International Journal for Numerical Methods in Fluids

Steijl, R.; Hoeijmakers, H. W. M.

doi: 10.1002/fld.750pmid: N/A

A fourth‐order accurate solution method for the three‐dimensional Helmholtz equations is described that is based on a compact finite‐difference stencil for the Laplace operator. Similar discretization methods for the Poisson equation have been presented by various researchers for Dirichlet boundary conditions. Here, the complicated issue of imposing Neumann boundary conditions is described in detail. The method is then applied to model Helmholtz problems to verify the accuracy of the discretization method. The implementation of the solution method is also described. The Helmholtz solver is used as the basis for a fourth‐order accurate solver for the incompressible Navier–Stokes equations. Numerical results obtained with this Navier–Stokes solver for the temporal evolution of a three‐dimensional instability in a counter‐rotating vortex pair are discussed. The time‐accurate Navier–Stokes simulations show the resolving properties of the developed discretization method and the correct prediction of the initial growth rate of the three‐dimensional instability in the vortex pair. Copyright © 2004 John Wiley & Sons, Ltd.

Chakravorty, Saugata; Mathew, Joseph

doi: 10.1002/fld.741pmid: N/A

A method for computing low Mach number flows using high‐resolution interpolation and difference formulas, within the framework of the Marker and Cell (MAC) scheme, is presented. This increases the range of wavenumbers that are properly resolved on a given grid so that a sufficiently accurate solution can be obtained without extensive grid refinement. Results using this scheme are presented for three problems. The first is the two‐dimensional Taylor–Green flow which has a closed form solution. The second is the evolution of perturbations to constant‐density, plane channel flow for which linear stability solutions are known. The third is the oscillatory instability of a variable density plane jet. In this case, unless the sharp density gradients are resolved, the calculations would breakdown. Under‐resolved calculations gave solutions containing vortices which grew in place rather than being convected out. With the present scheme, regular oscillations of this instability were obtained and vortices were convected out regularly. Stable computations were possible over a wider range of sensitive parameters such as density ratio and co‐flow velocity ratio. Copyright © 2004 John Wiley Sons, Ltd.

Zhang, Xiang Kun; Kwon, Kie‐Chan; Youn, Sung‐Kie

doi: 10.1002/fld.758pmid: N/A

A least‐squares meshfree method based on the first‐order velocity–pressure–vorticity formulation for two‐dimensional incompressible Navier–Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least‐squares method. Equal‐order moving least‐squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix‐free element‐by‐element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier–Stokes problem and the flow over a square obstacle for time‐dependent Navier–Stokes problem are investigated for the presented least‐squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright © 2004 John Wiley & Sons, Ltd.

Lam, K.; Jiang, G. D.; Liu, Y.; So, R. M. C.

doi: 10.1002/fld.759pmid: N/A

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 104, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.

Lee, T. S.; Liao, Wei; Low, H. T.

doi: 10.1002/fld.755pmid: N/A

A numerical investigation on the characteristics of transitional turbulent flow over series bell‐shape stenoses for a physiological pulsatile flow is presented in the present study. The flow behaviours for the physiological pulsatile flow are studied by considering the effects of the Reynolds number, Womersley number, constriction ratio and spacing ratio of the stenoses on the pulsatile turbulent flow fields. Especially, the mutual influences between the double stenoses under different flow conditions are considered. The numerical results show that the variation of these flow parameters puts significant impacts on the flow developments in the arteries with series stenoses. The double stenoses lead to the higher peak turbulence disturbance and the greater area with comparatively high turbulence intensity distal to the stenoses in comparison with the single stenosis. The analysis shows that for the physiological pulsatile flow, the downstream stenosis usually does not have perceptible influences on the upstream flow fields. Copyright © 2004 John Wiley & Sons, Ltd.