International Journal for Numerical Methods in Fluids

Hanchi, S.; Oualli, H.; Askovic, R.; Bouabdallah, A.

doi: 10.1002/fld.473pmid: N/A

A periodic superimposed motion may notably influence the flow structure and the development of the convective heat transfer relative to non‐deformable case. In particular, a radial deformation of a circular cylinder, may cause a possible synchronization with the cylinder wake, which is itself periodic when Vortex Street takes place. This synchronization phenomenon, often called ‘lock‐in’, may cause undesirable effects, but may also constitute a way of controlling the wake development. Body deformability may be used as wake control device that would favourably affect the interplay of primary and secondary vorticities, thus reducing the drag coefficient. These numerical and experimental studies are done herein for a Reynolds number equal to 23500. The problem is resolved by using the Navier–Stokes equations in the vorticity‐stream function form. The vorticity transport equation is solved by a second‐order finite difference method in both directions of the domains. The Poisson equation for the stream‐function is solved by a SOR method. The advance in time is achieved by a second‐order Adams–Bashforth scheme. The effect of turbulence is represented by eddy viscosity νt, which is determined by a sub‐grid‐scale model. In the present study, we use a Smagorinsky model. Copyright © 2003 John Wiley & Sons, Ltd.

Allen, C. B.

doi: 10.1002/fld.474pmid: N/A

An upwind Euler solver is presented, and applied to multibladed lifting hovering rotor flow. These flows can be simulated as a steady case, in a blade‐fixed rotating co‐ordinate system. However, forward flight simulation will always require an unsteady solution. Hence, as a stepping stone in the development of a forward flight simulation tool, both explicit steady and implicit unsteady simulations of the same hovering case are presented. Convergence of the two approaches is examined and compared, in terms of residual history, cost, and solution evolution, as a means of both validating the unsteady formulation and considering implications for forward flight simulation. Consideration of the solution evolution and wake capturing shows that for hovering rotor cases, the unsteady and steady solutions are the same, but the unsteady solution is more expensive in terms of CPU time. It is also shown that for hover, the fewer real time‐steps taken per revolution the more efficient the implicit scheme is. However, this is a characteristic of the case, which results in smooth solution variation between time steps. It is also demonstrated that for rotary flow simulation, the global residual is not a useful quantity to assess convergence. The residual reaches a very low (constant in the implicit case) value while the solution is still evolving. Copyright © 2003 John Wiley & Sons, Ltd.

Fraccarollo, L.; Capart, H.; Zech, Y.

doi: 10.1002/fld.475pmid: N/A

A Godunov method is proposed for the computation of open‐channel flows in conditions of rapid bed erosion and intense sediment transport. Generalized shallow water equations govern the evolution of three distinct interfaces: the water free‐surface, the boundary between pure water and a sediment transport layer, and the morphodynamic bottom profile. Based on the HLL scheme of Harten, Lax and Van Leer (1983), a finite volume numerical solver is constructed, then extended to second‐order accuracy using Strang splitting and MUSCL extrapolation. Lateralisation of the momentum flux is adopted to handle the non‐conservative product associated with bottom slope. Computational results for erosional dam‐break waves are compared with experimental measurements and semi‐analytical Riemann solutions. Copyright © 2003 John Wiley & Sons, Ltd.

Wille, S. Ø.; Staff, Ø.; Loula, A. F. D.

doi: 10.1002/fld.477pmid: N/A

A parallel ILU preconditioning algorithm for the incompressible Navier–Stokes equations has been designed, implemented and tested. The computational mesh is divided into N subdomains which are processed in parallel in different processors. During ILU factorization, matrices and vectors associated with the nodes on the interface between the subdomains are communicated to the equation matrices to the adjacent subdomain. The bases for the parallel algorithm are an appropriate node ordering scheme and a segregation of velocity and pressure degrees of freedom. The inner nodes of the subdomain are numbered first and then the nodes on the interface between the subdomains. To avoid division by zero during the ILU factorization, the equations corresponding to the velocity degrees of freedom are assembled first in the global equation matrix, followed by the equations corresponding to the pressure degrees of freedom. Copyright © 2003 John Wiley & Sons, Ltd.

Tkalich, Pavlo; Chan, Eng Soon

doi: 10.1002/fld.483pmid: N/A

Using the upstream polynomial approximation a series of accurate two‐dimensional explicit numerical schemes is developed for the solution of the convection–diffusion equation. A third‐order polynomial approximation (TOP) of the convection term and a consistent second‐order approximation of the diffusion term are combined in a single‐step flux‐difference algorithm. Stability analysis confirms that the TOP‐12 scheme satisfies the CFL condition for two dimensions. Using smaller and narrower flux stencils compared to algorithms of similar accuracy, the TOP‐12 scheme is more efficient in terms of computations per single node. Numerical tests and comparison with other well‐known algorithms show a high performance of the developed schemes. Copyright © 2003 John Wiley & Sons, Ltd.