International Journal for Numerical Methods in Fluids

Autret, A.; Grandotto, M.; Dekeyser, I.

doi: 10.1002/fld.1650080903pmid: N/A

This paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a k‐ϵ turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ϵ is proposed as a numerical treatment for physically meaningless values of k and ϵ. Results obtained for a recirculating flow in a two‐dimensional channel with a sudden expansion in width are presented and compared with experimental values.

Tidd, D. M.; Thatcher, R. W.; Kaye, A.

doi: 10.1002/fld.1650080904pmid: N/A

In this paper the position of the free surface of a swirling fluid held in by surface tension is calculated by the finite element method. A new locally mass‐conserving quadratic velocity, linear pressure triangular element is used to overcome non‐physical solutions produced by the well known Taylor‐Hood element.

Abdallah, S.; Dreyer, J.

doi: 10.1002/fld.1650080905pmid: N/A

In a recent paper Gresho and Sani showed that Dirichlet and Neumann boundary conditions for the pressure Poisson equation give the same solution. The purpose of this paper is to confirm this (for one case at least) by numerically solving the pressure equation with Dirichlet and Neumann boundary conditions for the inviscid stagnation point flow problem. The Dirichlet boundary condition is obtained by integrating the tangential component of the momentum equation along the boundary. The Neumann boundary condition is obtained by applying the normal component of the momentum equation at the boundary. In this work solutions for the Neumann problem exist only if a compatibility condition is satisfied. A consistent finite difference procedure which satisfies this condition on non‐staggered grids is used for the solution of the pressure equation with Neumann conditions. Two test cases are computed. In the first case the velocity field is given from the analytical solution and the pressure is recovered from the solution of the associated Poisson equation. The computed results are identical for both Dirichlet and Neumann boundary conditions. However, the Dirichlet problem converges faster than the Neumann case. In the second test case the velocity field is computed from the momentum equations, which are solved iteratively with the pressure Poisson equation. In this case the Neumann problem converges faster than the Dirichlet problem.

Demirdžić, I.; Perić, M.

doi: 10.1002/fld.1650080906pmid: N/A

In the numerical solutions of fluid flow problems in moving co‐ordinates, an additional conservation equation, namely the space conservation law, has to be solved simultaneously with the mass, momentum and energy conservation equations. In this paper a method of incorporating the space conservation law into a finite volume procedure is proposed and applied to a number of test cases. The results show that the method is efficient and produces accurate results for all grid velocities and time steps for which temporal accuracy suffices. It is also demonstrated, by analysis and test calculations, that not satisfying the space conservation law in a numerical solution procedure introduces errors in the form of artificial mass sources. These errors can be made negligible only by choosing a sufficiently small time step, which sometimes may be smaller than required by the temporal discretization accuracy.

Jagannathan, Sridhar

doi: 10.1002/fld.1650080907pmid: N/A

The focus of this paper is the analysis of spatially two‐dimensional non‐linear free surface problems. The critical aspects of the problem concern the treatment of the non‐linear free surface, the body boundary condition for large motions and the imposition of suitable radiation conditions. To address such complexities, time domain simulation was chosen as the method of analysis. With the use of a finite domain for simulation, a major concern is with the radiation condition to be applied at the open or truncation boundary. For the two‐dimensional problem at hand, no theoretical radiation conditions are known to exist. An extension of the Orlanski open boundary condition, based on phase velocity determination at the free surface, is proposed. Three categories of problems were analysed using numerical simulation‐namely, freely moving steep waves, waves over a submerged body and forced body motion. Simulation results have been compared with linear theory and experiments.

Sidén, Gunnar L. D.; Lynch, Daniel R.

doi: 10.1002/fld.1650080908pmid: N/A

The shallow water wave equation is derived in a general deforming co‐ordinate system. A weak form is developed which displays the natural boundary condition prominently and which may be implemented on C0 elements. A time‐stepping algorithm is implemented with clastic mapping of interior node motion. Lossless test cases show agreement with analytic solutions. A simple hypothetical test case shows intuitively good behaviour at length scales approaching those required of estuarine simulations.

Glaister, P.

doi: 10.1002/fld.1650080909pmid: N/A

A finite difference scheme based on flux difference splitting is presented for the solution of the two‐dimensional Euler equations of gas dynamics in a generalized co‐ordinate system. The scheme is based on numerical characteristic decomposition and solves locally linearized Riemann problems using upwind differencing. The decomposition is for a generalized co‐ordinate system and a convex equation of state. This ensures good shock‐capturing properties when incorporated with operator splitting and the advantage of using body‐fitted co‐ordinates. The resulting scheme is applied to supersonic flow of real air' past a circular cylinder.

Leslie, D. C.; Gao, S.

doi: 10.1002/fld.1650080910pmid: N/A

In a spectral LES code it is not possible to treat the actual eddy viscosity implicitly. We have therefore examined the effect on stability of adding a constant pseudo‐viscosity to the implicit term and subtracting it from the explicit term: stability limits have been derived theoretically and verified computationally for two different treatments of the explicit term. We have also studied the effect of a stochastic temporal variation of the eddy viscosity.