Stability of a Crank-Nicolson pressure correction scheme based on staggered discretizations

In this study, the effect of pressure on the disturbed interface for two-phase stratified regime will be discussed. It is assumed that the two phases are in potential flow condition, a pressure correction algorithm for the two-fluid model is carefully implemented to minimize its effect on numerical stability. Numerical analysis is applied using the finite difference method. Actually pressure correction scheme is employed to solve the viscous potential flow model. It is designed to increase the computational stability when the flow is near the ill-posedness condition. The viscous potential flow theory fits the only pressure experimental data for air and water well.

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A Pressure-Correction Scheme for Rotational Navier-Stokes Equations and Its Application to Rotating Turbulent Flows

Communications in Computational Physics ◽

10.4208/cicp.301109.040310s ◽

2011 ◽

Vol 9 (3) ◽

pp. 740-755 ◽

Cited By ~ 11

Author(s):

Dinesh A. Shetty ◽

Jie Shen ◽

Abhilash J. Chandy ◽

Steven H. Frankel

Keyword(s):

Boundary Conditions ◽

Turbulent Flows ◽

Incompressible Flows ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Pressure Correction ◽

Correction Scheme ◽

Diagonalization Method ◽

Pseudo Spectral

AbstractThe rotational incremental pressure-correction (RIPC) scheme, described in Timmermans et al. [Int. J. Numer. Methods. Fluids., 22 (1996)] and Shen et al. [Math. Comput., 73 (2003)] for non-rotational Navier-Stokes equations, is extended to rotating incompressible flows. The method is implemented in the context of a pseudo Fourier-spectral code and applied to several rotating laminar and turbulent flows. The performance of the scheme and the computational results are compared to the so-called diagonalization method (DM) developed by Morinishi et al. [Int. J. Heat. Fluid. Flow., 22 (2001)]. The RIPC predictions are in excellent agreement with the DM predictions, while being simpler to implement and computationally more efficient. The RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or periodic boundary conditions, and can be used in complex geometries and with other suitable boundary conditions.

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A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow

SIAM Journal on Scientific and Statistical Computing ◽

10.1137/0907059 ◽

1986 ◽

Vol 7 (3) ◽

pp. 870-891 ◽

Cited By ~ 440

Author(s):

J. van Kan

Keyword(s):

Incompressible Flow ◽

Second Order ◽

Pressure Correction ◽

Viscous Incompressible Flow ◽

Correction Scheme

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A cell-centred pressure-correction scheme for the compressible Euler equations

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drz024 ◽

2019 ◽

Vol 40 (3) ◽

pp. 1792-1837

Author(s):

Raphaèle Herbin ◽

Jean-Claude Latché ◽

Chady Zaza

Keyword(s):

Internal Energy ◽

Euler Equations ◽

Compressible Euler Equations ◽

Computational Domain ◽

Time Step ◽

Existence Of A Solution ◽

Pressure Correction ◽

Stability Properties ◽

Correction Scheme ◽

Compressible Euler

Abstract We propose a robust pressure-correction scheme for the numerical solution of the compressible Euler equations discretized by a collocated finite volume method. The scheme is based on an internal energy formulation, which ensures that the internal energy is positive. More generally, the scheme enjoys fundamental stability properties: without restriction on the time step, both the density and the internal energy are positive, the integral of the total energy over the computational domain is preserved thanks to an estimate on the discrete kinetic energy and a discrete entropy inequality is satisfied. These stability properties ensure the existence of a solution to the scheme. The internal energy balance features a corrective source term, which is needed for the scheme to compute the correct shock solutions; we are indeed able to prove a Lax-consistency-type convergence result, in the sense that, under some compactness assumptions, the limit of a converging sequence of approximate solutions obtained with space and time discretization steps tending to zero is an entropy weak solution of the Euler equations. Moreover, constant pressure and velocity are preserved through contact discontinuities. The obtained theoretical results and the scheme accuracy are verified by numerical experiments; a numerical stabilization is introduced in order to reduce the oscillations that appear for some tests. The qualitative behaviour of the scheme is assessed on one-dimensional and two-dimensional Riemann problems and compared with other schemes.

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