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LI, CHIN‐HSIEN; GLOWINSKI, ROLAND
doi: 10.1002/(SICI)1097-0363(19960730)23:2<77::AID-FLD403>3.0.CO;2-1pmid: N/A
Based upon the operator‐splitting method designed by the authors to solve the Navier–Stokes equations with variable density and viscosity, a segregated time‐marching solution scheme is proposed for solving the low‐Mach‐number flow model with the acoustic waves being filtered out. This solution scheme does not rely on the correction for global mass conservation to maintain solution accuracy. With this advantage the scheme can be directly applied to general low‐Mach‐number flow problems with confidence.
doi: 10.1002/(SICI)1097-0363(19960730)23:2<105::AID-FLD413>3.0.CO;2-Epmid: N/A
A method of modelling the contribution of finite‐size organized streams and fluid structures to the processes of turbulent transport is presented for the example of developed turbulent pipe flow. The method is applied to construct the turbulent length (L) and eddy viscosity coefficient (νt) employed to compute the average characteristics of the flow. The average effects of action of these organized fluid structures and streams are modelled as the final results of discrete displacements of certain model turbulent signals between nodes associated in pairs as well as the results of effective discrete displacements of these pairs. The displacement of information about the organization of two nodes into a pair identifies the displacement of the pair. These nodes constitute a network whose parameters have been established a priori analytically by considering a sequence of model turbulent lengths scaled with their distance to the wall. The model turbulent signals are evaluated at respective discrete nodes with the help of a certain finite difference turbulence model closed by L and νt and realized on an appropriate numerical grid. The non‐uniform grid spacing has been related unambiguously in a rational way to the sequence of model turbulent lengths. Results elucidating specific features of this discrete modelling, particularly its differences from the continuous approach, are presented. Good agreement of the results with available experimental data is demonstrated. The average characteristics of the flow structure predicted for a wide range of Reynolds number (Re) are unique or bifurcated for particular Re intervals. The latter case suggests the occurrence of switching from one type of flow structure organization to another with the ambient conditions unchanged.
doi: 10.1002/(SICI)1097-0363(19960730)23:2<125::AID-FLD414>3.0.CO;2-9pmid: N/A
Studies on the numerical simulation of high‐Reynolds‐number flows encounter difficulties due to the wide range of characteristic length and time scales existing in the flow field. These are often much smaller than the computational grid size. A new approach based on a ‘model‐free ’ local average direct numerical simulation is presented which incorporates a strategy to filter the non‐resolvable scales by means of an integration over the domain and to recover the contribution of the subgrid scales by using an integral formulation developed for them. The resulting weak formulation allows us to define a numerical flux that, thanks to the filtering operation, is highly accurate. Several computation test‐cases concerning theoretical accuracy and the Navier–Stokes equations at high Reynolds number are carried out without using any turbulence model. The obtained accuracy for all computations confirms that this approach can be considered a valid contribution in the field of direct numerical simulation.
doi: 10.1002/(SICI)1097-0363(19960730)23:2<143::AID-FLD416>3.0.CO;2-7pmid: N/A
In order to simulate flows in the shallow water limit, the full incompressible Navier–Stokes equations with free boundaries are solved using a single layer of finite elements. This implies a polynomial approximation of the velocity profile in the vertical direction, which in turn distorts the wave speed. This fact is verified by numerical results: the wave speed depends on the vertical discretization. When at least two layers of finite elements are used, the boundary layer at the bottom can be simulated and the correct solution for the shallow water limit is recovered. Then this algorithm is applied to the prediction of Tsunami event.
YANG, YUE‐TZU; CHEN, CHA'O‐KUANG; CHIU, CHI‐FANG
doi: 10.1002/(SICI)1097-0363(19960730)23:2<163::AID-FLD417>3.0.CO;2-2pmid: N/A
The purpose of this investigation is to study the convective heat transfer from a horizontal circular cylinder under the effect of a solid plane wall. The full Navier–Stokes and energy equations for two‐dimensi onal steady flow are solved by a finite element method. The variations in surface shear stress, local pressure and Nusselt number around the surface of the cylinder as well as the predicted values of average Nusselt number, location of separation and some flow and temperature fields are presented. It is found that the average Nusselt number and drag force increase as the gap between the cylinder and the wall is increased.
CHOQUET, RÉMI; ERHEL, JOCELYNE
doi: 10.1002/(SICI)1097-0363(19960730)23:2<177::AID-FLD418>3.0.CO;2-Npmid: N/A
This paper addresses the resolution of non‐linear problems arising from an implicit time discretization in CFD problems. We study the convergence of the Newton–GMRES algorithm with a Jacobian approximated by a finite difference scheme and with restarting in GMRES. In our numerical experiments we observe, as predicted by the theory, the impact of the matrix‐free approximations. A second‐order scheme clearly improves the convergence in the Newton process.
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