International Journal for Numerical Methods in Fluids

Gerges, Hany; McCorquodale, John A.

doi: 10.1002/(SICI)1097-0363(19970330)24:6<537::AID-FLD506>3.0.CO;2-7pmid: N/A

A new numerical model has been developed to simulate the transport of dye in primary sedimentation tanks operating under neutral density conditions. A multidimensional algorithm based on a new skew third‐order upwinding scheme (STOUS) is used to eliminate numerical diffusion. This algorithm introduces cross‐difference terms to overcome the instability problems of the componentwise one‐dimensional formulae for simulating multi‐dimensional flows. Small physically unrealistic overshooting and undershooting have been avoided by using a well‐established technique known as the universal limiter. A well‐known rotating velocity field test was used to show the capability of STOUS in eliminating numerical diffusion. The STOUS results are compared with another third‐order upwinding technique known as UTOPIA. The velocity field is obtained by solving the equations of motion in the vorticity–streamfunction formulation. A k– ϵ model is used to simulate the turbulence phenomena. The velocity field compares favourably with previous measurements and with UTOPIA results. An additional differential equation governing the unsteady transport of dye in a steady flow field is solved to calculate the dye concentration and to produce flow‐through curves (FTCs) which are used in evaluating the hydraulic efficiency of settling tanks. The resulting FTC was compared with both measurements and numerical results predicted by various discretization schemes. © 1997 by John Wiley & Sons, Ltd.

Taigbenu, Akpofure E.; Onyejekwe, Okey O.

doi: 10.1002/(SICI)1097-0363(19970330)24:6<563::AID-FLD509>3.0.CO;2-7pmid: N/A

The transient one‐dimensional Burgers equation is solved by a mixed formulation of the Green element method (GEM) which is based essentially on the singular integral theory of the boundary element method (BEM). The GEM employs the fundamental solution of the term with the highest derivative to construct a system of discrete first‐order non‐ linear equations in terms of the primary variable, the velocity, and its spatial derivative which are solved by a two‐level generalized and a modified time discretization scheme and by the Newton–Raphson algorithm. We found that the two‐level scheme with a weight of 0ċ67 and the modified fully implicit scheme with a weight of 1ċ5 offered some marginal gains in accuracy. Three numerical examples which cover a wide range of flow regimes are used to demonstrate the capabilities of the present formulation. Improvement of the present formulation over an earlier BE formulation which uses a linearized operator of the differential equation is demonstrated. © 1997 by John Wiley & Sons, Ltd.

Kuo, T. C.; Pan, C.; Chieng, C. C.; Yang, A. S.

doi: 10.1002/(SICI)1097-0363(19970330)24:6<579::AID-FLD510>3.0.CO;2-Epmid: N/A

A comprehensively theoretical model is developed and numerically solved to investigate the phase distribution phenomena in a two‐dimensional, axisymmetric, developing, two‐phase bubbly flow. The Eulerian approach treats the fluid phase as a continuum and solved Eulerian conservation equations for the liquid phase. The Lagrangian bubbles are tracked by solving the equation of motion for the gas phase. The interphase momentum changes are included in the equations. The numerical model successfully predicts detailed flow velocity profiles for both liquid and gas phases. The development of the wall‐peaking phenomenon of the void fraction and velocity profiles is also characterized for the developing flow. For 42 experiments in which the mean void fraction is less than 20 per cent, numerical calculations demonstrate that the predictions agree well with Liu's experimental data. © 1997 by John Wiley & Sons, Ltd.

Siegel, P.; Mosé, R.; Ackerer, Ph.; Jaffre, J.

doi: 10.1002/(SICI)1097-0363(19970330)24:6<595::AID-FLD512>3.0.CO;2-Ipmid: N/A

When transport is advection‐dominated, classical numerical methods introduce excessive artificial diffusion and spurious oscillations. Special methods are required to overcome these phenomena. To solve the advection‒diffusion equation, a numerical method is developed using a discontinuous finite element method for the discretization of the advective terms. At the discontinuities of the approximate solution, numerical advective fluxes are calculated using one‐dimensional approximate Riemann solvers. The method is stabilized with a multidimensional slope limiter which introduces small amounts of numerical diffusion when sharp concentration fronts occur. In addition, the diffusive term is discretized using a mixed hybrid finite element method. With this approach, numerical oscillations are completely avoided for a full range of cell Peclet numbers. The combination of discontinuous and mixed finite elements can be easily applied to 2D and 3D models using various types of elements in regular and irregular meshes. Numerical tests show good agreement with 1D and 2D analytical solutions. This approach is compared at the same time with two different numerical methods, a standard mixed finite method and a finite volume approach with high‐resolution upwind terms. Regular and irregular meshes are used for the numerical tests to study the mesh effects on the numerical results. Our data show that in all cases this approach performs well. © 1997 by John Wiley & Sons, Ltd.

Medale, Marc; Jaeger, Marc

doi: 10.1002/(SICI)1097-0363(19970330)24:6<615::AID-FLD514>3.0.CO;2-Hpmid: N/A

A numerical model has been developed for the 2D simulation of free surface flows or, more generally speaking, moving interface ones. The bulk fluids on both sides of the interface are taken into account in simulating the incompressible laminar flow state. In the case of heat transfer the whole system, i.e. walls as well as possible obstacles, is considered. This model is based on finite element analysis with an Eulerian approach and an unstructured fixed mesh. A special technique to localize the interface allows its temporal evolution through this mesh. Several numerical examples are presented to demonstrate the capabilities of the model. © 1997 by John Wiley & Sons, Ltd.