International Journal for Numerical Methods in Fluids

Afshar, M. H.; Lashckarbolok, M.

doi: 10.1002/fld.1735pmid: N/A

Int. J. Numer. Meth. Fluids (in press) Published online in Wiley InterScience (www.interscience.wiley.com) (DOI: 10.1002/fld.1571) The authors apologizes the respected readers of the Int. J. Numer. Meth. Fluids for the unnoticed error in the formula (35) in Page 7 of the paper. The correct formula is 35 \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document} $$F_l=\left(\sum\limits_{i=1}^{M_{d}}(L(N_l))_i^{\rm{T}} {\mathbf{f}}_i+\alpha\sum\limits_{i=1}^{M_{t}}(B(N_l))_i^{\rm{T}} {\mathbf{g}}_{i}+\beta\sum\limits_{i=1}^{M_{u}}((N_l))_i^{\rm{T}}\bar{u}_{i}\right),\quad l=1,\ldots,n$$ \end{document}

Popescu, Mihaela; Vedder, Rick; Shyy, Wei

doi: 10.1002/fld.1517pmid: N/A

Computational aeroacoustics requires numerical techniques capable of yielding low artificial dispersion and dissipation to preserve the amplitude and the frequency characteristics of the physical processes. Furthermore, for engineering applications, the techniques need to handle irregular geometries associated with realistic configurations. We address these issues by developing an optimized prefactored compact finite volume (OPC‐fv) scheme along with a Cartesian cut‐cell technique. The OPC‐fv scheme seeks to minimize numerical dispersion and dissipation while satisfying the conservation laws. The cut‐cell approach treats irregularly shaped boundaries using divide‐and‐merge procedures for the Cartesian cells while maintaining a desirable level of accuracy. We assess these techniques using several canonical test problems, involving different levels of physical and geometric complexities. Richardson extrapolation is an effective tool for evaluating solutions of no high gradients or discontinuities, and is used to evaluate the performance of the solution technique. It is demonstrated that while the cut‐cell method has a modest effect on the order of accuracy, it is a robust method. The combined OPC‐fv scheme and the Cartesian cut‐cell technique offer good accuracy as well as geometric flexibility. Copyright © 2008 John Wiley & Sons, Ltd.

Gokarn, A.; Battaglia, F.; Fox, R. O.; Hill, J. C.; Reveillon, J.

doi: 10.1002/fld.1560pmid: N/A

This paper presents a detailed procedure to solve incompressible high Reynolds number turbulent flows using large eddy simulations (LES) on distributed memory machines. The filtered Navier–Stokes equations are discretized using a partial‐staggered variable arrangement and solved using a finite difference grid. A second‐order central difference scheme and sixth‐order compact scheme are employed for the spatial derivatives. A third‐order low storage Runge–Kutta method is used for the temporal derivatives. Validation of the numerical scheme is performed first by simulating a driven cavity flow and flow over a backward‐facing step. The dynamic Smagorinsky subgrid turbulence model is then validated for flow in a channel. Simulations are validated with relevant data available in literature. Since LES is computationally expensive, the solver is parallelized using message passing interface. An efficient parallel linear equation solver is utilized for solving the elliptical pressure Poisson equation. The parallel program is tested for solutions of flow in a complex flow configuration and preliminary results are compared with experimental data. Performance of the program for the same geometry is tested on a parallel cluster up to 256 processors. The novel approach in this work is the use of a partial‐staggered variable arrangement for LES of turbulent flows, obviating the need for any form of artificial dissipation that might mask the subgrid effect on the solution. Copyright © 2007 John Wiley & Sons, Ltd.

Muldoon, Frank; Acharya, Sumanta

doi: 10.1002/fld.1565pmid: N/A

The immersed boundary approach for the modeling of complex geometries in incompressible flows is examined critically from the perspective of satisfying boundary conditions and mass conservation. It is shown that the system of discretized equations for mass and momentum can be inconsistent, if the velocity is used in defining the force density to satisfy the boundary conditions. As a result, the velocity is generally not divergence free and the pressure at locations in the vicinity of the immersed boundary is not physical. However, the use of the pseudo‐velocities in defining the force density, as frequently done when the governing equations are solved using a fractional step or projection method, combined with the use of the specified velocity on the immersed boundary, is shown to result in a consistent set of equations which allows a divergence‐free velocity but, depending on the time step, is shown to have the undesirable effects of inaccurately satisfying the boundary conditions and allowing a significant permeability of the immersed boundary. If the time step is reduced sufficiently, the boundary conditions on the immersed boundary can be satisfied. However, this entails an unacceptable increase in computational expense. Two new methods that satisfy the boundary conditions and allow a divergence‐free velocity while avoiding the increased computational expense are presented and shown to be second‐order accurate in space. The first new method is based on local time step reduction. This method is suitable for problems where the immersed boundary does not move. For these problems, the first new method is shown to be closely related to the second new method. The second new method uses an optimization scheme to minimize the deviation from the interpolation stencil used to represent the immersed boundary while ensuring a divergence‐free velocity. This method performs well for all problems, including those where the immersed boundary moves relative to the grid. Additional results include showing that the force density that is added to satisfy the boundary conditions at the immersed boundary is unbounded as the time step is reduced and that the pressure in the vicinity of the immersed boundary is unphysical, being strongly a function of the time step. A method of computing the total force on an immersed boundary which takes into account the specifics of the numerical solver used in the iterative process and correctly computes the total force irrespective of the residual level is also presented. Copyright © 2007 John Wiley & Sons, Ltd.

Shamekhi, Abazar; Sadeghy, Kayvan

doi: 10.1002/fld.1529pmid: N/A

This study presents characteristic‐based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was initially introduced in finite element framework. In this work, the general equations of flow have been represented in the meshfree context. A new finite element and MFree code is developed for solving flow problems. This computational code is capable of solving both time‐dependent and steady‐state flow problems. Numerical simulation of some known benchmark flow problems has been studied. Computational results of MFree method have been compared to those of finite element method. The results obtained have been verified by known numerical, analytical and experimental data in the literature. A number of shape functions are used for field variable interpolation. The performance of each interpolation method is discussed. It is concluded that the MFree method is more accurate than FEM if the same numbers of nodes are used for each solver. Meshfree CBS algorithm is completely stable even at high Reynolds numbers. Copyright © 2007 John Wiley & Sons, Ltd.

Afshar, M. H.; Lashckarbolok, M.

doi: 10.1002/fld.1571pmid: N/A

Meshless methods are new approaches for solving partial differential equations. The main characteristic of all these methods is that they do not require the traditional mesh to construct a numerical formulation. They require node generation instead of mesh generation. In other words, there is no pre‐specified connectivity or relationships among the nodes. This characteristic make these methods powerful. For example, an adaptive process which requires high computational effort in mesh‐dependent methods can be very economically solved with meshless methods. In this paper, a posteriori error estimate and adaptive refinement strategy is developed in conjunction with the collocated discrete least‐squares (CDLS) meshless method. For this, an error estimate is first developed for a CDLS meshless method. The proposed error estimator is shown to be naturally related to the least‐squares functional, providing a suitable posterior measure of the error in the solution. A mesh moving strategy is then used to displace the nodal points such that the errors are evenly distributed in the solution domain. Efficiency and effectiveness of the proposed error estimator and adaptive refinement process are tested against two hyperbolic benchmark problems, one with shocked and the other with low gradient smooth solutions. These experiments show that the proposed adaptive process is capable of producing stable and accurate results for the difficult problems considered. Copyright © 2007 John Wiley & Sons, Ltd.

Papadimitriou, D. I.; Giannakoglou, K. C.

doi: 10.1002/fld.1584pmid: N/A

In this paper, four approaches to compute the Hessian matrix of an objective function used often in aerodynamic inverse design problems are presented. The computationally less expensive among them is selected and applied to the reconstruction of cascade airfoils that reproduce a prescribed pressure distribution over their walls, under inviscid and viscous flow considerations. The selected approach is based on the direct sensitivity analysis method for the computation of first derivatives, followed by the discrete adjoint method for the computation of the Hessian matrix. The applications presented in this paper show that the Newton method, based on exact Hessian matrices, outperforms other gradient‐based algorithms such as steepest descent or BFGS algorithm. Copyright © 2007 John Wiley & Sons, Ltd.

Boureghda, Abdellatif

doi: 10.1002/fld.1591pmid: N/A

A mathematical model is presented which describes the diffusion of oxygen in absorbing tissue, and numerical solution of its partial differential equation is obtained by the finite difference equations. The diffusion with absorption model is associated with the process of a moving boundary which marks the furthest penetration of oxygen in the absorbing cylindrically shaped sections of tissue and also allows for an initial distribution of oxygen through the absorbing tissue. Copyright © 2007 John Wiley & Sons, Ltd.

Rempfer, Dietmar

doi: 10.1002/fld.1750pmid: N/A

In Sani et al. (Int. J. Numer. Meth. Fluids 2006; 50:673–682), the authors claim to provide a proof of well‐posedness for certain formulations of the Navier–Stokes equations for incompressible flow. We consider the proof of their main Theorem 1 incomplete, and point out some inconsistencies in the above paper. Copyright © 2008 John Wiley & Sons, Ltd.

Gresho, Philip M.; Pironneau, Olivier

doi: 10.1002/fld.1762pmid: N/A