An implicit centered scheme for steady and unsteady incompressible one and two-phase flows

Granier, Benoît; Lerat, A.; Wu, Zhanjun

doi:10.1016/s0045-7930(96)00046-1

Cited by 8 publications

(3 citation statements)

References 41 publications

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“…33×33, 65×65, and 133×133, and the time behavior of the drag on the upper lid is depicted in Figure 7. As can be seen, the drag reaching a maximum of 30 becomes periodic in a short period of time agreeing very well with the result presented in [7]. The same problem was then run on a 65×65 mesh by using three different time steps ( t = 0.01, t = 0.05, t = 0.1) and the resulting graphs were depicted in Figure 8.…”

Section: Test 3: Unsteady Oscillatory Lid-driven Cavity Testsupporting

confidence: 84%

Numerical solutions of liquid metal flows by incompressible magneto‐hydrodynamics with heat transfer

Şentürk

Tessarotto

Aslan

2008

Numerical Methods in Fluids

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SUMMARYA two-dimensional incompressible magneto-hydrodynamic code is presented in order to solve the steady state or transient magnetized or neutral convection problems with the effect of heat transfer. The code utilizes a numerical matrix distribution scheme that runs on structured or unstructured triangular meshes and employs a dual time-stepping technique with multi-stage Runge-Kutta algorithm. The code can be used to simulate the natural convection with internal heat generation and absorption and nonlinear timedependent evolution of heated and magnetized liquid metals exposed to external fields. MAGNETO-HYDRODYNAMIC EQUATIONSIn this work, it is assumed that the flow is characterized by two-dimensional (2D) incompressible Navier-Stokes-Fourier plus Maxwell equations in the quasi-static approximation (i.e. Magnetohydrodynamic (MHD) equations). The MHD system is coupled with the temperature effects through gravitational force by means of the Bousinessq approximation. In addition, the fluid is assumed to be electrically conducting and locally quasi-neutral at the same time. As a consequence, not only the fluid flow contributes to the electric and magnetic field distributions in the medium but

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Section: Test 3: Unsteady Oscillatory Lid-driven Cavity Testsupporting

confidence: 84%

Numerical solutions of liquid metal flows by incompressible magneto‐hydrodynamics with heat transfer

Şentürk

Tessarotto

Aslan

2008

Numerical Methods in Fluids

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“…This is because, the numerical formula, Equation (76), used for drag calculation depends on both x and y but not on t. As seen from Figure 6, the drag changes within [−32, +32] and the period of the oscillations is nearly 6.2. These values are the same as the results presented in [23], stating that time accurate solutions can be obtained by the code presented here. …”

Section: Unsteady Oscillatory Lid Testsupporting

confidence: 68%

A visual incompressible magneto‐hydrodynamics solver with radiation, mass, and heat transfer

Aslan

2009

Numerical Methods in Fluids

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SUMMARYA visual two-dimensional (2D) nonlinear magneto-hydrodynamics (MHD) code that is able to solve steady state or transient charged or neutral convection problems under the radiation, mass, and heat transfer effects is presented. The flows considered are incompressible and the divergence conditions on the velocity and magnetic fields are handled by similar relaxation schemes in the form of pseudo-iterations between the real time levels. The numerical method utilizes a matrix distribution scheme that runs on structured or unstructured triangular meshes. The time-dependent algorithm developed here utilizes a semi-implicit dual time stepping technique with multistage Runge-Kutta (RK) algorithm. It is possible for the user to choose different normalizations (natural, forced, Boussinesq, Prandtl, double-diffusive and radiation convection) automatically. The code is visual and runs interactively with the user. The graphics algorithms work multithreaded and allow the user to follow certain flow features (color graphs, vector graphs, one-dimensional profiles) during runs, see (Comput. Fluids 2007; 36:961-973) for details. With the code presented here nonlinear steady or time-dependent evolution of heated and stratified neutral and charged liquids, convection of mixture of neutral and charged gases, double-diffusive and salinity natural convection flows with internal heat generation/absorption and radiative heat transfer flows can be investigated. In addition, the numerical method (combining concentration, radiation, heat transfer, and MHD effects) takes the advantage of local time stepping and employs simplified residual jacobian matrix to increase pseudo-convergence rate. This code is currently being improved to simulate three-dimensional problems with parallel processing.

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“…Similar approaches have been employed in numerous previous studies on cavitation flows. Granier et al [28] applied the incompressible scheme to a flat-plate flow, a lid-driven cavity flow, and the impingement of a liquid drop on a solid wall. Senocak and Shyy [29] developed a pressure-based compressible solver and applied it to cavitation flow over hemispherical and blunt bodies.…”

Section: Full Viscous Approachmentioning

confidence: 99%

Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise

2018

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Abstract:In this study, cavitation flow around a hydrofoil and its radiated hydro-acoustic fields were numerically investigated, with an emphasis on the effects of viscous flux vectors. The full three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations were numerically solved. The mass transfer model was adopted to model phase changes between liquid water and vapor. To resolve the numerical instability problem arising from the rapid changes in local density and speed of sound of the mixture, the preconditioning and dual-time stepping methods were employed. The filter-based turbulent model was applied to resolve the unstable cavitation flow field more accurately. In splitting the viscous terms, three approaches for dealing with viscous flux vectors were considered: the so-called viscous lagging, full viscous, and thin-layer models. Radiated hydro-acoustic waves were predicted by applying the Ffowcs Williams and Hawkings equations. The effects of the viscous flux vectors on the predicted flow fields and its radiated noise were then examined by comparing the hydro-dynamic forces, velocity distribution, volume fraction, far-field sound directivities, and sound spectrum of the three approaches. The results revealed that the thin-layer model can provide predictions as accurate as the full viscous model, but required less computational time.

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An implicit centered scheme for steady and unsteady incompressible one and two-phase flows

Cited by 8 publications

References 41 publications

Numerical solutions of liquid metal flows by incompressible magneto‐hydrodynamics with heat transfer

Numerical solutions of liquid metal flows by incompressible magneto‐hydrodynamics with heat transfer

A visual incompressible magneto‐hydrodynamics solver with radiation, mass, and heat transfer

Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise

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