International Journal for Numerical Methods in Fluids

doi: 10.1002/fld.1650141101pmid: N/A

Miyata, Hideaki; Yamada, Yoshihiro

doi: 10.1002/fld.1650141102pmid: N/A

A finite difference simulation method is developed for 3D flow about a body of complex geometry. The Navier–Stokes equation is approximated by a high‐order‐accurate difference scheme in the framework of rectangular co‐ordinate systems. The configuration of the 3D body is represented by use of both surface porosity and volume porosity and the no‐slip body boundary conditions are approximately implemented on the boundary cells. The validity of the method is demonstrated by a numerical test of flow past a sphere at a Reynolds number of 1000. The complicated structure of separated vortices is well revealed by this test computation. The versatility of the method is shown by application to an ocean‐engineering problem of flow about a bay with an island.

Chen, Liyong; Vorus, William S.

doi: 10.1002/fld.1650141103pmid: N/A

Vortex methods have found wide applications in various practical problems. The use of vortex methods in free surface flow problems, however, is still very limited. This paper demonstrates a vortex method for practical computation of non‐linear free surface flows produced by moving bodies. The method is a potential flow formulation which uses the exact non‐linear free surface boundary condition at the exact location of the instantaneous free surface. The position of the free surface, on which vortices are distributed, is updated using a Lagrangian scheme following the fluid particles on the free surface. The vortex densities are updated by the non‐linear dynamic boundary condition, derived from the Euler equations, with an iterative Lagrangian numerical scheme. The formulation is tested numerically for a submerged circular cylinder in unsteady translation. The iteration is shown to converge for all cases. The results of the unsteady simulations agree well with classical linearized solutions. The stability of the method is also discussed.

Dick, E.; Linden, J.

doi: 10.1002/fld.1650141104pmid: N/A

The steady Navier–Stokes equations in primitive variables are discretized in conservative form by a vertex‐centred finite volume method Flux difference splitting is applied to the convective part to obtain an upwind discretization. The diffusive part is discretized in the central way. In its first‐order formulation, flux difference splitting leads to a discretization of so‐called vector positive type. This allows the use of classical relaxation methods in collective form. An alternating line Gauss–Seidel relaxation method is chosen here. This relaxation method is used as a smoother in a multigrid method. The components of this multigrid method are: full approximation scheme with F‐cycles, bilinear prolongation, full weighting for residual restriction and injection of grid functions. Higher‐order accuracy is achieved by the flux extrapolation method. In this approach the first‐order convective fluxes are modified by adding second‐order corrections involving flux limiting. Here the simple MinMod limiter is chosen. In the multigrid formulation the second‐order discrete system is solved by defect correction. Computational results are shown for the well known GAMM backward‐facing step problem and for a channel with a half‐circular obstruction.

Jaeger, Marc; Dhatt, Gouri

doi: 10.1002/fld.1650141105pmid: N/A

An extended κ–ϵ model (to include low‐Reynolds‐number regions) employing weighting functions is presented. Wall functions for the near‐wall zones are developed giving correct boundary values for the Shear stress and κ–ϵ. A finite element model using a penalty formulation for incompressible turbulent flow is applied to Solve a flow between two plates. Results with mesh boundaries situated in the near‐wall region and a: the wall are compared with measured values.

Nachbin, A.; Papanicolaou, G. C.

doi: 10.1002/fld.1650141106pmid: N/A

We study numerically the linear water wave equations for shallow channels with rapidly varying bottom topography. We do not use the shallow water approximation because it is not valid when the bottom is rapidly varying. We use the boundary element method because it allows accurate tracking of the surface waves for long times. We present the results of a range of numerical validation experiments and a comparison between propagation over a periodic and a random rough bottom topography.

Swarbrick, S. J.; Nassehi, V.

doi: 10.1002/fld.1650141107pmid: N/A

This paper presents an algorithm for two‐dimensional Steady viscoelastic flow Simulation in which the Solution of the momentum and continuity equations is decoupled from that of the constitutive equations. The governing equations are discretized by the finite element method, with 3 × 3 element subdivision for the stress field approximation. Non‐consistent Streamline upwinding is also used. Results are given for flow through a converging channel and through an abrupt planar 4:1 contraction.

Swarbrick, S. J.; Nassehi, V.

doi: 10.1002/fld.1650141108pmid: N/A

We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper.

doi: 10.1002/fld.1650141109pmid: N/A

doi: 10.1002/fld.1650141110pmid: N/A