A Meshfree Method for the Analysis of Planar Flows of Inviscid Fluids

Говорухин, В. Н.

doi:10.1007/978-3-642-32979-1_11

Cited by 5 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Calculations based on reference analytical solutions, convergence tests, and results of other authors were all applied to validate the particle-spectral method and demonstrate its efficacy. In articles 40,41,60 proposing and discussing the original version of the particle-spectral method, various tests demonstrate its validity. Because outer dissipation exists in the problem under investigation, the numerical simulation of an inviscid incompressible flow through a channel is computationally simpler than in a closed domain.…”

Section: Validation Of the Methodsmentioning

confidence: 99%

“…In articles 40,41,60 proposing and discussing the original version of the particle–spectral method, various tests demonstrate its validity. Because outer dissipation exists in the problem under investigation, the numerical simulation of an inviscid incompressible flow through a channel is computationally simpler than in a closed domain.…”

Section: Description Of the Particle‐spectral Approachmentioning

confidence: 99%

“…This includes simulating the formation of a dipole structure and the evolution of an initial elliptical vortex patch. This includes simulating the formation of a dipole structure, 41 the dynamics of the Chaplygin–Lamb dipole, of quadrupole vortex structure, 60 and the evolution of an initial elliptical vortex patch 40 . These calculations are all in good agreement with known theoretical results: the washing out of small perturbations for a finite time, the persistence of unsteady motions with no flow through the domain, and the conservation of steady and quasi‐steady flows and their vorticity and energy integrals over the flow domain for long times.…”

Section: Description Of the Particle‐spectral Approachmentioning

confidence: 99%

See 2 more Smart Citations

An extended and improved particle‐spectral method for analysis of unsteady inviscid incompressible flows through a channel of finite length

Говорухин

2022

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

This paper addresses the development of a method to simulate and analyze unsteady flows of incompressible and inviscid fluids in rectangular channels. Mathematically, the flow problem formulates as Euler equations in terms of the stream function and vorticity. The normal velocity and the vorticity aregiven at the inlet of the channel, and only the normal velocity is specified at the outlet. The particle-spectral method describes the vorticity field change in a Lagrangian sense by dynamics of marker particles and an Eulerian description of the velocity field using the global Galerkin approximation. The method involves the subdivision of flow domain on rectangular cells; the approximation of vorticity distribution in cells by least-squares method; Galerkin coefficients calculation using analytical integration on space variables. For time integration, the five-stage Runge-Kutta method of the third accuracy order and the sixth one of symplecticity with adaptive step size control uses. The extension of the particle-spectral approach comprises algorithms for fluid flows qualitative analysis jointly with the time simulation of unsteady flows. This includes the trajectories of marker particles calculation, computing the particle's residence time in the channel, kinetic energy dynamics, and algorithms for analyzing the dynamics and mixing of vortex patches. Test calculations based on reference solutions showed the effectiveness and good accuracy of the particle-spectral approach. Using the developed method the dynamics of one and two initial vortex patches in the channel were investigated. We found the final state of their long-time dynamics is time-periodic or quasi-periodic movements. The application of qualitative analysis algorithms demonstrates these final states produce a chaotic scattering of fluid particles in the flow-through zone of the channel. K E Y W O R D Sflowing through channel, inviscid incompressible fluid, particle-spectral method, vortex dynamics

show abstract

Section: Validation Of the Methodsmentioning

confidence: 99%

Section: Description Of the Particle‐spectral Approachmentioning

confidence: 99%