: moving over nine diameters downstream of the trailing edge, the SPL is in accordance with the other models. Since international standards characterize control devices with the noise measured 1 m downstream of them, the modified APE formulation provides reliable and faster noise prediction for those devices with outlet diameter, d, such that 9d < 1 m.

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