Finite Volume Formulation of a Third-Order Residual-Based Compact Scheme for Unsteady Flow Computations

2014 ◽  
pp. 37-58
Author(s):  
Karim Grimich ◽  
Bertrand Michel ◽  
Paola Cinnella ◽  
Alain Lerat
Keyword(s):  
Unsteady Flow ◽  
Finite Volume ◽  
Compact Scheme ◽  
Third Order

scholarly journals Numerical investigation of unsteady flow past a circular cylinder using 2-D finite volume method

1970 ◽  
Vol 4 (1) ◽  
pp. 27-42 ◽  
Author(s):  
Md Mahbubar Rahman ◽  
Md. Mashud Karim ◽  
Md Abdul Alim
Keyword(s):  
Circular Cylinder ◽  
Unsteady Flow ◽  
Turbulent Flow ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Turbulence Models ◽  
Drag Coefficients ◽  
Pressure Formulation ◽  
Lift And Drag ◽  
Volume Method

The dynamic characteristics of the pressure and velocity fields of unsteady incompressible laminar and turbulent wakes behind a circular cylinder are investigated numerically and analyzed physically. The governing equations, written in the velocity pressure formulation are solved using 2-D finite volume method. The initial mechanism for vortex shedding is demonstrated and unsteady body forces are evaluated. The turbulent flow for Re = 1000 & 3900 are simulated using k-? standard, k-? Realizable and k-? SST turbulence models. The capabilities of these turbulence models to compute lift and drag coefficients are also verified. The frequencies of the drag and lift oscillations obtained theoretically agree well with the experimental results. The pressure and drag coefficients for different Reynolds numbers were also computed and compared with experimental and other numerical results. Due to faster convergence, 2-D finite volume method is found very much prospective for turbulent flow as well as laminar flow.Keywords: Viscous unsteady flow, laminar & turbulent flow, finite volume method, circular cylinder.DOI: 10.3329/jname.v4i1.914Journal of Naval Architecture and Marine Engineering 4(2007) 27-42

Winter model in the quasi-continuum limit

2020 ◽  
Vol 35 (06) ◽  
pp. 2050026
Author(s):  
U. G. Aglietti
Keyword(s):  
Finite Volume ◽  
Perturbative Expansion ◽  
Multiscale Methods ◽  
Secular Term ◽  
Spectral Lines ◽  
Analytic Description ◽  
Third Order ◽  
Usual Model ◽  
Weakly Coupled ◽  
Secular Terms

We study Winter or [Formula: see text]-shell model at finite volume (length), describing a small resonating cavity weakly-coupled to a large one. For generic values of the coupling, a resonance of the usual model corresponds, in the finite-volume case, to a compression of the spectral lines; for specific values of the coupling, a resonance corresponds instead to a degenerate or a quasi-degenerate doublet. A secular term of the form [Formula: see text] occurs in the perturbative expansion of the momenta (or of the energies) of the particle at third order in [Formula: see text], where [Formula: see text] is the coupling among the cavities and [Formula: see text] is the ratio of the length of the large cavity over the length of the small one. These secular terms, which tend to spoil the convergence of the perturbative series in the large volume case, [Formula: see text], are resummed to all orders in [Formula: see text] by means of standard multiscale methods. The resulting improved perturbative expansions provide a rather complete analytic description of resonance dynamics at finite volume.

scholarly journals A conservative numerical scheme for Rosenau-RLW equation based on multiple integral finite volume method

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Cui Guo ◽  
Fang Li ◽  
Wenping Zhang ◽  
Yuesheng Luo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Lagrange Interpolation ◽  
Numerical Scheme ◽  
Multiple Integral ◽  
Third Order ◽  
Unconditionally Stable ◽  
Fully Discrete ◽  
Second Order In Time ◽  
Volume Method

Abstract A multiple integral finite volume method combined and Lagrange interpolation are applied in this paper to the Rosenau-RLW (RRLW) equation. We construct a two-level implicit fully discrete scheme for the RRLW equation. The numerical scheme has the accuracy of third order in space and second order in time, respectively. The solvability and uniqueness of the numerical solution are shown. We verify that the numerical scheme keeps the original equation characteristic of energy conservation. It is proved that the numerical scheme is convergent in the order of $O(\tau ^{2} + h^{3})$ O ( τ 2 + h 3 ) and unconditionally stable. A numerical experiment is given to demonstrate the validity and accuracy of scheme.

scholarly journals Compact third-order limiter functions for finite volume methods

2009 ◽  
Vol 228 (11) ◽  
pp. 4118-4145 ◽  
Author(s):  
Miroslav Čada ◽  
Manuel Torrilhon
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Third Order

A finite volume formulation for compact scheme with applications to LES

2001 ◽  
Author(s):  
Sergey Smirnov ◽  
Chris Lacor ◽  
Martine Baelmans
Keyword(s):  
Finite Volume ◽  
Compact Scheme

scholarly journals Accuracy analysis and improvement for the cell-centered scheme with the quasi-one-dimensional reconstriction

2021 ◽  
pp. 1-32 ◽  
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Transport Equation ◽  
Finite Volume ◽  
Constant Velocity ◽  
Truncation Error ◽  
Finite Volume Scheme ◽  
Accuracy Analysis ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Reconstruction

We study the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction. For the model transport equation with a constant velocity, we prove that on translationally-invariant (TI) triangular meshes it possesses the second order of the truncation error and, if the solution is steady, the third order of the solution error. We offer the modification possessing the third order of the solution error on TI-meshes for unsteady solutions also and verify its accuracy on unstructured meshes.

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