International Journal for Numerical Methods in Fluids

Cruchaga, Marcela; Celentano, Diego; Breitkopf, Piotr; Villon, Pierre; Rassineux, Alain

doi: 10.1002/fld.2073pmid: N/A

Classical Lagrangian schemes applied to update the front position between two immiscible incompressible fluids have been long recognized to provide a sharp representation of the interface. However, the main drawback of these approaches is the progressive distortion in the distribution of the markers used to identify the material front. To avoid this problem, a 3D interface remeshing algorithm is proposed in this work. In addition, the remeshed front is enforced to preserve the global volume. These aspects are incorporated in an existing fluid dynamics formulation for the analysis of two‐fluid flows problems. The resulting formulation, called as the 3D‐moving Lagrangian interface remeshing technique, is applied in the numerical analysis of two‐fluid flow problems. Copyright © 2009 John Wiley & Sons, Ltd.

Sellier, Mathieu; Panda, Satyananda

doi: 10.1002/fld.2086pmid: N/A

The combination of substrate unevenness and capillarity is known to induce far‐reaching perturbations at the free surface of thin liquid films. These might be undesired and this paper explores the possibility to control the free surface of thin liquid films to give it a prescribed profile by a suitable design of the underlying substrate. This corresponds to the inverse of the widely studied forward problem, which considers the effect of substrate unevenness on a free surface. Assuming that the steady free surface profile can be described by the lubrication approximation, this optimal control problem is shown to be governed by a first‐order partial differential equation, which is solved numerically using the method of characteristics. The proposed method is successfully tested for a range of desired free surface profiles and the domain of existence of a solution to the inverse problem is probed. Expectedly, it is shown that, owing to surface tension, not all free surface profiles can be achieved but in some cases capillarity can be beaten and a prescribed free surface profile obtained. Copyright © 2009 John Wiley & Sons, Ltd.

Nigro, A.; De Bartolo, C.; Hartmann, R.; Bassi, F.

doi: 10.1002/fld.2083pmid: N/A

In this work we present a discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of the steady‐state solution at very low Mach number flows using an explicit scheme. The algorithm is based on a perturbed formulation of the compressible Euler equations and employs the preconditioning of both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). The performance of the scheme is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different very low Mach numbers using various degrees of polynomial approximation. We present numerical results computed with and without perturbed variables, which illustrate the influence of the cancellation errors on both the convergence and the accuracy of the DG solutions at low Mach numbers. Copyright © 2009 John Wiley & Sons, Ltd.

Mifsud, M. J.; Shaw, S. T.; MacManus, D. G.

doi: 10.1002/fld.2085pmid: N/A

In this paper a high‐fidelity aerodynamic model is presented for use in parametric studies of weapon aerodynamics. The method employs a reduced‐order model obtained from the proper orthogonal decomposition (POD) of an ensemble of computational fluid dynamics (CFD) solutions with varying parameters. This decomposition produces an optimal linear set of orthogonal basis functions that best describe the ensemble of numerical solutions. These solutions are then projected onto this set of basis functions to provide a finite set of scalar coefficients that represent the solutions. A pseudo‐continuous representation of these projection coefficients is constructed, which allows predictions to be made of parameter combinations not in the original set of observations. The paper explores the performance of a few design‐of‐experiment approaches for the generation of the initial ensemble of computational experiments. Response surface construction methods based on parametric and non‐parametric models for the pseudo‐continuous representation of the projection coefficients are also evaluated. The model has been applied to two‐flow problems related to high‐speed weapon aerodynamics, inviscid flow around a flare‐stabilized hypersonic projectile and supersonic turbulent flow around a fin‐stabilized projectile with drooping nose control. Comparisons of model predictions with high‐fidelity CFD simulations suggest that the POD provides a reliable and robust approach to the construction of reduced‐order models. The practicality of the model is shown to be sensitive to the technique used to generate the ensemble of observations from which the model is constructed, while the accuracy of the approach depends on the pseudo‐continuous representation of the projection coefficients. Copyright © 2009 John Wiley & Sons, Ltd.

Mortensen, Mikael; Reif, Bjørn Anders Pettersson; Wasberg, Carl Erik

doi: 10.1002/fld.2091pmid: N/A

The objective of this paper is to assess the accuracy of low‐order finite volume (FV) methods applied to the v2 − f turbulence model of Durbin (Theoret. Comput. Fluid Dyn. 1991; 3:1–13) in the near vicinity of solid walls. We are not (like many others) concerned with the stability of solvers ‐ the topic at hand is simply whether the mathematical properties of the v2 − f model can be captured by the given, widespread, numerical method. The v2 − f model is integrated all the way up to solid walls, where steep gradients in turbulence parameters are observed. The full resolution of wall gradients imposes quite high demands on the numerical schemes and it is not evident that common (second order) FV codes can fully cope with such demands. The v2 − f model is studied in a statistically one‐dimensional, fully developed channel flow where we compare FV schemes with a highly accurate spectral element reference implementation. For the FV method a higher‐order face interpolation scheme, using Lagrange interpolation polynomials up to arbitrary order, is described. It is concluded that a regular second‐order FV scheme cannot give an accurate representation of all model parameters, independent of mesh density. To match the spectral element solution an extended source treatment (we use three‐point Gauss–Lobatto quadrature), as well as a higher‐order discretization of diffusion is required. Furthermore, it is found that the location of the first internal node need to be well within y+=1. Copyright © 2009 John Wiley & Sons, Ltd.

Palani, G.; Kim, Kwang‐Yong

doi: 10.1002/fld.2082pmid: N/A

An analysis is performed to study the free convection of a dusty‐gas flow along a semi‐infinite isothermal vertical cylinder. The governing equations of the flow problem are transformed into non‐dimensional form and the resulting nonlinear, coupled parabolic partial differential equations have been solved numerically using an implicit finite difference scheme of Crank–Nicholson type. The flow variables such as gas–velocity, dust‐particle velocity and temperature, shearing stress and heat transfer coefficients are calculated numerically for various parameters occurring in the problem. It is observed that due to the presence of dust particles, the gas velocity is found to decrease. Copyright © 2009 John Wiley & Sons, Ltd.