International Journal for Numerical Methods in Fluids

Lörstad, Daniel; Francois, Marianne; Shyy, Wei; Fuchs, Laszlo

doi: 10.1002/fld.746pmid: N/A

The volume of fluid (VOF) and immersed boundary (IB) methods are two popular computational techniques for multi‐fluid dynamics. To help shed light on the performance of both techniques, we present accuracy assessment, which includes interfacial geometry, detailed and global fluid flow characteristics, and computational robustness. The investigation includes the simulations of a droplet under static equilibrium as a limiting test case and a droplet rising due to gravity for Re⩽1000. Surface tension force models are key issues in both VOF and IB and alternative treatments are examined resulting in improved solution accuracy. A refined curvature model for VOF is also presented. With the newly developed interfacial treatments incorporated, both IB and VOF perform comparably well for the droplet dynamics under different flow parameters and fluid properties. Copyright © 2004 John Wiley & Sons, Ltd.

Liang, Q.; Borthwick, A. G. L.; Stelling, G.

doi: 10.1002/fld.748pmid: N/A

Flooding due to the failure of a dam or dyke has potentially disastrous consequences. This paper presents a Godunov‐type finite volume solver of the shallow water equations based on dynamically adaptive quadtree grids. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) scheme is used to evaluate interface fluxes in both wet‐ and dry‐bed applications. The numerical model is validated against results from alternative numerical models for idealized circular and rectangular dam breaks. Close agreement is achieved with experimental measurements from the CADAM dam break test and data from a laboratory dyke break undertaken at Delft University of Technology. Copyright © 2004 John Wiley Sons, Ltd.

Jiang, Song; Ni, Guoxi

doi: 10.1002/fld.751pmid: N/A

We present a γ‐model BGK scheme for the numerical simulation of compressible multifluids. The scheme is based on the incorporation of a conservative γ‐model scheme given in (J. Comput. Phys. 1996; 125:150–160) into the gas kinetic BGK scheme (J. Comput. Phys. 1993; 109:53–66, J. Comput. Phys. 1994; 114:9–17), and is simple to implement. Several numerical examples presented in this paper validate the scheme in the application of compressible multimaterial flows. Copyright © 2004 John Wiley & Sons, Ltd.

Dohrmann, Clark R.; Bochev, Pavel B.

doi: 10.1002/fld.752pmid: N/A

A new stabilized finite element method for the Stokes problem is presented. The method is obtained by modification of the mixed variational equation by using local L2 polynomial pressure projections. Our stabilization approach is motivated by the inherent inconsistency of equal‐order approximations for the Stokes equations, which leads to an unstable mixed finite element method. Application of pressure projections in conjunction with minimization of the pressure–velocity mismatch eliminates this inconsistency and leads to a stable variational formulation. Unlike other stabilization methods, the present approach does not require specification of a stabilization parameter or calculation of higher‐order derivatives, and always leads to a symmetric linear system. The new method can be implemented at the element level and for affine families of finite elements on simplicial grids it reduces to a simple modification of the weak continuity equation. Numerical results are presented for a variety of equal‐order continuous velocity and pressure elements in two and three dimensions. Copyright © 2004 John Wiley & Sons, Ltd.

Houzeaux, G.; Codina, R.

doi: 10.1002/fld.757pmid: N/A

In this paper, we present a numerical model to simulate the lost foam casting process. We introduce this particular casting first in order to capture the different physical processes in play during a casting. We briefly comment on the possible physical and numerical models used to envisage the numerical simulation. Next we present a model which aims to solve ‘part of’ the complexities of the casting, together with a simple energy budget that enables us to obtain an equation for the velocity of the metal front advance. Once the physical model is established we develop a finite element method to solve the governing equations. The numerical and physical methodologies are then validated through the solution of a two‐ and a three‐dimensional example. Finally, we discuss briefly some possible improvements of the numerical model in order to capture more physical phenomena. Copyright © 2004 John Wiley & Sons, Ltd.